id sid tid token lemma pos cana-1623 1 1 communications communication NOUN cana-1623 1 2 on on ADP cana-1623 1 3 applied apply VERB cana-1623 1 4 nonlinear nonlinear ADJ cana-1623 1 5 analysis analysis NOUN cana-1623 1 6 issn issn NOUN cana-1623 1 7 : : PUNCT cana-1623 1 8 1074 1074 NUM cana-1623 1 9 - - PUNCT cana-1623 1 10 133x 133x NUM cana-1623 1 11 vol vol NOUN cana-1623 1 12 32 32 NUM cana-1623 1 13 no no NOUN cana-1623 1 14 . . NOUN cana-1623 1 15 1 1 NUM cana-1623 1 16 ( ( PUNCT cana-1623 1 17 2025 2025 NUM cana-1623 1 18 ) ) PUNCT cana-1623 1 19 90 90 NUM cana-1623 1 20 https://internationalpubls.com https://internationalpubls.com X cana-1623 1 21 application application NOUN cana-1623 1 22 of of ADP cana-1623 1 23 the the DET cana-1623 1 24 inverse inverse ADJ cana-1623 1 25 weibull weibull NOUN cana-1623 1 26 distribution distribution NOUN cana-1623 1 27 to to ADP cana-1623 1 28 agricultural agricultural ADJ cana-1623 1 29 data datum NOUN cana-1623 1 30 based base VERB cana-1623 1 31 on on ADP cana-1623 1 32 intuitionistic intuitionistic ADJ cana-1623 1 33 fuzzy fuzzy ADJ cana-1623 1 34 sets set NOUN cana-1623 1 35 s. s. PROPN cana-1623 1 36 sujatha1 sujatha1 PROPN cana-1623 1 37 * * PROPN cana-1623 1 38 , , PUNCT cana-1623 1 39 a. a. PROPN cana-1623 1 40 dinesh dinesh PROPN cana-1623 1 41 kumar2 kumar2 PROPN cana-1623 1 42 , , PUNCT cana-1623 1 43 r. r. PROPN cana-1623 1 44 sivaraman3 sivaraman3 PROPN cana-1623 1 45 & & CCONJ cana-1623 1 46 m. m. PROPN cana-1623 1 47 vasuki4 vasuki4 PROPN cana-1623 2 1 1 1 NUM cana-1623 2 2 * * NOUN cana-1623 2 3 research research NOUN cana-1623 2 4 scholar scholar NOUN cana-1623 2 5 , , PUNCT cana-1623 2 6 department department NOUN cana-1623 2 7 of of ADP cana-1623 2 8 mathematics mathematic NOUN cana-1623 2 9 , , PUNCT cana-1623 2 10 khadir khadir PROPN cana-1623 2 11 mohideen mohideen PROPN cana-1623 2 12 college college PROPN cana-1623 2 13 ( ( PUNCT cana-1623 2 14 affiliated affiliate VERB cana-1623 2 15 to to PART cana-1623 2 16 bharathidasan bharathidasan VERB cana-1623 2 17 university university NOUN cana-1623 2 18 ) ) PUNCT cana-1623 2 19 , , PUNCT cana-1623 2 20 adhirampattinam adhirampattinam PROPN cana-1623 2 21 , , PUNCT cana-1623 2 22 tamil tamil PROPN cana-1623 2 23 nadu nadu PROPN cana-1623 2 24 , , PUNCT cana-1623 2 25 india india PROPN cana-1623 2 26 . . PUNCT cana-1623 2 27 email email NOUN cana-1623 2 28 : : PUNCT cana-1623 2 29 suja01rakshi@gmail.com suja01rakshi@gmail.com NUM cana-1623 2 30 2 2 NUM cana-1623 2 31 assistant assistant NOUN cana-1623 2 32 professor professor NOUN cana-1623 2 33 , , PUNCT cana-1623 2 34 department department NOUN cana-1623 2 35 of of ADP cana-1623 2 36 mathematics mathematic NOUN cana-1623 2 37 , , PUNCT cana-1623 2 38 khadir khadir PROPN cana-1623 2 39 mohideen mohideen PROPN cana-1623 2 40 college college PROPN cana-1623 2 41 ( ( PUNCT cana-1623 2 42 affiliated affiliate VERB cana-1623 2 43 to to PART cana-1623 2 44 bharathidasan bharathidasan VERB cana-1623 2 45 university university NOUN cana-1623 2 46 ) ) PUNCT cana-1623 2 47 , , PUNCT cana-1623 2 48 adhirampattinam adhirampattinam PROPN cana-1623 2 49 , , PUNCT cana-1623 2 50 tamil tamil PROPN cana-1623 2 51 nadu nadu PROPN cana-1623 2 52 , , PUNCT cana-1623 2 53 india india PROPN cana-1623 2 54 . . PUNCT cana-1623 2 55 email email NOUN cana-1623 2 56 : : PUNCT cana-1623 3 1 dradineshkumar@gmail.com dradineshkumar@gmail.com PROPN cana-1623 3 2 3 3 NUM cana-1623 3 3 associate associate NOUN cana-1623 3 4 professor professor NOUN cana-1623 3 5 , , PUNCT cana-1623 3 6 department department NOUN cana-1623 3 7 of of ADP cana-1623 3 8 mathematics mathematic NOUN cana-1623 3 9 , , PUNCT cana-1623 3 10 dwaraka dwaraka PROPN cana-1623 3 11 doss doss PROPN cana-1623 3 12 goverdhan goverdhan PROPN cana-1623 3 13 doss doss PROPN cana-1623 3 14 vaishnav vaishnav PROPN cana-1623 3 15 college college PROPN cana-1623 3 16 , , PUNCT cana-1623 3 17 chennai chennai PROPN cana-1623 3 18 , , PUNCT cana-1623 3 19 tamil tamil PROPN cana-1623 3 20 nadu nadu PROPN cana-1623 3 21 , , PUNCT cana-1623 3 22 india india PROPN cana-1623 3 23 . . PUNCT cana-1623 3 24 email email NOUN cana-1623 3 25 : : PUNCT cana-1623 3 26 rsivaraman1729@yahoo.co.in rsivaraman1729@yahoo.co.in PROPN cana-1623 3 27 4 4 NUM cana-1623 3 28 assistant assistant NOUN cana-1623 3 29 professor professor NOUN cana-1623 3 30 , , PUNCT cana-1623 3 31 department department NOUN cana-1623 3 32 of of ADP cana-1623 3 33 mathematics mathematics PROPN cana-1623 3 34 , , PUNCT cana-1623 3 35 srinivasan srinivasan PROPN cana-1623 3 36 college college PROPN cana-1623 3 37 of of ADP cana-1623 3 38 arts art NOUN cana-1623 3 39 and and CCONJ cana-1623 3 40 science science NOUN cana-1623 3 41 ( ( PUNCT cana-1623 3 42 affiliated affiliate VERB cana-1623 3 43 to to PART cana-1623 3 44 bharathidasan bharathidasan VERB cana-1623 3 45 university university NOUN cana-1623 3 46 ) ) PUNCT cana-1623 3 47 , , PUNCT cana-1623 3 48 perambalur perambalur VERB cana-1623 3 49 , , PUNCT cana-1623 3 50 tamil tamil PROPN cana-1623 3 51 nadu nadu PROPN cana-1623 3 52 , , PUNCT cana-1623 3 53 india india PROPN cana-1623 3 54 . . PUNCT cana-1623 3 55 email email NOUN cana-1623 3 56 : : PUNCT cana-1623 4 1 vasuki.scas@gmail.com vasuki.scas@gmail.com X cana-1623 4 2 * * PUNCT cana-1623 4 3 corresponding correspond VERB cana-1623 4 4 author author NOUN cana-1623 4 5 : : PUNCT cana-1623 4 6 suja01rakshi@gmail.com suja01rakshi@gmail.com NUM cana-1623 4 7 article article NOUN cana-1623 4 8 history history NOUN cana-1623 4 9 : : PUNCT cana-1623 4 10 received receive VERB cana-1623 4 11 : : PUNCT cana-1623 4 12 08 08 NUM cana-1623 4 13 - - SYM cana-1623 4 14 07 07 NUM cana-1623 4 15 - - PUNCT cana-1623 4 16 2024 2024 NUM cana-1623 4 17 revised revise VERB cana-1623 4 18 : : PUNCT cana-1623 4 19 21 21 NUM cana-1623 4 20 - - SYM cana-1623 4 21 08 08 NUM cana-1623 4 22 - - PUNCT cana-1623 4 23 2024 2024 NUM cana-1623 4 24 accepted accept VERB cana-1623 4 25 : : PUNCT cana-1623 4 26 04 04 NUM cana-1623 4 27 - - PUNCT cana-1623 4 28 09 09 NUM cana-1623 4 29 - - PUNCT cana-1623 4 30 2024 2024 NUM cana-1623 4 31 abstract abstract NOUN cana-1623 4 32 : : PUNCT cana-1623 4 33 the the DET cana-1623 4 34 inverse inverse ADJ cana-1623 4 35 weibull weibull NOUN cana-1623 4 36 distribution distribution NOUN cana-1623 4 37 ( ( PUNCT cana-1623 4 38 iwd iwd PROPN cana-1623 4 39 ) ) PUNCT cana-1623 4 40 is be AUX cana-1623 4 41 a a DET cana-1623 4 42 frequently frequently ADV cana-1623 4 43 used use VERB cana-1623 4 44 model model NOUN cana-1623 4 45 in in ADP cana-1623 4 46 dependability dependability NOUN cana-1623 4 47 analysis analysis NOUN cana-1623 4 48 that that PRON cana-1623 4 49 finds find VERB cana-1623 4 50 widespread widespread ADJ cana-1623 4 51 use use NOUN cana-1623 4 52 in in ADP cana-1623 4 53 a a DET cana-1623 4 54 variety variety NOUN cana-1623 4 55 of of ADP cana-1623 4 56 scientific scientific ADJ cana-1623 4 57 domains domain NOUN cana-1623 4 58 . . PUNCT cana-1623 5 1 this this DET cana-1623 5 2 work work NOUN cana-1623 5 3 examines examine VERB cana-1623 5 4 the the DET cana-1623 5 5 intuitionistic intuitionistic ADJ cana-1623 5 6 fuzzy fuzzy ADJ cana-1623 5 7 lifespan lifespan NOUN cana-1623 5 8 data data NOUN cana-1623 5 9 - - PUNCT cana-1623 5 10 based base VERB cana-1623 5 11 dependability dependability NOUN cana-1623 5 12 estimation estimation NOUN cana-1623 5 13 of of ADP cana-1623 5 14 the the DET cana-1623 5 15 iwd iwd PROPN cana-1623 5 16 . . PROPN cana-1623 6 1 prior prior ADV cana-1623 6 2 to to ADP cana-1623 6 3 deriving derive VERB cana-1623 6 4 the the DET cana-1623 6 5 ideas idea NOUN cana-1623 6 6 of of ADP cana-1623 6 7 intuitionistic intuitionistic ADJ cana-1623 6 8 fuzzy fuzzy ADJ cana-1623 6 9 conditional conditional ADJ cana-1623 6 10 expectation expectation NOUN cana-1623 6 11 , , PUNCT cana-1623 6 12 intuitionistic intuitionistic ADJ cana-1623 6 13 fuzzy fuzzy ADJ cana-1623 6 14 probability probability NOUN cana-1623 6 15 function function NOUN cana-1623 6 16 , , PUNCT cana-1623 6 17 and and CCONJ cana-1623 6 18 intuitionistic intuitionistic ADJ cana-1623 6 19 fuzzy fuzzy ADJ cana-1623 6 20 conditional conditional ADJ cana-1623 6 21 density density NOUN cana-1623 6 22 , , PUNCT cana-1623 6 23 the the DET cana-1623 6 24 associated associate VERB cana-1623 6 25 concepts concept NOUN cana-1623 6 26 of of ADP cana-1623 6 27 fuzzy fuzzy ADJ cana-1623 6 28 set set NOUN cana-1623 6 29 theory theory NOUN cana-1623 6 30 are be AUX cana-1623 6 31 examined examine VERB cana-1623 6 32 . . PUNCT cana-1623 7 1 in in ADP cana-1623 7 2 conventional conventional ADJ cana-1623 7 3 estimations estimation NOUN cana-1623 7 4 , , PUNCT cana-1623 7 5 the the DET cana-1623 7 6 maximum maximum ADJ cana-1623 7 7 likelihood likelihood NOUN cana-1623 7 8 estimators estimator NOUN cana-1623 7 9 for for ADP cana-1623 7 10 reliability reliability NOUN cana-1623 7 11 and and CCONJ cana-1623 7 12 parameters parameter NOUN cana-1623 7 13 are be AUX cana-1623 7 14 obtained obtain VERB cana-1623 7 15 . . PUNCT cana-1623 8 1 the the DET cana-1623 8 2 maximum maximum ADJ cana-1623 8 3 likelihood likelihood NOUN cana-1623 8 4 estimates estimate NOUN cana-1623 8 5 are be AUX cana-1623 8 6 obtained obtain VERB cana-1623 8 7 using use VERB cana-1623 8 8 the the DET cana-1623 8 9 em em PROPN cana-1623 8 10 algorithm algorithm NOUN cana-1623 8 11 because because SCONJ cana-1623 8 12 of of ADP cana-1623 8 13 the the DET cana-1623 8 14 nonlinearity nonlinearity NOUN cana-1623 8 15 . . PUNCT cana-1623 9 1 the the DET cana-1623 9 2 gamma gamma PROPN cana-1623 9 3 prior prior ADV cana-1623 9 4 is be AUX cana-1623 9 5 chosen choose VERB cana-1623 9 6 in in ADP cana-1623 9 7 the the DET cana-1623 9 8 bayesian bayesian NOUN cana-1623 9 9 estimation estimation NOUN cana-1623 9 10 process process NOUN cana-1623 9 11 , , PUNCT cana-1623 9 12 and and CCONJ cana-1623 9 13 the the DET cana-1623 9 14 symmetric symmetric ADJ cana-1623 9 15 entropy entropy NOUN cana-1623 9 16 and and CCONJ cana-1623 9 17 scale scale NOUN cana-1623 9 18 square square ADJ cana-1623 9 19 error error NOUN cana-1623 9 20 loss loss NOUN cana-1623 9 21 functions function NOUN cana-1623 9 22 , , PUNCT cana-1623 9 23 respectively respectively ADV cana-1623 9 24 , , PUNCT cana-1623 9 25 are be AUX cana-1623 9 26 used use VERB cana-1623 9 27 to to PART cana-1623 9 28 estimate estimate VERB cana-1623 9 29 the the DET cana-1623 9 30 parameters parameter NOUN cana-1623 9 31 and and CCONJ cana-1623 9 32 reliability reliability NOUN cana-1623 9 33 . . PUNCT cana-1623 10 1 the the DET cana-1623 10 2 lindley lindley NOUN cana-1623 10 3 approximation approximation NOUN cana-1623 10 4 is be AUX cana-1623 10 5 used use VERB cana-1623 10 6 to to PART cana-1623 10 7 approximate approximate VERB cana-1623 10 8 the the DET cana-1623 10 9 bayesian bayesian NOUN cana-1623 10 10 estimates estimate NOUN cana-1623 10 11 due due ADP cana-1623 10 12 to to ADP cana-1623 10 13 the the DET cana-1623 10 14 complexity complexity NOUN cana-1623 10 15 of of ADP cana-1623 10 16 the the DET cana-1623 10 17 integrals integral NOUN cana-1623 10 18 . . PUNCT cana-1623 11 1 according accord VERB cana-1623 11 2 to to ADP cana-1623 11 3 the the DET cana-1623 11 4 simulation simulation NOUN cana-1623 11 5 results result NOUN cana-1623 11 6 , , PUNCT cana-1623 11 7 the the DET cana-1623 11 8 maximum maximum ADJ cana-1623 11 9 likelihood likelihood NOUN cana-1623 11 10 estimate estimate NOUN cana-1623 11 11 is be AUX cana-1623 11 12 not not PART cana-1623 11 13 as as ADV cana-1623 11 14 appropriate appropriate ADJ cana-1623 11 15 for for ADP cana-1623 11 16 reliability reliability NOUN cana-1623 11 17 estimation estimation NOUN cana-1623 11 18 as as ADP cana-1623 11 19 the the DET cana-1623 11 20 bayesian bayesian NOUN cana-1623 11 21 estimation estimation NOUN cana-1623 11 22 . . PUNCT cana-1623 12 1 ultimately ultimately ADV cana-1623 12 2 , , PUNCT cana-1623 12 3 the the DET cana-1623 12 4 efficacy efficacy NOUN cana-1623 12 5 of of ADP cana-1623 12 6 these these DET cana-1623 12 7 suggested suggest VERB cana-1623 12 8 techniques technique NOUN cana-1623 12 9 is be AUX cana-1623 12 10 demonstrated demonstrate VERB cana-1623 12 11 using use VERB cana-1623 12 12 a a DET cana-1623 12 13 collection collection NOUN cana-1623 12 14 of of ADP cana-1623 12 15 agriculture agriculture NOUN cana-1623 12 16 production production NOUN cana-1623 12 17 data datum NOUN cana-1623 12 18 . . PUNCT cana-1623 13 1 these these DET cana-1623 13 2 techniques technique NOUN cana-1623 13 3 yield yield VERB cana-1623 13 4 an an DET cana-1623 13 5 accurate accurate ADJ cana-1623 13 6 evaluation evaluation NOUN cana-1623 13 7 of of ADP cana-1623 13 8 the the DET cana-1623 13 9 intuitive intuitive ADJ cana-1623 13 10 fuzzy fuzzy ADJ cana-1623 13 11 life life NOUN cana-1623 13 12 data datum NOUN cana-1623 13 13 's 's PART cana-1623 13 14 reliability reliability NOUN cana-1623 13 15 , , PUNCT cana-1623 13 16 serving serve VERB cana-1623 13 17 as as ADP cana-1623 13 18 a a DET cana-1623 13 19 crucial crucial ADJ cana-1623 13 20 point point NOUN cana-1623 13 21 of of ADP cana-1623 13 22 reference reference NOUN cana-1623 13 23 for for ADP cana-1623 13 24 reliability reliability NOUN cana-1623 13 25 analysis analysis NOUN cana-1623 13 26 in in ADP cana-1623 13 27 the the DET cana-1623 13 28 scientific scientific ADJ cana-1623 13 29 community community NOUN cana-1623 13 30 . . PUNCT cana-1623 14 1 using use VERB cana-1623 14 2 intuitionistic intuitionistic ADJ cana-1623 14 3 fuzzy fuzzy ADJ cana-1623 14 4 values value NOUN cana-1623 14 5 for for ADP cana-1623 14 6 real real ADJ cana-1623 14 7 - - PUNCT cana-1623 14 8 time time NOUN cana-1623 14 9 data datum NOUN cana-1623 14 10 , , PUNCT cana-1623 14 11 the the DET cana-1623 14 12 present present ADJ cana-1623 14 13 work work NOUN cana-1623 14 14 investigated investigate VERB cana-1623 14 15 the the DET cana-1623 14 16 reliability reliability NOUN cana-1623 14 17 estimation estimation NOUN cana-1623 14 18 , , PUNCT cana-1623 14 19 cumulative cumulative ADJ cana-1623 14 20 density density NOUN cana-1623 14 21 function function NOUN cana-1623 14 22 , , PUNCT cana-1623 14 23 and and CCONJ cana-1623 14 24 probability probability NOUN cana-1623 14 25 density density NOUN cana-1623 14 26 function function NOUN cana-1623 14 27 of of ADP cana-1623 14 28 the the DET cana-1623 14 29 inverse inverse ADJ cana-1623 14 30 weibull weibull NOUN cana-1623 14 31 distribution distribution NOUN cana-1623 14 32 . . PUNCT cana-1623 15 1 we we PRON cana-1623 15 2 examined examine VERB cana-1623 15 3 andra andra PRON cana-1623 15 4 agricultural agricultural ADJ cana-1623 15 5 output output NOUN cana-1623 15 6 in in ADP cana-1623 15 7 2019 2019 NUM cana-1623 15 8 in in ADP cana-1623 15 9 this this DET cana-1623 15 10 analysis analysis NOUN cana-1623 15 11 . . PUNCT cana-1623 16 1 the the DET cana-1623 16 2 comparison comparison NOUN cana-1623 16 3 thus thus ADV cana-1623 16 4 showed show VERB cana-1623 16 5 that that SCONJ cana-1623 16 6 the the DET cana-1623 16 7 estimation estimation NOUN cana-1623 16 8 of of ADP cana-1623 16 9 fuzziness fuzziness NOUN cana-1623 16 10 values value NOUN cana-1623 16 11 is be AUX cana-1623 16 12 better well ADJ cana-1623 16 13 than than ADP cana-1623 16 14 the the DET cana-1623 16 15 real real ADJ cana-1623 16 16 - - PUNCT cana-1623 16 17 time time NOUN cana-1623 16 18 data datum NOUN cana-1623 16 19 . . PUNCT cana-1623 17 1 keywords keyword NOUN cana-1623 17 2 : : PUNCT cana-1623 17 3 agriculture agriculture NOUN cana-1623 17 4 data datum NOUN cana-1623 17 5 , , PUNCT cana-1623 17 6 inverse inverse ADJ cana-1623 17 7 weibull weibull NOUN cana-1623 17 8 distribution distribution NOUN cana-1623 17 9 , , PUNCT cana-1623 17 10 intuitionistic intuitionistic ADJ cana-1623 17 11 fuzzy fuzzy ADJ cana-1623 17 12 set set NOUN cana-1623 17 13 , , PUNCT cana-1623 17 14 reliability reliability NOUN cana-1623 17 15 estimation estimation NOUN cana-1623 17 16 . . PUNCT cana-1623 18 1 mathematical mathematical ADJ cana-1623 18 2 subject subject ADJ cana-1623 18 3 classification classification NOUN cana-1623 18 4 ( ( PUNCT cana-1623 18 5 2020 2020 NUM cana-1623 18 6 ): ): PUNCT cana-1623 18 7 03e72 03e72 NUM cana-1623 18 8 , , PUNCT cana-1623 18 9 62a86 62a86 NUM cana-1623 18 10 . . PUNCT cana-1623 19 1 mailto:suja01rakshi@gmail.com mailto:suja01rakshi@gmail.com X cana-1623 19 2 mailto:dradineshkumar@gmail.com mailto:dradineshkumar@gmail.com NOUN cana-1623 20 1 mailto:rsivaraman1729@yahoo.co.in mailto:rsivaraman1729@yahoo.co.in PROPN cana-1623 20 2 mailto:vasuki.scas@gmail.com mailto:vasuki.scas@gmail.com PROPN cana-1623 20 3 mailto:suja01rakshi@gmail.com mailto:suja01rakshi@gmail.com PROPN cana-1623 20 4 communications communication NOUN cana-1623 20 5 on on ADP cana-1623 20 6 applied apply VERB cana-1623 20 7 nonlinear nonlinear ADJ cana-1623 20 8 analysis analysis NOUN cana-1623 20 9 issn issn NOUN cana-1623 20 10 : : PUNCT cana-1623 20 11 1074 1074 NUM cana-1623 20 12 - - PUNCT cana-1623 20 13 133x 133x NUM cana-1623 20 14 vol vol NOUN cana-1623 20 15 32 32 NUM cana-1623 20 16 no no NOUN cana-1623 20 17 . . NOUN cana-1623 20 18 1 1 NUM cana-1623 20 19 ( ( PUNCT cana-1623 20 20 2025 2025 NUM cana-1623 20 21 ) ) PUNCT cana-1623 21 1 91 91 NUM cana-1623 21 2 https://internationalpubls.com https://internationalpubls.com X cana-1623 21 3 1 1 NUM cana-1623 21 4 . . PUNCT cana-1623 21 5 introduction introduction NOUN cana-1623 21 6 real real ADJ cana-1623 21 7 - - PUNCT cana-1623 21 8 world world NOUN cana-1623 21 9 models model NOUN cana-1623 21 10 can can AUX cana-1623 21 11 be be AUX cana-1623 21 12 more more ADV cana-1623 21 13 accurate accurate ADJ cana-1623 21 14 when when SCONJ cana-1623 21 15 fuzzy fuzzy ADJ cana-1623 21 16 sets set NOUN cana-1623 21 17 of of ADP cana-1623 21 18 numbers number NOUN cana-1623 21 19 are be AUX cana-1623 21 20 used use VERB cana-1623 21 21 , , PUNCT cana-1623 21 22 especially especially ADV cana-1623 21 23 when when SCONJ cana-1623 21 24 it it PRON cana-1623 21 25 comes come VERB cana-1623 21 26 to to ADP cana-1623 21 27 uncertainty uncertainty NOUN cana-1623 21 28 models model NOUN cana-1623 21 29 like like ADP cana-1623 21 30 statistical statistical ADJ cana-1623 21 31 fluctuations fluctuation NOUN cana-1623 21 32 in in ADP cana-1623 21 33 observed observed ADJ cana-1623 21 34 lifetime lifetime NOUN cana-1623 21 35 . . PUNCT cana-1623 22 1 voids void NOUN cana-1623 22 2 are be AUX cana-1623 22 3 another another DET cana-1623 22 4 type type NOUN cana-1623 22 5 of of ADP cana-1623 22 6 uncertainty uncertainty NOUN cana-1623 22 7 that that PRON cana-1623 22 8 arises arise VERB cana-1623 22 9 when when SCONJ cana-1623 22 10 an an DET cana-1623 22 11 observation observation NOUN cana-1623 22 12 is be AUX cana-1623 22 13 not not PART cana-1623 22 14 a a DET cana-1623 22 15 precise precise ADJ cana-1623 22 16 number number NOUN cana-1623 22 17 but but CCONJ cana-1623 22 18 rather rather ADV cana-1623 22 19 a a DET cana-1623 22 20 fuzzy fuzzy ADJ cana-1623 22 21 one one NUM cana-1623 22 22 . . PUNCT cana-1623 23 1 zadeh zadeh PROPN cana-1623 23 2 used use VERB cana-1623 23 3 the the DET cana-1623 23 4 term term NOUN cana-1623 23 5 " " PUNCT cana-1623 23 6 fuzzy fuzzy ADJ cana-1623 23 7 variable variable NOUN cana-1623 23 8 " " PUNCT cana-1623 23 9 in in ADP cana-1623 23 10 1965 1965 NUM cana-1623 23 11 [ [ X cana-1623 23 12 1 1 X cana-1623 23 13 ] ] PUNCT cana-1623 23 14 to to PART cana-1623 23 15 refer refer VERB cana-1623 23 16 to to ADP cana-1623 23 17 incorrect incorrect ADJ cana-1623 23 18 linguistic linguistic ADJ cana-1623 23 19 idiom idiom NOUN cana-1623 23 20 and and CCONJ cana-1623 23 21 vernacular vernacular ADJ cana-1623 23 22 . . PUNCT cana-1623 24 1 fuzzy fuzzy ADJ cana-1623 24 2 set set PROPN cana-1623 24 3 theory theory NOUN cana-1623 24 4 got get VERB cana-1623 24 5 its its PRON cana-1623 24 6 start start NOUN cana-1623 24 7 with with ADP cana-1623 24 8 this this PRON cana-1623 24 9 . . PUNCT cana-1623 25 1 a a DET cana-1623 25 2 fuzzy fuzzy ADJ cana-1623 25 3 set set NOUN cana-1623 25 4 is be AUX cana-1623 25 5 made make VERB cana-1623 25 6 up up ADP cana-1623 25 7 of of ADP cana-1623 25 8 elements element NOUN cana-1623 25 9 with with ADP cana-1623 25 10 different different ADJ cana-1623 25 11 membership membership NOUN cana-1623 25 12 levels level NOUN cana-1623 25 13 . . PUNCT cana-1623 26 1 the the DET cana-1623 26 2 rayleigh rayleigh PROPN cana-1623 26 3 lifetime lifetime NOUN cana-1623 26 4 distribution distribution NOUN cana-1623 26 5 to to PART cana-1623 26 6 study study VERB cana-1623 26 7 the the DET cana-1623 26 8 dependability dependability NOUN cana-1623 26 9 properties property NOUN cana-1623 26 10 of of ADP cana-1623 26 11 systems system NOUN cana-1623 26 12 , , PUNCT cana-1623 26 13 where where SCONJ cana-1623 26 14 the the DET cana-1623 26 15 lifespan lifespan ADJ cana-1623 26 16 parameter parameter NOUN cana-1623 26 17 is be AUX cana-1623 26 18 taken take VERB cana-1623 26 19 to to PART cana-1623 26 20 be be AUX cana-1623 26 21 a a DET cana-1623 26 22 generalized generalized ADJ cana-1623 26 23 intuitionistic intuitionistic ADJ cana-1623 26 24 fuzzy fuzzy ADJ cana-1623 26 25 number number NOUN cana-1623 26 26 , , PUNCT cana-1623 26 27 when when SCONJ cana-1623 26 28 the the DET cana-1623 26 29 systems system NOUN cana-1623 26 30 follow follow VERB cana-1623 26 31 a a DET cana-1623 26 32 generalised generalise VERB cana-1623 26 33 intuitionistic intuitionistic ADJ cana-1623 26 34 fuzzy fuzzy ADJ cana-1623 26 35 rayleigh rayleigh NOUN cana-1623 26 36 lifetime lifetime NOUN cana-1623 26 37 distribution distribution NOUN cana-1623 26 38 , , PUNCT cana-1623 26 39 generalised generalise VERB cana-1623 26 40 intuitionistic intuitionistic ADJ cana-1623 26 41 fuzzy fuzzy ADJ cana-1623 26 42 dependability dependability NOUN cana-1623 26 43 , , PUNCT cana-1623 26 44 generalised generalise VERB cana-1623 26 45 intuitionistic intuitionistic ADJ cana-1623 26 46 fuzzy fuzzy ADJ cana-1623 26 47 hazard hazard NOUN cana-1623 26 48 function function NOUN cana-1623 26 49 , , PUNCT cana-1623 26 50 and and CCONJ cana-1623 26 51 generalised generalise VERB cana-1623 26 52 intuitionistic intuitionistic ADJ cana-1623 26 53 fuzzy fuzzy ADJ cana-1623 26 54 mean mean ADJ cana-1623 26 55 time time NOUN cana-1623 26 56 to to ADP cana-1623 26 57 failure failure NOUN cana-1623 26 58 are be AUX cana-1623 26 59 explored explore VERB cana-1623 26 60 along along ADP cana-1623 26 61 with with ADP cana-1623 26 62 their their PRON cana-1623 26 63 cut cut NOUN cana-1623 26 64 sets set NOUN cana-1623 26 65 . . PUNCT cana-1623 27 1 with with ADP cana-1623 27 2 this this DET cana-1623 27 3 method method NOUN cana-1623 27 4 , , PUNCT cana-1623 27 5 the the DET cana-1623 27 6 danger danger NOUN cana-1623 27 7 and and CCONJ cana-1623 27 8 dependability dependability NOUN cana-1623 27 9 curves curve NOUN cana-1623 27 10 for for ADP cana-1623 27 11 each each DET cana-1623 27 12 unique unique ADJ cana-1623 27 13 cut cut NOUN cana-1623 27 14 set set VERB cana-1623 27 15 resemble resemble VERB cana-1623 27 16 a a DET cana-1623 27 17 band band NOUN cana-1623 27 18 with with ADP cana-1623 27 19 upper upper ADJ cana-1623 27 20 and and CCONJ cana-1623 27 21 lower low ADJ cana-1623 27 22 bounds bound NOUN cana-1623 27 23 . . PUNCT cana-1623 28 1 a a DET cana-1623 28 2 numerical numerical ADJ cana-1623 28 3 example example NOUN cana-1623 28 4 is be AUX cana-1623 28 5 provided provide VERB cana-1623 28 6 to to PART cana-1623 28 7 demonstrate demonstrate VERB cana-1623 28 8 the the DET cana-1623 28 9 suggested suggest VERB cana-1623 28 10 methodology methodology NOUN cana-1623 28 11 . . PUNCT cana-1623 29 1 additional additional ADJ cana-1623 29 2 reliability reliability NOUN cana-1623 29 3 study study NOUN cana-1623 29 4 is be AUX cana-1623 29 5 conducted conduct VERB cana-1623 29 6 for for ADP cana-1623 29 7 both both CCONJ cana-1623 29 8 the the DET cana-1623 29 9 parallel parallel ADJ cana-1623 29 10 and and CCONJ cana-1623 29 11 series series NOUN cana-1623 29 12 systems system NOUN cana-1623 29 13 [ [ X cana-1623 29 14 2 2 NUM cana-1623 29 15 ] ] PUNCT cana-1623 29 16 . . PUNCT cana-1623 30 1 an an DET cana-1623 30 2 intuitionistic intuitionistic ADJ cana-1623 30 3 fuzzy fuzzy ADJ cana-1623 30 4 weibull weibull NOUN cana-1623 30 5 lifetime lifetime NOUN cana-1623 30 6 distribution distribution NOUN cana-1623 30 7 to to PART cana-1623 30 8 examine examine VERB cana-1623 30 9 the the DET cana-1623 30 10 fuzzy fuzzy ADJ cana-1623 30 11 dependability dependability NOUN cana-1623 30 12 of of ADP cana-1623 30 13 a a DET cana-1623 30 14 few few ADJ cana-1623 30 15 systems system NOUN cana-1623 30 16 , , PUNCT cana-1623 30 17 because because SCONJ cana-1623 30 18 of of ADP cana-1623 30 19 data datum NOUN cana-1623 30 20 imperfection imperfection NOUN cana-1623 30 21 and and CCONJ cana-1623 30 22 uncertainty uncertainty NOUN cana-1623 30 23 , , PUNCT cana-1623 30 24 fuzzy fuzzy ADJ cana-1623 30 25 lifetime lifetime NOUN cana-1623 30 26 parameters parameter NOUN cana-1623 30 27 are be AUX cana-1623 30 28 postulated postulate VERB cana-1623 30 29 . . PUNCT cana-1623 31 1 when when SCONJ cana-1623 31 2 systems system NOUN cana-1623 31 3 follow follow VERB cana-1623 31 4 intuitionistic intuitionistic ADJ cana-1623 31 5 fuzzy fuzzy ADJ cana-1623 31 6 weibull weibull NOUN cana-1623 31 7 lifetime lifetime NOUN cana-1623 31 8 distribution distribution NOUN cana-1623 31 9 , , PUNCT cana-1623 31 10 expressions expression NOUN cana-1623 31 11 for for ADP cana-1623 31 12 fuzzy fuzzy ADJ cana-1623 31 13 dependability dependability NOUN cana-1623 31 14 , , PUNCT cana-1623 31 15 fuzzy fuzzy ADJ cana-1623 31 16 mean mean ADJ cana-1623 31 17 time time NOUN cana-1623 31 18 to to ADP cana-1623 31 19 failure failure NOUN cana-1623 31 20 , , PUNCT cana-1623 31 21 fuzzy fuzzy ADJ cana-1623 31 22 hazard hazard NOUN cana-1623 31 23 function function NOUN cana-1623 31 24 , , PUNCT cana-1623 31 25 and and CCONJ cana-1623 31 26 their their PRON cana-1623 31 27 𝛼-cut 𝛼-cut NOUN cana-1623 31 28 have have AUX cana-1623 31 29 been be AUX cana-1623 31 30 addressed address VERB cana-1623 31 31 . . PUNCT cana-1623 32 1 to to PART cana-1623 32 2 demonstrate demonstrate VERB cana-1623 32 3 the the DET cana-1623 32 4 process process NOUN cana-1623 32 5 for for ADP cana-1623 32 6 calculating calculate VERB cana-1623 32 7 the the DET cana-1623 32 8 fuzzy fuzzy ADJ cana-1623 32 9 reliability reliability NOUN cana-1623 32 10 characteristics characteristic NOUN cana-1623 32 11 of of ADP cana-1623 32 12 systems system NOUN cana-1623 32 13 , , PUNCT cana-1623 32 14 a a DET cana-1623 32 15 numerical numerical ADJ cana-1623 32 16 example example NOUN cana-1623 32 17 is be AUX cana-1623 32 18 also also ADV cana-1623 32 19 provided provide VERB cana-1623 32 20 by by ADP cana-1623 32 21 [ [ X cana-1623 32 22 3 3 NUM cana-1623 32 23 ] ] PUNCT cana-1623 32 24 . . PUNCT cana-1623 33 1 an an DET cana-1623 33 2 intuitionistic intuitionistic ADJ cana-1623 33 3 fuzzy fuzzy ADJ cana-1623 33 4 random random ADJ cana-1623 33 5 variable variable NOUN cana-1623 33 6 with with ADP cana-1623 33 7 exact exact ADJ cana-1623 33 8 parameters parameter NOUN cana-1623 33 9 was be AUX cana-1623 33 10 created create VERB cana-1623 33 11 and and CCONJ cana-1623 33 12 used use VERB cana-1623 33 13 to to PART cana-1623 33 14 assess assess VERB cana-1623 33 15 the the DET cana-1623 33 16 reliability reliability NOUN cana-1623 33 17 functions function NOUN cana-1623 33 18 of of ADP cana-1623 33 19 a a DET cana-1623 33 20 k k NOUN cana-1623 33 21 - - PUNCT cana-1623 33 22 out out ADP cana-1623 33 23 - - PUNCT cana-1623 33 24 of of ADP cana-1623 33 25 - - PUNCT cana-1623 33 26 n n NOUN cana-1623 33 27 system system NOUN cana-1623 33 28 . . PUNCT cana-1623 34 1 some some DET cana-1623 34 2 reliability reliability NOUN cana-1623 34 3 evaluation evaluation NOUN cana-1623 34 4 criteria criterion NOUN cana-1623 34 5 were be AUX cana-1623 34 6 explored explore VERB cana-1623 34 7 and and CCONJ cana-1623 34 8 interpreted interpret VERB cana-1623 34 9 . . PUNCT cana-1623 35 1 numerical numerical ADJ cana-1623 35 2 assessments assessment NOUN cana-1623 35 3 were be AUX cana-1623 35 4 also also ADV cana-1623 35 5 presented present VERB cana-1623 35 6 to to PART cana-1623 35 7 demonstrate demonstrate VERB cana-1623 35 8 the the DET cana-1623 35 9 determination determination NOUN cana-1623 35 10 of of ADP cana-1623 35 11 system system NOUN cana-1623 35 12 dependability dependability NOUN cana-1623 35 13 criteria criterion NOUN cana-1623 35 14 in in ADP cana-1623 35 15 the the DET cana-1623 35 16 form form NOUN cana-1623 35 17 of of ADP cana-1623 35 18 intuitionistic intuitionistic ADJ cana-1623 35 19 fuzzy fuzzy ADJ cana-1623 35 20 numbers number NOUN cana-1623 35 21 [ [ X cana-1623 35 22 4 4 NUM cana-1623 35 23 ] ] PUNCT cana-1623 35 24 . . PUNCT cana-1623 36 1 finally finally ADV cana-1623 36 2 , , PUNCT cana-1623 36 3 many many ADJ cana-1623 36 4 potential potential ADJ cana-1623 36 5 engineering engineering NOUN cana-1623 36 6 applications application NOUN cana-1623 36 7 for for ADP cana-1623 36 8 the the DET cana-1623 36 9 suggested suggest VERB cana-1623 36 10 technique technique NOUN cana-1623 36 11 were be AUX cana-1623 36 12 discussed discuss VERB cana-1623 36 13 . . PUNCT cana-1623 37 1 generalized generalized ADJ cana-1623 37 2 intuitionistic intuitionistic ADJ cana-1623 37 3 fuzzy fuzzy ADJ cana-1623 37 4 numbers number NOUN cana-1623 37 5 are be AUX cana-1623 37 6 used use VERB cana-1623 37 7 to to PART cana-1623 37 8 assess assess VERB cana-1623 37 9 the the DET cana-1623 37 10 reliability reliability NOUN cana-1623 37 11 of of ADP cana-1623 37 12 various various ADJ cana-1623 37 13 systems system NOUN cana-1623 37 14 . . PUNCT cana-1623 38 1 the the DET cana-1623 38 2 reliability reliability NOUN cana-1623 38 3 features feature NOUN cana-1623 38 4 of of ADP cana-1623 38 5 systems system NOUN cana-1623 38 6 using use VERB cana-1623 38 7 the the DET cana-1623 38 8 pareto pareto ADJ cana-1623 38 9 lifespan lifespan ADJ cana-1623 38 10 distribution distribution NOUN cana-1623 38 11 are be AUX cana-1623 38 12 explored explore VERB cana-1623 38 13 , , PUNCT cana-1623 38 14 under under ADP cana-1623 38 15 the the DET cana-1623 38 16 assumption assumption NOUN cana-1623 38 17 that that SCONJ cana-1623 38 18 the the DET cana-1623 38 19 lifetime lifetime NOUN cana-1623 38 20 scale scale NOUN cana-1623 38 21 parameter parameter NOUN cana-1623 38 22 is be AUX cana-1623 38 23 a a DET cana-1623 38 24 generalized generalized ADJ cana-1623 38 25 intuitionistic intuitionistic ADJ cana-1623 38 26 fuzzy fuzzy ADJ cana-1623 38 27 number number NOUN cana-1623 38 28 . . PUNCT cana-1623 39 1 in in ADP cana-1623 39 2 general general ADJ cana-1623 39 3 , , PUNCT cana-1623 39 4 the the DET cana-1623 39 5 cut cut NOUN cana-1623 39 6 sets set VERB cana-1623 39 7 for for ADP cana-1623 39 8 the the DET cana-1623 39 9 generalized generalized ADJ cana-1623 39 10 intuitionistic intuitionistic ADJ cana-1623 39 11 fuzzy fuzzy ADJ cana-1623 39 12 reliability reliability NOUN cana-1623 39 13 function function NOUN cana-1623 39 14 , , PUNCT cana-1623 39 15 generalised generalise VERB cana-1623 39 16 intuitionistic intuitionistic ADJ cana-1623 39 17 fuzzy fuzzy ADJ cana-1623 39 18 conditional conditional ADJ cana-1623 39 19 reliability reliability NOUN cana-1623 39 20 function function NOUN cana-1623 39 21 , , PUNCT cana-1623 39 22 generalized generalized ADJ cana-1623 39 23 intuitionistic intuitionistic ADJ cana-1623 39 24 fuzzy fuzzy ADJ cana-1623 39 25 hazard hazard NOUN cana-1623 39 26 function function NOUN cana-1623 39 27 , , PUNCT cana-1623 39 28 and and CCONJ cana-1623 39 29 generalized generalized ADJ cana-1623 39 30 intuitionistic intuitionistic ADJ cana-1623 39 31 fuzzy fuzzy ADJ cana-1623 39 32 mean mean ADJ cana-1623 39 33 time time NOUN cana-1623 39 34 to to ADP cana-1623 39 35 failure failure NOUN cana-1623 39 36 are be AUX cana-1623 39 37 examined examine VERB cana-1623 39 38 . . PUNCT cana-1623 40 1 the the DET cana-1623 40 2 reliability reliability NOUN cana-1623 40 3 functions function NOUN cana-1623 40 4 listed list VERB cana-1623 40 5 above above ADV cana-1623 40 6 are be AUX cana-1623 40 7 discussed discuss VERB cana-1623 40 8 for for ADP cana-1623 40 9 generalized generalized ADJ cana-1623 40 10 intuitionistic intuitionistic ADJ cana-1623 40 11 fuzzy fuzzy ADJ cana-1623 40 12 pareto pareto ADJ cana-1623 40 13 lifespan lifespan NOUN cana-1623 40 14 systems system NOUN cana-1623 40 15 . . PUNCT cana-1623 41 1 furthermore furthermore ADV cana-1623 41 2 , , PUNCT cana-1623 41 3 reliability reliability NOUN cana-1623 41 4 analysis analysis NOUN cana-1623 41 5 of of ADP cana-1623 41 6 series series NOUN cana-1623 41 7 and and CCONJ cana-1623 41 8 parallel parallel ADJ cana-1623 41 9 systems system NOUN cana-1623 41 10 is be AUX cana-1623 41 11 performed perform VERB cana-1623 41 12 , , PUNCT cana-1623 41 13 and and CCONJ cana-1623 41 14 a a DET cana-1623 41 15 numerical numerical ADJ cana-1623 41 16 example example NOUN cana-1623 41 17 is be AUX cana-1623 41 18 provided provide VERB cana-1623 41 19 [ [ X cana-1623 41 20 5 5 NUM cana-1623 41 21 ] ] PUNCT cana-1623 41 22 . . PUNCT cana-1623 42 1 the the DET cana-1623 42 2 intuitionistic intuitionistic ADJ cana-1623 42 3 fuzzy fuzzy ADJ cana-1623 42 4 sets set NOUN cana-1623 42 5 ( ( PUNCT cana-1623 42 6 ifs ifs PROPN cana-1623 42 7 ) ) PUNCT cana-1623 42 8 idea idea NOUN cana-1623 42 9 , , PUNCT cana-1623 42 10 along along ADP cana-1623 42 11 with with ADP cana-1623 42 12 the the DET cana-1623 42 13 triangle triangle NOUN cana-1623 42 14 fuzzy fuzzy ADJ cana-1623 42 15 number number NOUN cana-1623 42 16 ( ( PUNCT cana-1623 42 17 tfn tfn NOUN cana-1623 42 18 ) ) PUNCT cana-1623 42 19 and and CCONJ cana-1623 42 20 weibull weibull PROPN cana-1623 42 21 lifetime lifetime NOUN cana-1623 42 22 distribution distribution NOUN cana-1623 42 23 , , PUNCT cana-1623 42 24 is be AUX cana-1623 42 25 used use VERB cana-1623 42 26 to to PART cana-1623 42 27 determine determine VERB cana-1623 42 28 the the DET cana-1623 42 29 same same ADJ cana-1623 42 30 system system NOUN cana-1623 42 31 's 's PART cana-1623 42 32 fuzzy fuzzy ADJ cana-1623 42 33 dependability dependability NOUN cana-1623 42 34 . . PUNCT cana-1623 43 1 in in ADP cana-1623 43 2 addition addition NOUN cana-1623 43 3 , , PUNCT cana-1623 43 4 an an DET cana-1623 43 5 averaging averaging NOUN cana-1623 43 6 operator operator NOUN cana-1623 43 7 with with ADP cana-1623 43 8 equal equal ADJ cana-1623 43 9 weights weight NOUN cana-1623 43 10 is be AUX cana-1623 43 11 applied apply VERB cana-1623 43 12 to to ADP cana-1623 43 13 a a DET cana-1623 43 14 set set NOUN cana-1623 43 15 of of ADP cana-1623 43 16 three three NUM cana-1623 43 17 triangular triangular NOUN cana-1623 43 18 intuitionistic intuitionistic ADJ cana-1623 43 19 fuzzy fuzzy ADJ cana-1623 43 20 numbers number NOUN cana-1623 43 21 . . PUNCT cana-1623 44 1 a a DET cana-1623 44 2 numerical numerical ADJ cana-1623 44 3 example example NOUN cana-1623 44 4 is be AUX cana-1623 44 5 solved solve VERB cana-1623 44 6 as as ADP cana-1623 44 7 an an DET cana-1623 44 8 illustration illustration NOUN cana-1623 44 9 [ [ X cana-1623 44 10 6 6 NUM cana-1623 44 11 ] ] PUNCT cana-1623 44 12 . . PUNCT cana-1623 45 1 communications communication NOUN cana-1623 45 2 on on ADP cana-1623 45 3 applied apply VERB cana-1623 45 4 nonlinear nonlinear ADJ cana-1623 45 5 analysis analysis NOUN cana-1623 45 6 issn issn NOUN cana-1623 45 7 : : PUNCT cana-1623 45 8 1074 1074 NUM cana-1623 45 9 - - PUNCT cana-1623 45 10 133x 133x NUM cana-1623 45 11 vol vol NOUN cana-1623 45 12 32 32 NUM cana-1623 45 13 no no NOUN cana-1623 45 14 . . NOUN cana-1623 45 15 1 1 NUM cana-1623 45 16 ( ( PUNCT cana-1623 45 17 2025 2025 NUM cana-1623 45 18 ) ) PUNCT cana-1623 45 19 92 92 NUM cana-1623 45 20 https://internationalpubls.com https://internationalpubls.com X cana-1623 46 1 the the DET cana-1623 46 2 simulation simulation NOUN cana-1623 46 3 results result NOUN cana-1623 46 4 demonstrated demonstrate VERB cana-1623 46 5 [ [ X cana-1623 46 6 7 7 X cana-1623 46 7 ] ] PUNCT cana-1623 46 8 that that SCONJ cana-1623 46 9 the the DET cana-1623 46 10 fuzzy fuzzy ADJ cana-1623 46 11 reliability reliability NOUN cana-1623 46 12 at at ADP cana-1623 46 13 the the DET cana-1623 46 14 estimation estimation NOUN cana-1623 46 15 stage stage NOUN cana-1623 46 16 of of ADP cana-1623 46 17 the the DET cana-1623 46 18 maximum maximum ADJ cana-1623 46 19 likelihood likelihood NOUN cana-1623 46 20 method method NOUN cana-1623 46 21 and and CCONJ cana-1623 46 22 the the DET cana-1623 46 23 mixed mixed ADJ cana-1623 46 24 thompson thompson PROPN cana-1623 46 25 method method NOUN cana-1623 46 26 outperform outperform VERB cana-1623 46 27 the the DET cana-1623 46 28 other other ADJ cana-1623 46 29 methods method NOUN cana-1623 46 30 in in ADP cana-1623 46 31 terms term NOUN cana-1623 46 32 of of ADP cana-1623 46 33 mean mean ADJ cana-1623 46 34 squared square VERB cana-1623 46 35 error error NOUN cana-1623 46 36 ( ( PUNCT cana-1623 46 37 mse mse NOUN cana-1623 46 38 ) ) PUNCT cana-1623 46 39 , , PUNCT cana-1623 46 40 indicating indicate VERB cana-1623 46 41 that that SCONJ cana-1623 46 42 the the DET cana-1623 46 43 use use NOUN cana-1623 46 44 of of ADP cana-1623 46 45 this this DET cana-1623 46 46 type type NOUN cana-1623 46 47 of of ADP cana-1623 46 48 estimation estimation NOUN cana-1623 46 49 is be AUX cana-1623 46 50 recommended recommend VERB cana-1623 46 51 . . PUNCT cana-1623 47 1 the the DET cana-1623 47 2 fuzzy fuzzy ADJ cana-1623 47 3 values value NOUN cana-1623 47 4 also also ADV cana-1623 47 5 outperform outperform VERB cana-1623 47 6 the the DET cana-1623 47 7 real real ADJ cana-1623 47 8 values value NOUN cana-1623 47 9 for for ADP cana-1623 47 10 all all DET cana-1623 47 11 sample sample NOUN cana-1623 47 12 sizes size NOUN cana-1623 47 13 . . PUNCT cana-1623 48 1 a a DET cana-1623 48 2 new new ADJ cana-1623 48 3 technique technique NOUN cana-1623 48 4 for for ADP cana-1623 48 5 analysing analyse VERB cana-1623 48 6 fuzzy fuzzy ADJ cana-1623 48 7 system system NOUN cana-1623 48 8 reliability reliability NOUN cana-1623 48 9 based base VERB cana-1623 48 10 on on ADP cana-1623 48 11 intuitionistic intuitionistic ADJ cana-1623 48 12 trapezoidal trapezoidal ADJ cana-1623 48 13 fuzzy fuzzy ADJ cana-1623 48 14 set set NOUN cana-1623 48 15 theory theory NOUN cana-1623 48 16 is be AUX cana-1623 48 17 described describe VERB cana-1623 48 18 , , PUNCT cana-1623 48 19 in in ADP cana-1623 48 20 which which PRON cana-1623 48 21 the the DET cana-1623 48 22 reliabilities reliability NOUN cana-1623 48 23 of of ADP cana-1623 48 24 system system NOUN cana-1623 48 25 components component NOUN cana-1623 48 26 are be AUX cana-1623 48 27 represented represent VERB cana-1623 48 28 by by ADP cana-1623 48 29 intuitionistic intuitionistic ADJ cana-1623 48 30 trapezoidal trapezoidal ADJ cana-1623 48 31 fuzzy fuzzy ADJ cana-1623 48 32 numbers number NOUN cana-1623 48 33 to to PART cana-1623 48 34 simulate simulate VERB cana-1623 48 35 uncertainty uncertainty NOUN cana-1623 48 36 and and CCONJ cana-1623 48 37 vagueness vagueness NOUN cana-1623 48 38 in in ADP cana-1623 48 39 real real ADJ cana-1623 48 40 - - PUNCT cana-1623 48 41 world world NOUN cana-1623 48 42 circumstances circumstance NOUN cana-1623 48 43 [ [ X cana-1623 48 44 8 8 NUM cana-1623 48 45 ] ] PUNCT cana-1623 48 46 . . PUNCT cana-1623 49 1 the the DET cana-1623 49 2 suggested suggest VERB cana-1623 49 3 method method NOUN cana-1623 49 4 may may AUX cana-1623 49 5 describe describe VERB cana-1623 49 6 and and CCONJ cana-1623 49 7 analyse analyse VERB cana-1623 49 8 fuzzy fuzzy ADJ cana-1623 49 9 system system NOUN cana-1623 49 10 reliability reliability NOUN cana-1623 49 11 in in ADP cana-1623 49 12 a a DET cana-1623 49 13 more more ADV cana-1623 49 14 adaptable adaptable ADJ cana-1623 49 15 and and CCONJ cana-1623 49 16 intelligent intelligent ADJ cana-1623 49 17 way way NOUN cana-1623 49 18 . . PUNCT cana-1623 50 1 the the DET cana-1623 50 2 suggested suggest VERB cana-1623 50 3 method method NOUN cana-1623 50 4 also also ADV cana-1623 50 5 compares compare VERB cana-1623 50 6 different different ADJ cana-1623 50 7 complex complex ADJ cana-1623 50 8 systems system NOUN cana-1623 50 9 using use VERB cana-1623 50 10 the the DET cana-1623 50 11 score score NOUN cana-1623 50 12 and and CCONJ cana-1623 50 13 accuracy accuracy NOUN cana-1623 50 14 functions function NOUN cana-1623 50 15 . . PUNCT cana-1623 51 1 the the DET cana-1623 51 2 score score NOUN cana-1623 51 3 function function NOUN cana-1623 51 4 can can AUX cana-1623 51 5 assist assist VERB cana-1623 51 6 the the DET cana-1623 51 7 decision decision NOUN cana-1623 51 8 maker maker NOUN cana-1623 51 9 in in ADP cana-1623 51 10 making make VERB cana-1623 51 11 his his PRON cana-1623 51 12 decision decision NOUN cana-1623 51 13 more more ADV cana-1623 51 14 efficiently efficiently ADV cana-1623 51 15 in in ADP cana-1623 51 16 a a DET cana-1623 51 17 decision decision NOUN cana-1623 51 18 - - PUNCT cana-1623 51 19 making make VERB cana-1623 51 20 dilemma dilemma NOUN cana-1623 51 21 . . PUNCT cana-1623 52 1 this this DET cana-1623 52 2 method method NOUN cana-1623 52 3 is be AUX cana-1623 52 4 then then ADV cana-1623 52 5 applied apply VERB cana-1623 52 6 to to ADP cana-1623 52 7 a a DET cana-1623 52 8 wireless wireless ADJ cana-1623 52 9 communication communication NOUN cana-1623 52 10 system system NOUN cana-1623 52 11 to to PART cana-1623 52 12 evaluate evaluate VERB cana-1623 52 13 its its PRON cana-1623 52 14 intuitionistic intuitionistic ADJ cana-1623 52 15 fuzzy fuzzy ADJ cana-1623 52 16 reliability reliability NOUN cana-1623 52 17 and and CCONJ cana-1623 52 18 availability availability NOUN cana-1623 52 19 , , PUNCT cana-1623 52 20 with with ADP cana-1623 52 21 each each DET cana-1623 52 22 performance performance NOUN cana-1623 52 23 state state NOUN cana-1623 52 24 and and CCONJ cana-1623 52 25 probability probability NOUN cana-1623 52 26 represented represent VERB cana-1623 52 27 by by ADP cana-1623 52 28 a a DET cana-1623 52 29 tifn tifn NOUN cana-1623 52 30 . . PUNCT cana-1623 53 1 the the DET cana-1623 53 2 acquired acquire VERB cana-1623 53 3 results result NOUN cana-1623 53 4 are be AUX cana-1623 53 5 also also ADV cana-1623 53 6 shown show VERB cana-1623 53 7 graphically graphically ADV cana-1623 53 8 for for ADP cana-1623 53 9 better well ADJ cana-1623 53 10 understanding understanding NOUN cana-1623 53 11 . . PUNCT cana-1623 54 1 this this DET cana-1623 54 2 work work NOUN cana-1623 54 3 contributes contribute VERB cana-1623 54 4 to to ADP cana-1623 54 5 a a DET cana-1623 54 6 better well ADJ cana-1623 54 7 understanding understanding NOUN cana-1623 54 8 of of ADP cana-1623 54 9 fmss fmss NOUN cana-1623 54 10 , , PUNCT cana-1623 54 11 making make VERB cana-1623 54 12 them they PRON cana-1623 54 13 more more ADV cana-1623 54 14 dependable dependable ADJ cana-1623 54 15 [ [ X cana-1623 54 16 9 9 NUM cana-1623 54 17 ] ] PUNCT cana-1623 54 18 . . PUNCT cana-1623 55 1 the the DET cana-1623 55 2 foundation foundation NOUN cana-1623 55 3 of of ADP cana-1623 55 4 reliability reliability NOUN cana-1623 55 5 engineering engineering NOUN cana-1623 55 6 is be AUX cana-1623 55 7 reliability reliability NOUN cana-1623 55 8 theory theory NOUN cana-1623 55 9 . . PUNCT cana-1623 56 1 reliability reliability NOUN cana-1623 56 2 analysis analysis NOUN cana-1623 56 3 is be AUX cana-1623 56 4 vital vital ADJ cana-1623 56 5 for for ADP cana-1623 56 6 developing develop VERB cana-1623 56 7 several several ADJ cana-1623 56 8 system system NOUN cana-1623 56 9 improvement improvement NOUN cana-1623 56 10 alternatives alternative NOUN cana-1623 56 11 during during ADP cana-1623 56 12 the the DET cana-1623 56 13 design design NOUN cana-1623 56 14 , , PUNCT cana-1623 56 15 configuration configuration NOUN cana-1623 56 16 , , PUNCT cana-1623 56 17 and and CCONJ cana-1623 56 18 tuning tune VERB cana-1623 56 19 stages stage NOUN cana-1623 56 20 , , PUNCT cana-1623 56 21 all all PRON cana-1623 56 22 of of ADP cana-1623 56 23 which which PRON cana-1623 56 24 are be AUX cana-1623 56 25 required require VERB cana-1623 56 26 for for ADP cana-1623 56 27 a a DET cana-1623 56 28 complex complex ADJ cana-1623 56 29 system system NOUN cana-1623 56 30 to to PART cana-1623 56 31 operate operate VERB cana-1623 56 32 efficiently efficiently ADV cana-1623 56 33 . . PUNCT cana-1623 57 1 this this DET cana-1623 57 2 work work NOUN cana-1623 57 3 focuses focus VERB cana-1623 57 4 on on ADP cana-1623 57 5 estimating estimate VERB cana-1623 57 6 the the DET cana-1623 57 7 reliability reliability NOUN cana-1623 57 8 of of ADP cana-1623 57 9 a a DET cana-1623 57 10 degradable degradable ADJ cana-1623 57 11 system system NOUN cana-1623 57 12 with with ADP cana-1623 57 13 imperfect imperfect ADJ cana-1623 57 14 coverage coverage NOUN cana-1623 57 15 and and CCONJ cana-1623 57 16 unknown unknown ADJ cana-1623 57 17 information information NOUN cana-1623 57 18 about about ADP cana-1623 57 19 its its PRON cana-1623 57 20 components[10 components[10 NOUN cana-1623 57 21 ] ] PUNCT cana-1623 57 22 . . PUNCT cana-1623 58 1 the the DET cana-1623 58 2 weibull weibull PROPN cana-1623 58 3 intuitionistic intuitionistic ADJ cana-1623 58 4 fuzzy fuzzy ADJ cana-1623 58 5 set set NOUN cana-1623 58 6 ( ( PUNCT cana-1623 58 7 wifs wifs PROPN cana-1623 58 8 ) ) PUNCT cana-1623 58 9 idea idea NOUN cana-1623 58 10 was be AUX cana-1623 58 11 utilised utilise VERB cana-1623 58 12 to to PART cana-1623 58 13 address address VERB cana-1623 58 14 data datum NOUN cana-1623 58 15 uncertainty uncertainty NOUN cana-1623 58 16 . . PUNCT cana-1623 59 1 the the DET cana-1623 59 2 trapezoidal trapezoidal ADJ cana-1623 59 3 intuitionistic intuitionistic ADJ cana-1623 59 4 fuzzy fuzzy ADJ cana-1623 59 5 number number NOUN cana-1623 59 6 ( ( PUNCT cana-1623 59 7 trifn trifn NOUN cana-1623 59 8 ) ) PUNCT cana-1623 59 9 and and CCONJ cana-1623 59 10 its its PRON cana-1623 59 11 arithmetic arithmetic ADJ cana-1623 59 12 operations operation NOUN cana-1623 59 13 are be AUX cana-1623 59 14 discussed discuss VERB cana-1623 59 15 . . PUNCT cana-1623 60 1 trapezoidal trapezoidal ADJ cana-1623 60 2 intuitionistic intuitionistic ADJ cana-1623 60 3 fuzzy fuzzy ADJ cana-1623 60 4 numbers number NOUN cana-1623 60 5 ( ( PUNCT cana-1623 60 6 trifn trifn NOUN cana-1623 60 7 ) ) PUNCT cana-1623 60 8 are be AUX cana-1623 60 9 used use VERB cana-1623 60 10 to to PART cana-1623 60 11 represent represent VERB cana-1623 60 12 the the DET cana-1623 60 13 failure failure NOUN cana-1623 60 14 rate rate NOUN cana-1623 60 15 of of ADP cana-1623 60 16 the the DET cana-1623 60 17 system system NOUN cana-1623 60 18 . . PUNCT cana-1623 61 1 simulation simulation NOUN cana-1623 61 2 results result NOUN cana-1623 61 3 indicate indicate VERB cana-1623 61 4 that that SCONJ cana-1623 61 5 bayesian bayesian NOUN cana-1623 61 6 estimation estimation NOUN cana-1623 61 7 outperforms outperform VERB cana-1623 61 8 maximum maximum ADJ cana-1623 61 9 likelihood likelihood NOUN cana-1623 61 10 estimation estimation NOUN cana-1623 61 11 for for ADP cana-1623 61 12 estimating estimate VERB cana-1623 61 13 dependability dependability NOUN cana-1623 61 14 . . PUNCT cana-1623 62 1 the the DET cana-1623 62 2 proposed propose VERB cana-1623 62 3 approaches approach NOUN cana-1623 62 4 are be AUX cana-1623 62 5 tested test VERB cana-1623 62 6 against against ADP cana-1623 62 7 real real ADJ cana-1623 62 8 data datum NOUN cana-1623 62 9 to to PART cana-1623 62 10 demonstrate demonstrate VERB cana-1623 62 11 their their PRON cana-1623 62 12 usefulness usefulness NOUN cana-1623 62 13 . . PUNCT cana-1623 63 1 these these DET cana-1623 63 2 approaches approach NOUN cana-1623 63 3 reliably reliably ADV cana-1623 63 4 evaluate evaluate VERB cana-1623 63 5 the the DET cana-1623 63 6 reliability reliability NOUN cana-1623 63 7 of of ADP cana-1623 63 8 intuitive intuitive ADJ cana-1623 63 9 fuzzy fuzzy ADJ cana-1623 63 10 life life NOUN cana-1623 63 11 data datum NOUN cana-1623 63 12 , , PUNCT cana-1623 63 13 serving serve VERB cana-1623 63 14 as as ADP cana-1623 63 15 a a DET cana-1623 63 16 valuable valuable ADJ cana-1623 63 17 reference reference NOUN cana-1623 63 18 for for ADP cana-1623 63 19 reliability reliability NOUN cana-1623 63 20 analysis analysis NOUN cana-1623 63 21 in in ADP cana-1623 63 22 science science NOUN cana-1623 63 23 [ [ X cana-1623 63 24 11 11 NUM cana-1623 63 25 ] ] PUNCT cana-1623 63 26 . . PUNCT cana-1623 64 1 the the DET cana-1623 64 2 current current ADJ cana-1623 64 3 work work NOUN cana-1623 64 4 used use VERB cana-1623 64 5 a a DET cana-1623 64 6 fuzzy fuzzy ADJ cana-1623 64 7 intuitionistic intuitionistic ADJ cana-1623 64 8 fuzzy fuzzy ADJ cana-1623 64 9 set set NOUN cana-1623 64 10 to to PART cana-1623 64 11 analyze analyze VERB cana-1623 64 12 the the DET cana-1623 64 13 inverse inverse ADJ cana-1623 64 14 weibull weibull NOUN cana-1623 64 15 distribution distribution NOUN cana-1623 64 16 's 's PART cana-1623 64 17 probability probability NOUN cana-1623 64 18 density density NOUN cana-1623 64 19 function function NOUN cana-1623 64 20 , , PUNCT cana-1623 64 21 cumulative cumulative ADJ cana-1623 64 22 density density NOUN cana-1623 64 23 function function NOUN cana-1623 64 24 , , PUNCT cana-1623 64 25 and and CCONJ cana-1623 64 26 reliability reliability NOUN cana-1623 64 27 estimation estimation NOUN cana-1623 64 28 with with ADP cana-1623 64 29 real real ADJ cana-1623 64 30 - - PUNCT cana-1623 64 31 time time NOUN cana-1623 64 32 data datum NOUN cana-1623 64 33 . . PUNCT cana-1623 65 1 this this DET cana-1623 65 2 study study NOUN cana-1623 65 3 focused focus VERB cana-1623 65 4 on on ADP cana-1623 65 5 andra andra PROPN cana-1623 65 6 's 's PART cana-1623 65 7 agriculture agriculture NOUN cana-1623 65 8 in in ADP cana-1623 65 9 2019 2019 NUM cana-1623 65 10 . . PUNCT cana-1623 66 1 2 2 X cana-1623 66 2 . . X cana-1623 66 3 fuzzy fuzzy ADJ cana-1623 66 4 mathematical mathematical ADJ cana-1623 66 5 approach approach NOUN cana-1623 66 6 . . PUNCT cana-1623 67 1 the the DET cana-1623 67 2 probability probability NOUN cana-1623 67 3 density density NOUN cana-1623 67 4 function function NOUN cana-1623 67 5 ( ( PUNCT cana-1623 67 6 pdf pdf NOUN cana-1623 67 7 ) ) PUNCT cana-1623 67 8 , , PUNCT cana-1623 67 9 cumulative cumulative ADJ cana-1623 67 10 distribution distribution NOUN cana-1623 67 11 function function NOUN cana-1623 67 12 ( ( PUNCT cana-1623 67 13 cdf cdf PROPN cana-1623 67 14 ) ) PUNCT cana-1623 67 15 , , PUNCT cana-1623 67 16 and and CCONJ cana-1623 67 17 reliability reliability NOUN cana-1623 67 18 function function NOUN cana-1623 67 19 of of ADP cana-1623 67 20 iwd iwd PROPN cana-1623 67 21 are be AUX cana-1623 67 22 defined define VERB cana-1623 67 23 as as SCONJ cana-1623 67 24 follows follow VERB cana-1623 67 25 : : PUNCT cana-1623 67 26 𝑦(𝑑 𝑦(𝑑 NUM cana-1623 67 27 ; ; PUNCT cana-1623 67 28 πœ† πœ† X cana-1623 67 29 , , PUNCT cana-1623 67 30 πœ‚ πœ‚ NOUN cana-1623 67 31 ) ) PUNCT cana-1623 67 32 = = SYM cana-1623 67 33 πœ†πœ‚π‘‘βˆ’πœ‚βˆ’1 πœ†πœ‚π‘‘βˆ’πœ‚βˆ’1 NOUN cana-1623 67 34 exp(βˆ’πœ†π‘‘βˆ’πœ‚ exp(βˆ’πœ†π‘‘βˆ’πœ‚ PRON cana-1623 67 35 ) ) PUNCT cana-1623 67 36 , , PUNCT cana-1623 67 37 𝑑 𝑑 X cana-1623 67 38 > > X cana-1623 67 39 0 0 PUNCT cana-1623 68 1 π‘Œ(𝑑 π‘Œ(𝑑 X cana-1623 68 2 ; ; PUNCT cana-1623 68 3 πœ† πœ† X cana-1623 68 4 , , PUNCT cana-1623 68 5 πœ‚ πœ‚ NOUN cana-1623 68 6 ) ) PUNCT cana-1623 68 7 = = SYM cana-1623 68 8 exp(βˆ’πœ†π‘‘βˆ’πœ‚ exp(βˆ’πœ†π‘‘βˆ’πœ‚ PROPN cana-1623 68 9 ) ) PUNCT cana-1623 68 10 , , PUNCT cana-1623 68 11 𝑑 𝑑 X cana-1623 68 12 > > X cana-1623 68 13 0 0 PUNCT cana-1623 68 14 𝑅(𝑑 𝑅(𝑑 NOUN cana-1623 68 15 ) ) PUNCT cana-1623 68 16 = = SYM cana-1623 69 1 1 1 NUM cana-1623 69 2 βˆ’ βˆ’ NUM cana-1623 69 3 exp(βˆ’πœ†π‘‘βˆ’πœ‚ exp(βˆ’πœ†π‘‘βˆ’πœ‚ PROPN cana-1623 69 4 ) ) PUNCT cana-1623 69 5 , , PUNCT cana-1623 69 6 𝑑 𝑑 X cana-1623 69 7 > > X cana-1623 69 8 0 0 NUM cana-1623 69 9 where where SCONJ cana-1623 69 10 πœ† πœ† DET cana-1623 69 11 > > X cana-1623 69 12 0 0 NUM cana-1623 69 13 is be AUX cana-1623 69 14 the the DET cana-1623 69 15 scale scale NOUN cana-1623 69 16 parameter parameter NOUN cana-1623 69 17 and and CCONJ cana-1623 69 18 πœ‚ πœ‚ NOUN cana-1623 69 19 > > X cana-1623 69 20 0 0 NUM cana-1623 69 21 is be AUX cana-1623 69 22 the the DET cana-1623 69 23 shape shape NOUN cana-1623 69 24 parameter parameter NOUN cana-1623 69 25 , , PUNCT cana-1623 69 26 communications communication NOUN cana-1623 69 27 on on ADP cana-1623 69 28 applied apply VERB cana-1623 69 29 nonlinear nonlinear ADJ cana-1623 69 30 analysis analysis NOUN cana-1623 69 31 issn issn NOUN cana-1623 69 32 : : PUNCT cana-1623 69 33 1074 1074 NUM cana-1623 69 34 - - PUNCT cana-1623 69 35 133x 133x NUM cana-1623 69 36 vol vol NOUN cana-1623 69 37 32 32 NUM cana-1623 69 38 no no NOUN cana-1623 69 39 . . NOUN cana-1623 69 40 1 1 NUM cana-1623 69 41 ( ( PUNCT cana-1623 69 42 2025 2025 NUM cana-1623 69 43 ) ) PUNCT cana-1623 69 44 93 93 NUM cana-1623 69 45 https://internationalpubls.com https://internationalpubls.com X cana-1623 70 1 a a DET cana-1623 70 2 fuzzy fuzzy ADJ cana-1623 70 3 set set NOUN cana-1623 70 4 expresses express VERB cana-1623 70 5 the the DET cana-1623 70 6 concept concept NOUN cana-1623 70 7 of of ADP cana-1623 70 8 fuzziness fuzziness NOUN cana-1623 70 9 . . PUNCT cana-1623 71 1 similarly similarly ADV cana-1623 71 2 to to ADP cana-1623 71 3 the the DET cana-1623 71 4 definition definition NOUN cana-1623 71 5 of of ADP cana-1623 71 6 the the DET cana-1623 71 7 characteristic characteristic ADJ cana-1623 71 8 function function NOUN cana-1623 71 9 of of ADP cana-1623 71 10 a a DET cana-1623 71 11 classical classical ADJ cana-1623 71 12 set set NOUN cana-1623 71 13 , , PUNCT cana-1623 71 14 the the DET cana-1623 71 15 definition definition NOUN cana-1623 71 16 of of ADP cana-1623 71 17 a a DET cana-1623 71 18 fuzzy fuzzy ADJ cana-1623 71 19 set set NOUN cana-1623 71 20 can can AUX cana-1623 71 21 be be AUX cana-1623 71 22 achieved achieve VERB cana-1623 71 23 by by ADP cana-1623 71 24 expanding expand VERB cana-1623 71 25 its its PRON cana-1623 71 26 domain domain NOUN cana-1623 71 27 . . PUNCT cana-1623 72 1 definition definition NOUN cana-1623 72 2 2.1 2.1 NUM cana-1623 72 3 let let VERB cana-1623 72 4 t t PROPN cana-1623 72 5 represent represent VERB cana-1623 72 6 a a DET cana-1623 72 7 non non ADJ cana-1623 72 8 - - ADJ cana-1623 72 9 empty empty ADJ cana-1623 72 10 universal universal ADJ cana-1623 72 11 set set NOUN cana-1623 72 12 . . PUNCT cana-1623 73 1 the the DET cana-1623 73 2 fuzzy fuzzy ADJ cana-1623 73 3 set set VERB cana-1623 73 4 οΏ½ οΏ½ PROPN cana-1623 73 5 Μƒ Μƒ PROPN cana-1623 73 6 οΏ½ οΏ½ PROPN cana-1623 73 7 is be AUX cana-1623 73 8 defined define VERB cana-1623 73 9 as as ADP cana-1623 73 10 οΏ½ οΏ½ PROPN cana-1623 73 11 Μƒ Μƒ PROPN cana-1623 73 12 οΏ½ οΏ½ NOUN cana-1623 73 13 = = SYM cana-1623 73 14 { { PUNCT cana-1623 73 15 < < X cana-1623 73 16 𝑑 𝑑 PROPN cana-1623 73 17 , , PUNCT cana-1623 73 18 πœ‡ πœ‡ ADP cana-1623 73 19 οΏ½ οΏ½ PROPN cana-1623 73 20 Μƒ Μƒ PROPN cana-1623 73 21 οΏ½ οΏ½ PROPN cana-1623 73 22 (𝑑)⟩ (𝑑)⟩ PROPN cana-1623 73 23 ∣ ∣ PROPN cana-1623 73 24 𝑑 𝑑 PROPN cana-1623 73 25 ∈ ∈ PROPN cana-1623 73 26 𝕋 𝕋 PROPN cana-1623 73 27 } } PUNCT cana-1623 73 28 , , PUNCT cana-1623 73 29 where where SCONJ cana-1623 73 30 πœ‡ πœ‡ ADP cana-1623 73 31 οΏ½ οΏ½ PROPN cana-1623 73 32 Μƒ Μƒ NOUN cana-1623 73 33 οΏ½ οΏ½ NOUN cana-1623 73 34 : : PUNCT cana-1623 73 35 𝕋 𝕋 PROPN cana-1623 73 36 β†’ β†’ SYM cana-1623 73 37 [ [ X cana-1623 73 38 0,1 0,1 NUM cana-1623 73 39 ] ] PUNCT cana-1623 73 40 ] ] PUNCT cana-1623 73 41 represents represent VERB cana-1623 73 42 the the DET cana-1623 73 43 degree degree NOUN cana-1623 73 44 of of ADP cana-1623 73 45 membership membership NOUN cana-1623 73 46 of of ADP cana-1623 73 47 t t PROPN cana-1623 73 48 in in ADP cana-1623 73 49 οΏ½ οΏ½ PROPN cana-1623 73 50 Μƒ Μƒ PROPN cana-1623 73 51 οΏ½ οΏ½ PROPN cana-1623 73 52 . . PUNCT cana-1623 73 53 . . PUNCT cana-1623 74 1 definition definition NOUN cana-1623 74 2 2.2 2.2 NUM cana-1623 74 3 let let VERB cana-1623 74 4 t t PROPN cana-1623 74 5 represent represent VERB cana-1623 74 6 a a DET cana-1623 74 7 non non ADJ cana-1623 74 8 - - ADJ cana-1623 74 9 empty empty ADJ cana-1623 74 10 universal universal ADJ cana-1623 74 11 set set NOUN cana-1623 74 12 . . PUNCT cana-1623 75 1 ifs ifs PROPN cana-1623 75 2 a a DET cana-1623 75 3 Μƒ Μƒ PROPN cana-1623 75 4 is be AUX cana-1623 75 5 defined define VERB cana-1623 75 6 as as ADP cana-1623 75 7 οΏ½ οΏ½ PROPN cana-1623 75 8 Μƒ Μƒ PROPN cana-1623 75 9 οΏ½ οΏ½ NOUN cana-1623 75 10 = = SYM cana-1623 75 11 { { PUNCT cana-1623 75 12 βŸ¨π‘‘ βŸ¨π‘‘ NOUN cana-1623 75 13 , , PUNCT cana-1623 75 14 πœ‡ πœ‡ ADP cana-1623 75 15 οΏ½ οΏ½ PROPN cana-1623 75 16 Μƒ Μƒ NOUN cana-1623 75 17 οΏ½ οΏ½ NOUN cana-1623 75 18 (𝑑 (𝑑 NOUN cana-1623 75 19 ) ) PUNCT cana-1623 75 20 , , PUNCT cana-1623 75 21 𝑣 𝑣 PROPN cana-1623 75 22 οΏ½ οΏ½ PROPN cana-1623 75 23 Μƒ Μƒ PROPN cana-1623 75 24 οΏ½ οΏ½ PROPN cana-1623 75 25 (𝑑 (𝑑 NOUN cana-1623 75 26 ) ) PUNCT cana-1623 75 27 > > PUNCT cana-1623 75 28 |𝑑 |𝑑 X cana-1623 75 29 ∈ ∈ PROPN cana-1623 75 30 𝕋 𝕋 PROPN cana-1623 75 31 } } PUNCT cana-1623 75 32 , , PUNCT cana-1623 75 33 where where SCONJ cana-1623 75 34 πœ‡ πœ‡ ADP cana-1623 75 35 οΏ½ οΏ½ PROPN cana-1623 75 36 Μƒ Μƒ NOUN cana-1623 75 37 οΏ½ οΏ½ NOUN cana-1623 75 38 : : PUNCT cana-1623 75 39 𝕋 𝕋 PROPN cana-1623 75 40 β†’ β†’ SYM cana-1623 75 41 [ [ X cana-1623 75 42 0,1 0,1 NUM cana-1623 75 43 ] ] PUNCT cana-1623 75 44 is be AUX cana-1623 75 45 the the DET cana-1623 75 46 degree degree NOUN cana-1623 75 47 of of ADP cana-1623 75 48 membership membership NOUN cana-1623 75 49 of of ADP cana-1623 75 50 t t PROPN cana-1623 75 51 in in ADP cana-1623 75 52 οΏ½ οΏ½ PROPN cana-1623 75 53 Μƒ Μƒ PROPN cana-1623 75 54 οΏ½ οΏ½ PROPN cana-1623 75 55 and and CCONJ cana-1623 75 56 𝑣 𝑣 ADP cana-1623 75 57 οΏ½ οΏ½ PROPN cana-1623 75 58 Μƒ Μƒ NOUN cana-1623 75 59 οΏ½ οΏ½ PROPN cana-1623 75 60 : : PUNCT cana-1623 75 61 𝕋 𝕋 PROPN cana-1623 75 62 β†’ β†’ SYM cana-1623 75 63 [ [ X cana-1623 75 64 0,1 0,1 NUM cana-1623 75 65 ] ] PUNCT cana-1623 75 66 is be AUX cana-1623 75 67 the the DET cana-1623 75 68 degree degree NOUN cana-1623 75 69 of of ADP cana-1623 75 70 nonmembership nonmembership NOUN cana-1623 75 71 of of ADP cana-1623 75 72 t t PROPN cana-1623 75 73 in in ADP cana-1623 75 74 οΏ½ οΏ½ PROPN cana-1623 75 75 Μƒ Μƒ PROPN cana-1623 75 76 οΏ½ οΏ½ PROPN cana-1623 75 77 . . PUNCT cana-1623 76 1 they they PRON cana-1623 76 2 satisfy satisfy VERB cana-1623 76 3 0 0 NUM cana-1623 76 4 ≀ ≀ PROPN cana-1623 76 5 πœ‡ πœ‡ ADP cana-1623 76 6 οΏ½ οΏ½ PROPN cana-1623 76 7 Μƒ Μƒ NOUN cana-1623 76 8 οΏ½ οΏ½ NOUN cana-1623 76 9 (𝑑 (𝑑 NOUN cana-1623 76 10 ) ) PUNCT cana-1623 77 1 + + CCONJ cana-1623 77 2 𝑣 𝑣 PRON cana-1623 77 3 οΏ½ οΏ½ PROPN cana-1623 77 4 Μƒ Μƒ PROPN cana-1623 77 5 οΏ½ οΏ½ PROPN cana-1623 77 6 (𝑑 (𝑑 NOUN cana-1623 77 7 ) ) PUNCT cana-1623 77 8 ≀ ≀ NOUN cana-1623 77 9 1 1 NUM cana-1623 77 10 for for ADP cana-1623 77 11 each each DET cana-1623 77 12 t. t. NOUN cana-1623 77 13 when when SCONJ cana-1623 77 14 t t PROPN cana-1623 77 15 has have VERB cana-1623 77 16 only only ADV cana-1623 77 17 one one NUM cana-1623 77 18 element element NOUN cana-1623 77 19 , , PUNCT cana-1623 77 20 οΏ½ οΏ½ PROPN cana-1623 77 21 Μƒ Μƒ NOUN cana-1623 77 22 οΏ½ οΏ½ NOUN cana-1623 78 1 = = PROPN cana-1623 78 2 < < X cana-1623 78 3 πœ‡ πœ‡ PART cana-1623 78 4 οΏ½ οΏ½ PROPN cana-1623 78 5 Μƒ Μƒ NOUN cana-1623 78 6 οΏ½ οΏ½ PROPN cana-1623 78 7 , , PUNCT cana-1623 78 8 𝑣 𝑣 PROPN cana-1623 78 9 οΏ½ οΏ½ PROPN cana-1623 78 10 Μƒ Μƒ NOUN cana-1623 78 11 οΏ½ οΏ½ PROPN cana-1623 78 12 > > X cana-1623 78 13 is be AUX cana-1623 78 14 frequently frequently ADV cana-1623 78 15 referred refer VERB cana-1623 78 16 to to ADP cana-1623 78 17 as as ADP cana-1623 78 18 intuitionistic intuitionistic ADJ cana-1623 78 19 fuzzy fuzzy ADJ cana-1623 78 20 number number NOUN cana-1623 78 21 . . PUNCT cana-1623 79 1 the the DET cana-1623 79 2 membership membership NOUN cana-1623 79 3 and and CCONJ cana-1623 79 4 non non ADJ cana-1623 79 5 - - ADJ cana-1623 79 6 membership membership ADJ cana-1623 79 7 functions function NOUN cana-1623 79 8 are be AUX cana-1623 79 9 : : PUNCT cana-1623 79 10 πœ‡aΜƒ(𝑑 πœ‡aΜƒ(𝑑 NOUN cana-1623 79 11 ) ) PUNCT cana-1623 79 12 = = PRON cana-1623 79 13 { { PUNCT cana-1623 79 14 𝛼 𝛼 NOUN cana-1623 79 15 𝑑 𝑑 NOUN cana-1623 79 16 βˆ’ βˆ’ PROPN cana-1623 79 17 π‘Ž π‘Ž NOUN cana-1623 79 18 𝑏 𝑏 NOUN cana-1623 79 19 βˆ’ βˆ’ PROPN cana-1623 79 20 π‘Ž π‘Ž PUNCT cana-1623 79 21 𝑑 𝑑 X cana-1623 79 22 ∈ ∈ PROPN cana-1623 80 1 [ [ X cana-1623 80 2 π‘Ž π‘Ž X cana-1623 80 3 , , PUNCT cana-1623 80 4 𝑏 𝑏 NOUN cana-1623 80 5 ] ] X cana-1623 80 6 𝛼 𝛼 NUM cana-1623 80 7 𝑑 𝑑 NOUN cana-1623 80 8 ∈ ∈ PROPN cana-1623 80 9 ( ( PUNCT cana-1623 80 10 𝑏 𝑏 NOUN cana-1623 80 11 , , PUNCT cana-1623 80 12 𝑐 𝑐 NOUN cana-1623 80 13 ) ) PUNCT cana-1623 80 14 𝛼 𝛼 PROPN cana-1623 80 15 𝑑 𝑑 NOUN cana-1623 80 16 βˆ’ βˆ’ PROPN cana-1623 80 17 𝑑 𝑑 PROPN cana-1623 80 18 𝑑 𝑑 PROPN cana-1623 80 19 βˆ’ βˆ’ PROPN cana-1623 80 20 𝑐 𝑐 PROPN cana-1623 80 21 𝑑 𝑑 PROPN cana-1623 80 22 ∈ ∈ PROPN cana-1623 81 1 [ [ X cana-1623 81 2 𝑐 𝑐 NOUN cana-1623 81 3 , , PUNCT cana-1623 81 4 𝑑 𝑑 NOUN cana-1623 81 5 ] ] X cana-1623 81 6 0 0 NUM cana-1623 81 7 else else ADV cana-1623 81 8 𝑣aΜƒ(𝑑 𝑣aΜƒ(𝑑 NOUN cana-1623 81 9 ) ) PUNCT cana-1623 81 10 = = PRON cana-1623 81 11 { { PUNCT cana-1623 82 1 𝑏 𝑏 NOUN cana-1623 82 2 βˆ’ βˆ’ PROPN cana-1623 82 3 𝑑 𝑑 PROPN cana-1623 83 1 𝑏 𝑏 NOUN cana-1623 83 2 βˆ’ βˆ’ PROPN cana-1623 83 3 π‘Ž π‘Ž PROPN cana-1623 83 4 + + X cana-1623 83 5 𝛽 𝛽 NOUN cana-1623 83 6 𝑑 𝑑 NOUN cana-1623 83 7 βˆ’ βˆ’ NUM cana-1623 83 8 π‘Ž π‘Ž NOUN cana-1623 83 9 𝑏 𝑏 NOUN cana-1623 83 10 βˆ’ βˆ’ PROPN cana-1623 83 11 π‘Ž π‘Ž PUNCT cana-1623 83 12 𝑑 𝑑 X cana-1623 83 13 ∈ ∈ PROPN cana-1623 83 14 [ [ X cana-1623 83 15 π‘Ž π‘Ž X cana-1623 83 16 , , PUNCT cana-1623 83 17 𝑏 𝑏 NOUN cana-1623 83 18 ] ] X cana-1623 83 19 𝛽 𝛽 NOUN cana-1623 83 20 𝑑this 𝑑thi VERB cana-1623 83 21 ∈ ∈ NOUN cana-1623 83 22 ( ( PUNCT cana-1623 83 23 𝑏 𝑏 NOUN cana-1623 83 24 , , PUNCT cana-1623 83 25 𝑐 𝑐 NOUN cana-1623 83 26 ) ) PUNCT cana-1623 83 27 𝑑 𝑑 NOUN cana-1623 83 28 βˆ’ βˆ’ PROPN cana-1623 83 29 𝑐 𝑐 PROPN cana-1623 83 30 𝑑 𝑑 PRON cana-1623 83 31 βˆ’ βˆ’ PROPN cana-1623 83 32 𝑐 𝑐 PROPN cana-1623 83 33 + + NUM cana-1623 83 34 𝛽 𝛽 PROPN cana-1623 83 35 𝑑 𝑑 PRON cana-1623 83 36 βˆ’ βˆ’ PROPN cana-1623 83 37 𝑑 𝑑 PROPN cana-1623 83 38 𝑑 𝑑 PROPN cana-1623 83 39 βˆ’ βˆ’ PROPN cana-1623 83 40 𝑐 𝑐 PROPN cana-1623 83 41 𝑑 𝑑 PROPN cana-1623 83 42 ∈ ∈ PROPN cana-1623 84 1 [ [ X cana-1623 84 2 𝑐 𝑐 NOUN cana-1623 84 3 , , PUNCT cana-1623 84 4 𝑑 𝑑 NOUN cana-1623 84 5 ] ] X cana-1623 84 6 1 1 NUM cana-1623 84 7 else else ADV cana-1623 84 8 where where SCONJ cana-1623 84 9 Ξ± Ξ± NOUN cana-1623 84 10 is be AUX cana-1623 84 11 the the DET cana-1623 84 12 maximum maximum ADJ cana-1623 84 13 membership membership NOUN cana-1623 84 14 degree degree NOUN cana-1623 84 15 and and CCONJ cana-1623 84 16 Ξ² Ξ² X cana-1623 84 17 is be AUX cana-1623 84 18 the the DET cana-1623 84 19 minimum minimum ADJ cana-1623 84 20 membership membership NOUN cana-1623 84 21 degree degree NOUN cana-1623 84 22 . . PUNCT cana-1623 85 1 in in ADP cana-1623 85 2 paper paper NOUN cana-1623 85 3 , , PUNCT cana-1623 85 4 we we PRON cana-1623 85 5 assume assume VERB cana-1623 85 6 t t PROPN cana-1623 85 7 be be AUX cana-1623 85 8 a a DET cana-1623 85 9 set set NOUN cana-1623 85 10 of of ADP cana-1623 85 11 real real ADJ cana-1623 85 12 numbers number NOUN cana-1623 85 13 , , PUNCT cana-1623 85 14 which which PRON cana-1623 85 15 is be AUX cana-1623 85 16 t t PROPN cana-1623 85 17 = = PROPN cana-1623 85 18 r. r. PROPN cana-1623 85 19 additionally additionally ADV cana-1623 85 20 , , PUNCT cana-1623 85 21 we we PRON cana-1623 85 22 assumed assume VERB cana-1623 85 23 that that SCONJ cana-1623 85 24 the the DET cana-1623 85 25 ifss ifss NOUN cana-1623 85 26 discussed discuss VERB cana-1623 85 27 in in ADP cana-1623 85 28 this this DET cana-1623 85 29 paper paper NOUN cana-1623 85 30 were be AUX cana-1623 85 31 traifns traifns NOUN cana-1623 85 32 . . PUNCT cana-1623 85 33 to to PART cana-1623 85 34 better well ADV cana-1623 85 35 investigate investigate VERB cana-1623 85 36 the the DET cana-1623 85 37 estimation estimation NOUN cana-1623 85 38 problem problem NOUN cana-1623 85 39 on on ADP cana-1623 85 40 the the DET cana-1623 85 41 basis basis NOUN cana-1623 85 42 of of ADP cana-1623 85 43 intuitionistic intuitionistic ADJ cana-1623 85 44 fuzzy fuzzy ADJ cana-1623 85 45 data datum NOUN cana-1623 85 46 , , PUNCT cana-1623 85 47 some some DET cana-1623 85 48 concepts concept NOUN cana-1623 85 49 in in ADP cana-1623 85 50 the the DET cana-1623 85 51 probability probability NOUN cana-1623 85 52 theory theory NOUN cana-1623 85 53 were be AUX cana-1623 85 54 extended extend VERB cana-1623 85 55 to to ADP cana-1623 85 56 intuitionistic intuitionistic ADJ cana-1623 85 57 fuzzy fuzzy ADJ cana-1623 85 58 random random ADJ cana-1623 85 59 variables variable NOUN cana-1623 85 60 . . PUNCT cana-1623 86 1 definition definition NOUN cana-1623 86 2 2.3 2.3 NUM cana-1623 86 3 consider consider VERB cana-1623 86 4 a a DET cana-1623 86 5 probability probability NOUN cana-1623 86 6 space space NOUN cana-1623 86 7 ( ( PUNCT cana-1623 86 8 ℝ𝑛 ℝ𝑛 PROPN cana-1623 86 9 , , PUNCT cana-1623 86 10 𝔄 𝔄 PROPN cana-1623 86 11 , , PUNCT cana-1623 86 12 𝒫 𝒫 PROPN cana-1623 86 13 ) ) PUNCT cana-1623 86 14 , , PUNCT cana-1623 86 15 the the DET cana-1623 86 16 probability probability NOUN cana-1623 86 17 of of ADP cana-1623 86 18 an an DET cana-1623 86 19 intuitionistic intuitionistic ADJ cana-1623 86 20 fuzzy fuzzy ADJ cana-1623 86 21 observation observation NOUN cana-1623 86 22 οΏ½ οΏ½ PROPN cana-1623 86 23 Μƒ Μƒ PROPN cana-1623 86 24 οΏ½ οΏ½ PROPN cana-1623 86 25 in in ADP cana-1623 86 26 ℝ𝑛 ℝ𝑛 PROPN cana-1623 86 27 is be AUX cana-1623 86 28 defined define VERB cana-1623 86 29 as as ADP cana-1623 86 30 𝑃( 𝑃( ADJ cana-1623 86 31 οΏ½ οΏ½ PROPN cana-1623 86 32 Μƒ Μƒ PROPN cana-1623 86 33 οΏ½ οΏ½ PROPN cana-1623 86 34 ) ) PUNCT cana-1623 86 35 = = SYM cana-1623 87 1 ∫ ∫ PROPN cana-1623 87 2 β€Š β€Š SPACE cana-1623 88 1 ℝ𝑛 ℝ𝑛 ADV cana-1623 88 2 β€Š β€Š SPACE cana-1623 88 3 1 1 NUM cana-1623 88 4 βˆ’ βˆ’ PROPN cana-1623 88 5 𝑣 𝑣 PRON cana-1623 88 6 οΏ½ οΏ½ PROPN cana-1623 88 7 Μƒ Μƒ PROPN cana-1623 88 8 οΏ½ οΏ½ NOUN cana-1623 88 9 (𝑑 (𝑑 NOUN cana-1623 88 10 ) ) PUNCT cana-1623 88 11 + + CCONJ cana-1623 88 12 πœ‡ πœ‡ PRON cana-1623 88 13 οΏ½ οΏ½ PROPN cana-1623 88 14 Μƒ Μƒ NOUN cana-1623 88 15 οΏ½ οΏ½ NOUN cana-1623 88 16 (𝑑 (𝑑 NOUN cana-1623 88 17 ) ) PUNCT cana-1623 88 18 2 2 NUM cana-1623 88 19 𝑑𝒫 𝑑𝒫 NOUN cana-1623 88 20 the the DET cana-1623 88 21 continuous continuous ADJ cana-1623 88 22 random random ADJ cana-1623 88 23 variable variable NOUN cana-1623 88 24 𝑇 𝑇 PROPN cana-1623 88 25 = = SYM cana-1623 88 26 ( ( PUNCT cana-1623 88 27 𝑇1 𝑇1 PROPN cana-1623 88 28 , , PUNCT cana-1623 88 29 𝑇2 𝑇2 NOUN cana-1623 88 30 , , PUNCT cana-1623 88 31 … … PUNCT cana-1623 88 32 , , PUNCT cana-1623 88 33 𝑇𝑛 𝑇𝑛 PROPN cana-1623 88 34 ) ) PUNCT cana-1623 88 35 follows follow VERB cana-1623 88 36 the the DET cana-1623 88 37 iw iw PROPN cana-1623 88 38 ( ( PUNCT cana-1623 88 39 πœ† πœ† NOUN cana-1623 88 40 , , PUNCT cana-1623 88 41 πœ‚ πœ‚ NOUN cana-1623 88 42 ) ) PUNCT cana-1623 88 43 , , PUNCT cana-1623 88 44 and and CCONJ cana-1623 88 45 its its PRON cana-1623 88 46 intuitionistic intuitionistic ADJ cana-1623 88 47 fuzzy fuzzy ADJ cana-1623 88 48 observations observation NOUN cana-1623 88 49 are be AUX cana-1623 88 50 denoted denote VERB cana-1623 88 51 by by ADP cana-1623 88 52 οΏ½ οΏ½ PROPN cana-1623 88 53 Μƒ Μƒ PROPN cana-1623 88 54 οΏ½ οΏ½ NOUN cana-1623 88 55 = = SYM cana-1623 88 56 ( ( PUNCT cana-1623 88 57 οΏ½ οΏ½ PROPN cana-1623 88 58 Μƒ Μƒ NOUN cana-1623 88 59 οΏ½ οΏ½ NOUN cana-1623 88 60 1 1 NUM cana-1623 88 61 , , PUNCT cana-1623 88 62 οΏ½ οΏ½ PROPN cana-1623 88 63 Μƒ Μƒ NOUN cana-1623 88 64 οΏ½ οΏ½ NOUN cana-1623 88 65 2 2 NUM cana-1623 88 66 , , PUNCT cana-1623 88 67 … … PUNCT cana-1623 88 68 , , PUNCT cana-1623 88 69 οΏ½ οΏ½ PROPN cana-1623 88 70 Μƒ Μƒ PROPN cana-1623 88 71 οΏ½ οΏ½ NOUN cana-1623 88 72 𝑛 𝑛 NOUN cana-1623 88 73 ) ) PUNCT cana-1623 88 74 . . PUNCT cana-1623 89 1 the the DET cana-1623 89 2 conditional conditional ADJ cana-1623 89 3 density density NOUN cana-1623 89 4 of of ADP cana-1623 89 5 random random ADJ cana-1623 89 6 variables variable NOUN cana-1623 89 7 in in ADP cana-1623 89 8 probability probability NOUN cana-1623 89 9 theory theory NOUN cana-1623 89 10 is be AUX cana-1623 89 11 introduced introduce VERB cana-1623 89 12 , , PUNCT cana-1623 89 13 and and CCONJ cana-1623 89 14 the the DET cana-1623 89 15 intuitionistic intuitionistic ADJ cana-1623 89 16 fuzzy fuzzy ADJ cana-1623 89 17 conditional conditional ADJ cana-1623 89 18 density density NOUN cana-1623 89 19 is be AUX cana-1623 89 20 given give VERB cana-1623 89 21 as as SCONJ cana-1623 89 22 follows follow VERB cana-1623 89 23 : : PUNCT cana-1623 89 24 communications communication NOUN cana-1623 89 25 on on ADP cana-1623 89 26 applied apply VERB cana-1623 89 27 nonlinear nonlinear ADJ cana-1623 89 28 analysis analysis NOUN cana-1623 89 29 issn issn NOUN cana-1623 89 30 : : PUNCT cana-1623 89 31 1074 1074 NUM cana-1623 89 32 - - PUNCT cana-1623 89 33 133x 133x NUM cana-1623 89 34 vol vol NOUN cana-1623 89 35 32 32 NUM cana-1623 89 36 no no NOUN cana-1623 89 37 . . NOUN cana-1623 89 38 1 1 NUM cana-1623 89 39 ( ( PUNCT cana-1623 89 40 2025 2025 NUM cana-1623 89 41 ) ) PUNCT cana-1623 89 42 94 94 NUM cana-1623 90 1 https://internationalpubls.com https://internationalpubls.com X cana-1623 90 2 𝑦(𝑑 𝑦(𝑑 PROPN cana-1623 90 3 ∣ ∣ PROPN cana-1623 90 4 οΏ½ οΏ½ PROPN cana-1623 90 5 Μƒ Μƒ PROPN cana-1623 90 6 οΏ½ οΏ½ PROPN cana-1623 90 7 ) ) PUNCT cana-1623 90 8 = = SYM cana-1623 90 9 𝑠(𝑑)𝑦(𝑑 𝑠(𝑑)𝑦(𝑑 NUM cana-1623 90 10 ; ; PUNCT cana-1623 90 11 πœ† πœ† X cana-1623 90 12 , , PUNCT cana-1623 90 13 πœ‚ πœ‚ NOUN cana-1623 90 14 ) ) PUNCT cana-1623 90 15 ∫ ∫ NOUN cana-1623 90 16 β€Š β€Š SPACE cana-1623 90 17 ℝ ℝ PROPN cana-1623 90 18 β€Š β€Š SPACE cana-1623 90 19 𝑠(𝑑)𝑦(𝑑 𝑠(𝑑)𝑦(𝑑 NUM cana-1623 90 20 ; ; PUNCT cana-1623 90 21 πœ† πœ† X cana-1623 90 22 , , PUNCT cana-1623 90 23 πœ‚)𝑑𝑑 πœ‚)𝑑𝑑 PROPN cana-1623 90 24 where where SCONJ cana-1623 90 25 𝑠(𝑑 𝑠(𝑑 PROPN cana-1623 90 26 ) ) PUNCT cana-1623 91 1 = = SYM cana-1623 92 1 1βˆ’π‘£ 1βˆ’π‘£ NUM cana-1623 92 2 οΏ½ οΏ½ PROPN cana-1623 92 3 Μƒ Μƒ PROPN cana-1623 92 4 οΏ½ οΏ½ PROPN cana-1623 92 5 (𝑑)+πœ‡ (𝑑)+πœ‡ PROPN cana-1623 92 6 οΏ½ οΏ½ PROPN cana-1623 92 7 Μƒ Μƒ PROPN cana-1623 92 8 οΏ½ οΏ½ PROPN cana-1623 92 9 (𝑑 (𝑑 NOUN cana-1623 92 10 ) ) PUNCT cana-1623 92 11 2 2 NUM cana-1623 92 12 . . PUNCT cana-1623 93 1 in in ADP cana-1623 93 2 this this DET cana-1623 93 3 case case NOUN cana-1623 93 4 , , PUNCT cana-1623 93 5 the the DET cana-1623 93 6 intuitionistic intuitionistic ADJ cana-1623 93 7 fuzzy fuzzy ADJ cana-1623 93 8 likelihood likelihood NOUN cana-1623 93 9 function function NOUN cana-1623 93 10 of of ADP cana-1623 93 11 iw⁑(πœ† iw⁑(πœ† PROPN cana-1623 93 12 , , PUNCT cana-1623 93 13 πœ‚ πœ‚ NOUN cana-1623 93 14 ) ) PUNCT cana-1623 93 15 is be AUX cana-1623 93 16 : : PUNCT cana-1623 93 17 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 93 18 , , PUNCT cana-1623 93 19 πœ‚ πœ‚ PROPN cana-1623 93 20 ∣ ∣ PROPN cana-1623 93 21 οΏ½ οΏ½ PROPN cana-1623 93 22 Μƒ Μƒ PROPN cana-1623 93 23 οΏ½ οΏ½ PROPN cana-1623 93 24 ) ) PUNCT cana-1623 93 25 = = SYM cana-1623 93 26 ∏ ∏ X cana-1623 93 27 β€Š β€Š SPACE cana-1623 93 28 𝑛 𝑛 PRON cana-1623 93 29 𝑖=1 𝑖=1 PROPN cana-1623 93 30 β€Š β€Š SPACE cana-1623 93 31 𝑃( 𝑃( X cana-1623 93 32 οΏ½ οΏ½ PROPN cana-1623 93 33 Μƒ Μƒ PROPN cana-1623 93 34 οΏ½ οΏ½ PROPN cana-1623 93 35 𝑖 𝑖 PROPN cana-1623 93 36 ∣ ∣ PROPN cana-1623 93 37 πœ† πœ† NOUN cana-1623 93 38 , , PUNCT cana-1623 93 39 πœ‚ πœ‚ NOUN cana-1623 93 40 ) ) PUNCT cana-1623 93 41 = = NOUN cana-1623 93 42 ∏ ∏ NUM cana-1623 93 43 β€Š β€Š SPACE cana-1623 93 44 𝑛 𝑛 PRON cana-1623 93 45 𝑖=1 𝑖=1 PROPN cana-1623 93 46 β€Š β€Š SPACE cana-1623 93 47 ∫ ∫ PROPN cana-1623 93 48 β€Š β€Š SPACE cana-1623 93 49 ℝ ℝ PROPN cana-1623 93 50 β€Š β€Š SPACE cana-1623 93 51 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 93 52 ; ; PUNCT cana-1623 93 53 πœ† πœ† X cana-1623 93 54 , , PUNCT cana-1623 93 55 πœ‚)𝑑𝑑 πœ‚)𝑑𝑑 PROPN cana-1623 93 56 where where SCONJ cana-1623 93 57 𝑠𝑖(𝑑 𝑠𝑖(𝑑 VERB cana-1623 93 58 ) ) PUNCT cana-1623 93 59 = = SYM cana-1623 93 60 1βˆ’π‘£ 1βˆ’π‘£ NUM cana-1623 93 61 οΏ½ οΏ½ PROPN cana-1623 93 62 Μƒ Μƒ PROPN cana-1623 93 63 οΏ½ οΏ½ PROPN cana-1623 93 64 𝑖(𝑑)+πœ‡ 𝑖(𝑑)+πœ‡ NUM cana-1623 93 65 οΏ½ οΏ½ PROPN cana-1623 93 66 Μƒ Μƒ PROPN cana-1623 93 67 οΏ½ οΏ½ NOUN cana-1623 93 68 𝑖(𝑑 𝑖(𝑑 NUM cana-1623 93 69 ) ) PUNCT cana-1623 93 70 2 2 NUM cana-1623 93 71 . . PUNCT cana-1623 94 1 finally finally ADV cana-1623 94 2 , , PUNCT cana-1623 94 3 intuitionistic intuitionistic ADJ cana-1623 94 4 fuzzy fuzzy ADJ cana-1623 94 5 conditional conditional ADJ cana-1623 94 6 expectation expectation NOUN cana-1623 94 7 is be AUX cana-1623 94 8 defined define VERB cana-1623 94 9 . . PUNCT cana-1623 95 1 using use VERB cana-1623 95 2 the the DET cana-1623 95 3 intuitionistic intuitionistic ADJ cana-1623 95 4 fuzzy fuzzy ADJ cana-1623 95 5 conditional conditional ADJ cana-1623 95 6 density density NOUN cana-1623 95 7 and and CCONJ cana-1623 95 8 observation observation NOUN cana-1623 95 9 οΏ½ οΏ½ PROPN cana-1623 95 10 Μƒ Μƒ PROPN cana-1623 95 11 οΏ½ οΏ½ PROPN cana-1623 95 12 = = SYM cana-1623 95 13 ( ( PUNCT cana-1623 95 14 οΏ½ οΏ½ PROPN cana-1623 95 15 Μƒ Μƒ NOUN cana-1623 95 16 οΏ½ οΏ½ NOUN cana-1623 95 17 1 1 NUM cana-1623 95 18 , , PUNCT cana-1623 95 19 οΏ½ οΏ½ PROPN cana-1623 95 20 Μƒ Μƒ NOUN cana-1623 95 21 οΏ½ οΏ½ NOUN cana-1623 95 22 2 2 NUM cana-1623 95 23 , , PUNCT cana-1623 95 24 … … PUNCT cana-1623 95 25 , , PUNCT cana-1623 95 26 οΏ½ οΏ½ PROPN cana-1623 95 27 Μƒ Μƒ PROPN cana-1623 95 28 οΏ½ οΏ½ NOUN cana-1623 95 29 𝑛 𝑛 NOUN cana-1623 95 30 ) ) PUNCT cana-1623 95 31 , , PUNCT cana-1623 95 32 the the DET cana-1623 95 33 intuitionistic intuitionistic ADJ cana-1623 95 34 fuzzy fuzzy ADJ cana-1623 95 35 conditional conditional ADJ cana-1623 95 36 expectation expectation NOUN cana-1623 95 37 of of ADP cana-1623 95 38 a a DET cana-1623 95 39 random random ADJ cana-1623 95 40 variable variable NOUN cana-1623 95 41 𝑇 𝑇 PROPN cana-1623 95 42 = = SYM cana-1623 95 43 ( ( PUNCT cana-1623 95 44 𝑇1 𝑇1 PROPN cana-1623 95 45 , , PUNCT cana-1623 95 46 𝑇2 𝑇2 NOUN cana-1623 95 47 , , PUNCT cana-1623 95 48 … … PUNCT cana-1623 95 49 , , PUNCT cana-1623 95 50 𝑇𝑛 𝑇𝑛 NOUN cana-1623 95 51 ) ) PUNCT cana-1623 95 52 is be AUX cana-1623 95 53 : : PUNCT cana-1623 95 54 𝐸(𝑇 𝐸(𝑇 PROPN cana-1623 95 55 ∣ ∣ PROPN cana-1623 95 56 οΏ½ οΏ½ PROPN cana-1623 95 57 Μƒ Μƒ PROPN cana-1623 95 58 οΏ½ οΏ½ PROPN cana-1623 95 59 )= )= PROPN cana-1623 95 60 ∫ ∫ PROPN cana-1623 95 61 β€Š β€Š SPACE cana-1623 95 62 ℝ ℝ PROPN cana-1623 95 63 β€Š β€Š SPACE cana-1623 95 64 𝑑𝑦(𝑑 𝑑𝑦(𝑑 NUM cana-1623 95 65 ∣ ∣ PROPN cana-1623 95 66 οΏ½ οΏ½ PROPN cana-1623 95 67 Μƒ Μƒ PROPN cana-1623 95 68 οΏ½ οΏ½ NOUN cana-1623 95 69 )𝑑𝑑 )𝑑𝑑 PUNCT cana-1623 96 1 = = SYM cana-1623 96 2 ∫ ∫ PROPN cana-1623 96 3 β€Š β€Š SPACE cana-1623 96 4 ℝ ℝ PROPN cana-1623 96 5 β€Š β€Š SPACE cana-1623 96 6 𝑑 𝑑 PROPN cana-1623 96 7 𝑠(𝑑)𝑦(𝑑 𝑠(𝑑)𝑦(𝑑 NUM cana-1623 96 8 ; ; PUNCT cana-1623 96 9 πœ† πœ† X cana-1623 96 10 , , PUNCT cana-1623 96 11 πœ‚ πœ‚ NOUN cana-1623 96 12 ) ) PUNCT cana-1623 96 13 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 96 14 , , PUNCT cana-1623 96 15 πœ‚ πœ‚ PROPN cana-1623 96 16 ∣ ∣ PROPN cana-1623 96 17 οΏ½ οΏ½ PROPN cana-1623 96 18 Μƒ Μƒ PROPN cana-1623 96 19 οΏ½ οΏ½ PROPN cana-1623 96 20 ) ) PUNCT cana-1623 96 21 𝑑𝑑 𝑑𝑑 ADP cana-1623 96 22 2.4 2.4 NUM cana-1623 96 23 maximum maximum ADJ cana-1623 96 24 likelihood likelihood NOUN cana-1623 96 25 estimation estimation NOUN cana-1623 96 26 the the DET cana-1623 96 27 above above ADJ cana-1623 96 28 equation equation NOUN cana-1623 96 29 shows show VERB cana-1623 96 30 the the DET cana-1623 96 31 intuitionistic intuitionistic ADJ cana-1623 96 32 fuzzy fuzzy ADJ cana-1623 96 33 likelihood likelihood NOUN cana-1623 96 34 function function NOUN cana-1623 96 35 of of ADP cana-1623 96 36 iw iw INTJ cana-1623 96 37 ( ( PUNCT cana-1623 96 38 πœ† πœ† NOUN cana-1623 96 39 , , PUNCT cana-1623 96 40 πœ‚ πœ‚ NOUN cana-1623 96 41 ) ) PUNCT cana-1623 96 42 thus thus ADV cana-1623 96 43 , , PUNCT cana-1623 96 44 the the DET cana-1623 96 45 intuitionistic intuitionistic ADJ cana-1623 96 46 fuzzy fuzzy ADJ cana-1623 96 47 log log NOUN cana-1623 96 48 - - PUNCT cana-1623 96 49 likelihood likelihood NOUN cana-1623 96 50 function function NOUN cana-1623 96 51 is be AUX cana-1623 96 52 given give VERB cana-1623 96 53 as as SCONJ cana-1623 96 54 follows follow VERB cana-1623 96 55 : : PUNCT cana-1623 97 1 𝐻(πœ† 𝐻(πœ† PROPN cana-1623 97 2 , , PUNCT cana-1623 97 3 πœ‚ πœ‚ PROPN cana-1623 97 4 ∣ ∣ PROPN cana-1623 97 5 οΏ½ οΏ½ PROPN cana-1623 97 6 Μƒ Μƒ PROPN cana-1623 97 7 οΏ½ οΏ½ PROPN cana-1623 97 8 ) ) PUNCT cana-1623 97 9 = = SYM cana-1623 97 10 ln ln PROPN cana-1623 97 11 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 97 12 , , PUNCT cana-1623 97 13 πœ‚ πœ‚ PROPN cana-1623 97 14 ∣ ∣ PROPN cana-1623 97 15 οΏ½ οΏ½ PROPN cana-1623 97 16 Μƒ Μƒ PROPN cana-1623 97 17 οΏ½ οΏ½ PROPN cana-1623 97 18 ) ) PUNCT cana-1623 97 19 = = PROPN cana-1623 97 20 βˆ‘ βˆ‘ PART cana-1623 97 21 β€Š β€Š SPACE cana-1623 97 22 𝑛 𝑛 PRON cana-1623 97 23 𝑖=1 𝑖=1 PUNCT cana-1623 97 24 β€Š β€Š SPACE cana-1623 97 25 ln ln PROPN cana-1623 98 1 [ [ X cana-1623 98 2 ∫ ∫ INTJ cana-1623 98 3 β€Š β€Š SPACE cana-1623 98 4 ℝ ℝ PROPN cana-1623 98 5 β€Š β€Š SPACE cana-1623 98 6 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 98 7 ; ; PUNCT cana-1623 98 8 πœ† πœ† X cana-1623 98 9 , , PUNCT cana-1623 98 10 πœ‚)𝑑𝑑 πœ‚)𝑑𝑑 PROPN cana-1623 98 11 ] ] X cana-1623 98 12 the the DET cana-1623 98 13 mles mle NOUN cana-1623 98 14 οΏ½ οΏ½ NOUN cana-1623 98 15 Μ‚ Μ‚ PROPN cana-1623 98 16 οΏ½ οΏ½ NOUN cana-1623 98 17 𝑀𝐿 𝑀𝐿 PROPN cana-1623 98 18 and and CCONJ cana-1623 98 19 οΏ½ οΏ½ PROPN cana-1623 98 20 Μ‚ Μ‚ VERB cana-1623 98 21 οΏ½ οΏ½ NOUN cana-1623 98 22 𝑀𝐿 𝑀𝐿 PROPN cana-1623 98 23 are be AUX cana-1623 98 24 obtained obtain VERB cana-1623 98 25 by by ADP cana-1623 98 26 the the DET cana-1623 98 27 below below ADJ cana-1623 98 28 equations equation NOUN cana-1623 98 29 : : PUNCT cana-1623 98 30 { { PUNCT cana-1623 98 31 βˆ‚π»(πœ† βˆ‚π»(πœ† NOUN cana-1623 98 32 , , PUNCT cana-1623 98 33 πœ‚ πœ‚ PROPN cana-1623 98 34 ∣ ∣ PROPN cana-1623 98 35 οΏ½ οΏ½ PROPN cana-1623 98 36 Μƒ Μƒ PROPN cana-1623 98 37 οΏ½ οΏ½ PROPN cana-1623 98 38 ) ) PUNCT cana-1623 98 39 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 99 1 = = NOUN cana-1623 99 2 0 0 NUM cana-1623 99 3 βˆ‚π»(πœ† βˆ‚π»(πœ† NOUN cana-1623 99 4 , , PUNCT cana-1623 99 5 πœ‚ πœ‚ PROPN cana-1623 99 6 ∣ ∣ PROPN cana-1623 99 7 οΏ½ οΏ½ PROPN cana-1623 99 8 Μƒ Μƒ PROPN cana-1623 99 9 οΏ½ οΏ½ PROPN cana-1623 99 10 ) ) PUNCT cana-1623 99 11 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 100 1 = = NOUN cana-1623 100 2 0 0 NUM cana-1623 100 3 where where SCONJ cana-1623 100 4 βˆ‚π»(πœ†,πœ‚βˆ£ βˆ‚π»(πœ†,πœ‚βˆ£ PROPN cana-1623 100 5 οΏ½ οΏ½ PROPN cana-1623 100 6 Μƒ Μƒ PROPN cana-1623 100 7 οΏ½ οΏ½ PROPN cana-1623 100 8 ) ) PUNCT cana-1623 100 9 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 100 10 and and CCONJ cana-1623 100 11 βˆ‚π»(πœ†,πœ‚βˆ£ βˆ‚π»(πœ†,πœ‚βˆ£ PROPN cana-1623 100 12 οΏ½ οΏ½ PROPN cana-1623 100 13 Μƒ Μƒ PROPN cana-1623 100 14 οΏ½ οΏ½ PROPN cana-1623 100 15 ) ) PUNCT cana-1623 100 16 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 100 17 are be AUX cana-1623 100 18 shown show VERB cana-1623 100 19 in in ADP cana-1623 100 20 below below ADP cana-1623 100 21 βˆ‚π»(πœ† βˆ‚π»(πœ† NOUN cana-1623 100 22 , , PUNCT cana-1623 101 1 πœ‚ πœ‚ PROPN cana-1623 101 2 ∣ ∣ PROPN cana-1623 101 3 οΏ½ οΏ½ PROPN cana-1623 101 4 Μƒ Μƒ PROPN cana-1623 101 5 οΏ½ οΏ½ PROPN cana-1623 101 6 ) ) PUNCT cana-1623 101 7 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 102 1 = = PUNCT cana-1623 102 2 βˆ‘ βˆ‘ NOUN cana-1623 102 3 β€Š β€Š SPACE cana-1623 102 4 𝑛 𝑛 PRON cana-1623 102 5 𝑖=1 𝑖=1 PROPN cana-1623 102 6 β€Š β€Š SPACE cana-1623 102 7 1 1 NUM cana-1623 102 8 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 102 9 , , PUNCT cana-1623 102 10 πœ‚ πœ‚ PROPN cana-1623 102 11 ∣ ∣ PROPN cana-1623 102 12 οΏ½ οΏ½ PROPN cana-1623 102 13 Μƒ Μƒ PROPN cana-1623 102 14 οΏ½ οΏ½ NOUN cana-1623 102 15 𝑖 𝑖 NUM cana-1623 102 16 ) ) PUNCT cana-1623 102 17 ∫ ∫ PROPN cana-1623 102 18 β€Š β€Š SPACE cana-1623 102 19 ℝ ℝ PROPN cana-1623 102 20 β€Š β€Š SPACE cana-1623 102 21 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 102 22 ) ) PUNCT cana-1623 102 23 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 102 24 ; ; PUNCT cana-1623 102 25 πœ† πœ† X cana-1623 102 26 , , PUNCT cana-1623 102 27 πœ‚ πœ‚ NOUN cana-1623 102 28 ) ) PUNCT cana-1623 102 29 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 102 30 𝑑𝑑 𝑑𝑑 ADP cana-1623 102 31 βˆ‚π»(πœ† βˆ‚π»(πœ† PROPN cana-1623 102 32 , , PUNCT cana-1623 102 33 πœ‚ πœ‚ PROPN cana-1623 102 34 ∣ ∣ PROPN cana-1623 102 35 οΏ½ οΏ½ PROPN cana-1623 102 36 Μƒ Μƒ PROPN cana-1623 102 37 οΏ½ οΏ½ PROPN cana-1623 102 38 ) ) PUNCT cana-1623 102 39 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 103 1 = = PRON cana-1623 103 2 βˆ‘ βˆ‘ NOUN cana-1623 103 3 β€Š β€Š SPACE cana-1623 103 4 𝑛 𝑛 PRON cana-1623 103 5 𝑖=1 𝑖=1 PROPN cana-1623 103 6 β€Š β€Š SPACE cana-1623 103 7 1 1 NUM cana-1623 103 8 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 103 9 , , PUNCT cana-1623 103 10 πœ‚ πœ‚ PROPN cana-1623 103 11 ∣ ∣ PROPN cana-1623 103 12 οΏ½ οΏ½ PROPN cana-1623 103 13 Μƒ Μƒ PROPN cana-1623 103 14 οΏ½ οΏ½ NOUN cana-1623 103 15 𝑖 𝑖 NUM cana-1623 103 16 ) ) PUNCT cana-1623 103 17 ∫ ∫ PROPN cana-1623 103 18 β€Š β€Š SPACE cana-1623 103 19 ℝ ℝ PROPN cana-1623 103 20 β€Š β€Š SPACE cana-1623 103 21 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 103 22 ) ) PUNCT cana-1623 103 23 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 103 24 ; ; PUNCT cana-1623 103 25 πœ† πœ† X cana-1623 103 26 , , PUNCT cana-1623 103 27 πœ‚ πœ‚ NOUN cana-1623 103 28 ) ) PUNCT cana-1623 103 29 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 103 30 𝑑𝑑 𝑑𝑑 ADP cana-1623 103 31 here here ADV cana-1623 103 32 , , PUNCT cana-1623 103 33 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 103 34 , , PUNCT cana-1623 103 35 πœ‚ πœ‚ PROPN cana-1623 103 36 ∣ ∣ PROPN cana-1623 103 37 οΏ½ οΏ½ PROPN cana-1623 103 38 Μƒ Μƒ PROPN cana-1623 103 39 οΏ½ οΏ½ NOUN cana-1623 103 40 𝑖 𝑖 NUM cana-1623 103 41 ) ) PUNCT cana-1623 103 42 = = NOUN cana-1623 103 43 ∫0 ∫0 ADP cana-1623 103 44 + + ADJ cana-1623 103 45 ∞ ∞ PROPN cana-1623 103 46 β€Š β€Š SPACE cana-1623 103 47 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 103 48 ; ; PUNCT cana-1623 103 49 πœ† πœ† X cana-1623 103 50 , , PUNCT cana-1623 103 51 πœ‚)𝑑𝑑 πœ‚)𝑑𝑑 PROPN cana-1623 103 52 , , PUNCT cana-1623 103 53 βˆ‚π‘¦(𝑑;πœ†,πœ‚ βˆ‚π‘¦(𝑑;πœ†,πœ‚ PROPN cana-1623 103 54 ) ) PUNCT cana-1623 103 55 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 103 56 and and CCONJ cana-1623 103 57 βˆ‚π‘¦(𝑑;πœ†,πœ‚ βˆ‚π‘¦(𝑑;πœ†,πœ‚ NUM cana-1623 103 58 ) ) PUNCT cana-1623 103 59 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 103 60 are be AUX cana-1623 103 61 shown show VERB cana-1623 103 62 in in ADP cana-1623 103 63 below below ADV cana-1623 103 64 : : PUNCT cana-1623 103 65 communications communication NOUN cana-1623 103 66 on on ADP cana-1623 103 67 applied apply VERB cana-1623 103 68 nonlinear nonlinear ADJ cana-1623 103 69 analysis analysis NOUN cana-1623 103 70 issn issn NOUN cana-1623 103 71 : : PUNCT cana-1623 103 72 1074 1074 NUM cana-1623 103 73 - - PUNCT cana-1623 103 74 133x 133x NUM cana-1623 103 75 vol vol NOUN cana-1623 103 76 32 32 NUM cana-1623 103 77 no no NOUN cana-1623 103 78 . . NOUN cana-1623 103 79 1 1 NUM cana-1623 103 80 ( ( PUNCT cana-1623 103 81 2025 2025 NUM cana-1623 103 82 ) ) PUNCT cana-1623 103 83 95 95 NUM cana-1623 103 84 https://internationalpubls.com https://internationalpubls.com X cana-1623 103 85 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 103 86 ; ; PUNCT cana-1623 103 87 πœ† πœ† X cana-1623 103 88 , , PUNCT cana-1623 103 89 πœ‚ πœ‚ NOUN cana-1623 103 90 ) ) PUNCT cana-1623 103 91 βˆ‚πœ† βˆ‚πœ† NOUN cana-1623 104 1 = = PUNCT cana-1623 104 2 1 1 NUM cana-1623 104 3 πœ† πœ† DET cana-1623 104 4 𝑦(𝑑 𝑦(𝑑 PROPN cana-1623 104 5 ; ; PUNCT cana-1623 104 6 πœ† πœ† X cana-1623 104 7 , , PUNCT cana-1623 104 8 πœ‚ πœ‚ NOUN cana-1623 104 9 ) ) PUNCT cana-1623 104 10 βˆ’ βˆ’ NOUN cana-1623 104 11 π‘‘βˆ’πœ‚π‘¦(𝑑 π‘‘βˆ’πœ‚π‘¦(𝑑 ADJ cana-1623 104 12 ; ; PUNCT cana-1623 104 13 πœ† πœ† X cana-1623 104 14 , , PUNCT cana-1623 104 15 πœ‚ πœ‚ NOUN cana-1623 104 16 ) ) PUNCT cana-1623 104 17 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 104 18 ; ; PUNCT cana-1623 104 19 πœ† πœ† X cana-1623 104 20 , , PUNCT cana-1623 104 21 πœ‚ πœ‚ NOUN cana-1623 104 22 ) ) PUNCT cana-1623 104 23 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 104 24 = = SYM cana-1623 104 25 1 1 NUM cana-1623 104 26 πœ‚ πœ‚ PRON cana-1623 104 27 𝑦(𝑑 𝑦(𝑑 NUM cana-1623 104 28 ; ; PUNCT cana-1623 104 29 πœ† πœ† X cana-1623 104 30 , , PUNCT cana-1623 104 31 πœ‚ πœ‚ NOUN cana-1623 104 32 ) ) PUNCT cana-1623 105 1 βˆ’ βˆ’ PROPN cana-1623 105 2 𝑦(𝑑 𝑦(𝑑 PROPN cana-1623 105 3 ; ; PUNCT cana-1623 105 4 πœ† πœ† X cana-1623 105 5 , , PUNCT cana-1623 105 6 πœ‚ πœ‚ NOUN cana-1623 105 7 ) ) PUNCT cana-1623 105 8 ln ln NOUN cana-1623 105 9 𝑑 𝑑 PROPN cana-1623 105 10 + + PROPN cana-1623 106 1 πœ†π‘‘βˆ’πœ‚π‘¦(𝑑 πœ†π‘‘βˆ’πœ‚π‘¦(𝑑 ADJ cana-1623 106 2 ; ; PUNCT cana-1623 106 3 πœ† πœ† X cana-1623 106 4 , , PUNCT cana-1623 106 5 πœ‚ πœ‚ NOUN cana-1623 106 6 ) ) PUNCT cana-1623 106 7 ln ln NOUN cana-1623 106 8 𝑑 𝑑 NOUN cana-1623 106 9 it it PRON cana-1623 106 10 is be AUX cana-1623 106 11 evident evident ADJ cana-1623 106 12 that that SCONJ cana-1623 106 13 the the DET cana-1623 106 14 equations equation NOUN cana-1623 106 15 above above ADV cana-1623 106 16 are be AUX cana-1623 106 17 nonlinear nonlinear ADJ cana-1623 106 18 and and CCONJ cana-1623 106 19 difficult difficult ADJ cana-1623 106 20 to to PART cana-1623 106 21 solve solve VERB cana-1623 106 22 . . PUNCT cana-1623 107 1 then then ADV cana-1623 107 2 we we PRON cana-1623 107 3 considered consider VERB cana-1623 107 4 the the DET cana-1623 107 5 em em PROPN cana-1623 107 6 algorithm algorithm NOUN cana-1623 107 7 . . PUNCT cana-1623 108 1 the the DET cana-1623 108 2 em em PROPN cana-1623 108 3 technique technique NOUN cana-1623 108 4 is be AUX cana-1623 108 5 equally equally ADV cana-1623 108 6 applicable applicable ADJ cana-1623 108 7 to to ADP cana-1623 108 8 intuitionistic intuitionistic ADJ cana-1623 108 9 fuzzy fuzzy ADJ cana-1623 108 10 data datum NOUN cana-1623 108 11 because because SCONJ cana-1623 108 12 the the DET cana-1623 108 13 observed observe VERB cana-1623 108 14 intuitionistic intuitionistic ADJ cana-1623 108 15 fuzzy fuzzy ADJ cana-1623 108 16 data datum NOUN cana-1623 108 17 can can AUX cana-1623 108 18 be be AUX cana-1623 108 19 viewed view VERB cana-1623 108 20 as as ADP cana-1623 108 21 imperfect imperfect ADJ cana-1623 108 22 characterizations characterization NOUN cana-1623 108 23 of of ADP cana-1623 108 24 the the DET cana-1623 108 25 completed complete VERB cana-1623 108 26 data datum NOUN cana-1623 108 27 . . PUNCT cana-1623 109 1 to to PART cana-1623 109 2 better well ADV cana-1623 109 3 illustrate illustrate VERB cana-1623 109 4 the the DET cana-1623 109 5 iterative iterative NOUN cana-1623 109 6 process process NOUN cana-1623 109 7 of of ADP cana-1623 109 8 the the DET cana-1623 109 9 em em PROPN cana-1623 109 10 method method NOUN cana-1623 109 11 , , PUNCT cana-1623 109 12 from from ADP cana-1623 109 13 above above ADP cana-1623 109 14 equation equation NOUN cana-1623 109 15 we we PRON cana-1623 109 16 get get VERB cana-1623 109 17 , , PUNCT cana-1623 109 18 βˆ‚π»(πœ† βˆ‚π»(πœ† NOUN cana-1623 109 19 , , PUNCT cana-1623 109 20 πœ‚ πœ‚ PROPN cana-1623 109 21 ∣ ∣ PROPN cana-1623 109 22 οΏ½ οΏ½ PROPN cana-1623 109 23 Μƒ Μƒ PROPN cana-1623 109 24 οΏ½ οΏ½ PROPN cana-1623 109 25 ) ) PUNCT cana-1623 109 26 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 110 1 = = PUNCT cana-1623 110 2 βˆ‘ βˆ‘ NOUN cana-1623 110 3 β€Š β€Š SPACE cana-1623 110 4 𝑛 𝑛 PRON cana-1623 110 5 𝑖=1 𝑖=1 PROPN cana-1623 110 6 β€Š β€Š SPACE cana-1623 110 7 1 1 NUM cana-1623 110 8 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 110 9 , , PUNCT cana-1623 110 10 πœ‚ πœ‚ PROPN cana-1623 110 11 ∣ ∣ PROPN cana-1623 110 12 οΏ½ οΏ½ PROPN cana-1623 110 13 Μƒ Μƒ PROPN cana-1623 110 14 οΏ½ οΏ½ PROPN cana-1623 110 15 𝑖)Μ…Μ… 𝑖)Μ…Μ… NOUN cana-1623 110 16 Μ…Μ… Μ…Μ… PROPN cana-1623 110 17 Μ…Μ… Μ…Μ… PROPN cana-1623 110 18 Μ…Μ… Μ…Μ… PROPN cana-1623 110 19 Μ…Μ… Μ…Μ… PROPN cana-1623 110 20 Μ…Μ… Μ…Μ… PROPN cana-1623 110 21 Μ…Μ… Μ…Μ… PROPN cana-1623 110 22 ∫ ∫ PROPN cana-1623 110 23 β€Š β€Š SPACE cana-1623 111 1 + + PROPN cana-1623 111 2 ∞ ∞ PROPN cana-1623 111 3 0 0 NUM cana-1623 111 4 β€Š β€Š SPACE cana-1623 111 5 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 111 6 ) ) PUNCT cana-1623 111 7 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 111 8 ; ; PUNCT cana-1623 111 9 πœ† πœ† X cana-1623 111 10 , , PUNCT cana-1623 111 11 πœ‚ πœ‚ NOUN cana-1623 111 12 ) ) PUNCT cana-1623 111 13 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 111 14 𝑑𝑑 𝑑𝑑 ADP cana-1623 111 15 = = NOUN cana-1623 111 16 βˆ‘ βˆ‘ NOUN cana-1623 111 17 β€Š β€Š SPACE cana-1623 111 18 𝑛 𝑛 PRON cana-1623 111 19 𝑖=1 𝑖=1 PROPN cana-1623 111 20 β€Š β€Š SPACE cana-1623 111 21 1 1 NUM cana-1623 111 22 β„Žβ€Ύ(πœ† β„Žβ€Ύ(πœ† PROPN cana-1623 111 23 , , PUNCT cana-1623 111 24 πœ‚ πœ‚ PROPN cana-1623 111 25 ∣ ∣ PROPN cana-1623 111 26 οΏ½ οΏ½ PROPN cana-1623 111 27 Μƒ Μƒ PROPN cana-1623 111 28 οΏ½ οΏ½ NOUN cana-1623 111 29 𝑖 𝑖 NUM cana-1623 111 30 ) ) PUNCT cana-1623 111 31 ∫ ∫ PROPN cana-1623 111 32 β€Š β€Š SPACE cana-1623 112 1 + + PROPN cana-1623 112 2 ∞ ∞ PROPN cana-1623 112 3 0 0 NUM cana-1623 112 4 β€Š β€Š SPACE cana-1623 112 5 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 112 6 ) ) PUNCT cana-1623 112 7 [ [ PUNCT cana-1623 112 8 1 1 NUM cana-1623 112 9 πœ† πœ† PRON cana-1623 112 10 𝑦(𝑑 𝑦(𝑑 NUM cana-1623 112 11 ; ; PUNCT cana-1623 112 12 πœ† πœ† X cana-1623 112 13 , , PUNCT cana-1623 112 14 πœ‚ πœ‚ NOUN cana-1623 112 15 ) ) PUNCT cana-1623 112 16 βˆ’ βˆ’ NOUN cana-1623 112 17 π‘‘βˆ’πœ‚π‘¦(𝑑 π‘‘βˆ’πœ‚π‘¦(𝑑 ADJ cana-1623 112 18 ; ; PUNCT cana-1623 112 19 πœ† πœ† X cana-1623 112 20 , , PUNCT cana-1623 112 21 πœ‚ πœ‚ NOUN cana-1623 112 22 ) ) PUNCT cana-1623 112 23 ] ] PUNCT cana-1623 112 24 𝑑𝑑 𝑑𝑑 ADP cana-1623 112 25 = = NOUN cana-1623 112 26 βˆ‘ βˆ‘ NOUN cana-1623 112 27 β€Š β€Š SPACE cana-1623 112 28 𝑛 𝑛 PRON cana-1623 112 29 𝑖=1 𝑖=1 PUNCT cana-1623 112 30 β€Š β€Š SPACE cana-1623 112 31 ∫ ∫ PROPN cana-1623 112 32 β€Š β€Š SPACE cana-1623 113 1 + + PROPN cana-1623 113 2 ∞ ∞ PROPN cana-1623 113 3 0 0 NUM cana-1623 113 4 β€Š β€Š SPACE cana-1623 113 5 1 1 NUM cana-1623 113 6 πœ† πœ† PROPN cana-1623 113 7 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 113 8 , , PUNCT cana-1623 113 9 πœ† πœ† NOUN cana-1623 113 10 , , PUNCT cana-1623 113 11 πœ‚ πœ‚ NOUN cana-1623 113 12 ) ) PUNCT cana-1623 113 13 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 113 14 , , PUNCT cana-1623 113 15 πœ‚ πœ‚ PROPN cana-1623 113 16 ∣ ∣ PROPN cana-1623 113 17 οΏ½ οΏ½ PROPN cana-1623 113 18 Μƒ Μƒ PROPN cana-1623 113 19 οΏ½ οΏ½ NOUN cana-1623 113 20 𝑖 𝑖 NUM cana-1623 113 21 ) ) PUNCT cana-1623 113 22 𝑑𝑑 𝑑𝑑 ADP cana-1623 113 23 βˆ’βˆ‘ βˆ’βˆ‘ PROPN cana-1623 113 24 β€Š β€Š SPACE cana-1623 113 25 𝑛 𝑛 PRON cana-1623 113 26 𝑖=1 𝑖=1 PROPN cana-1623 113 27 β€Š β€Š SPACE cana-1623 113 28 ∫ ∫ PROPN cana-1623 113 29 β€Š β€Š SPACE cana-1623 114 1 + + PROPN cana-1623 114 2 ∞ ∞ PROPN cana-1623 114 3 0 0 NUM cana-1623 114 4 β€Š β€Š SPACE cana-1623 114 5 π‘‘βˆ’πœ‚ π‘‘βˆ’πœ‚ PROPN cana-1623 114 6 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 114 7 ; ; PUNCT cana-1623 114 8 πœ† πœ† X cana-1623 114 9 , , PUNCT cana-1623 114 10 πœ‚ πœ‚ NOUN cana-1623 114 11 ) ) PUNCT cana-1623 114 12 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 114 13 , , PUNCT cana-1623 114 14 πœ‚ πœ‚ PROPN cana-1623 114 15 ∣ ∣ PROPN cana-1623 114 16 οΏ½ οΏ½ PROPN cana-1623 114 17 Μƒ Μƒ PROPN cana-1623 114 18 οΏ½ οΏ½ NOUN cana-1623 114 19 𝑖 𝑖 NUM cana-1623 114 20 ) ) PUNCT cana-1623 114 21 𝑑𝑑 𝑑𝑑 ADP cana-1623 114 22 = = SYM cana-1623 114 23 𝑛 𝑛 PROPN cana-1623 114 24 1 1 NUM cana-1623 114 25 πœ† πœ† DET cana-1623 114 26 βˆ’βˆ‘ βˆ’βˆ‘ PROPN cana-1623 114 27 β€Š β€Š SPACE cana-1623 114 28 𝑛 𝑛 DET cana-1623 114 29 𝑖=1 𝑖=1 PROPN cana-1623 114 30 β€Š β€Š SPACE cana-1623 114 31 𝐸1𝑖. 𝐸1𝑖. NOUN cana-1623 114 32 let let VERB cana-1623 114 33 βˆ‚π»(πœ† βˆ‚π»(πœ† NOUN cana-1623 114 34 , , PUNCT cana-1623 114 35 πœ‚ πœ‚ PROPN cana-1623 114 36 ∣ ∣ PROPN cana-1623 114 37 οΏ½ οΏ½ PROPN cana-1623 114 38 Μƒ Μƒ PROPN cana-1623 114 39 οΏ½ οΏ½ PROPN cana-1623 114 40 ) ) PUNCT cana-1623 114 41 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 115 1 = = PUNCT cana-1623 115 2 0 0 PROPN cana-1623 115 3 , , PUNCT cana-1623 115 4 where where SCONJ cana-1623 115 5 𝐸1𝑖 𝐸1𝑖 PROPN cana-1623 115 6 = = PUNCT cana-1623 115 7 𝐸(𝑇 𝐸(𝑇 PROPN cana-1623 115 8 βˆ’πœ‚ βˆ’πœ‚ PROPN cana-1623 115 9 ∣ ∣ PROPN cana-1623 115 10 οΏ½ οΏ½ PROPN cana-1623 115 11 Μƒ Μƒ PROPN cana-1623 115 12 οΏ½ οΏ½ NOUN cana-1623 115 13 𝑖 𝑖 NUM cana-1623 115 14 ) ) PUNCT cana-1623 115 15 = = SYM cana-1623 116 1 ∫ ∫ PROPN cana-1623 116 2 β€Š β€Š SPACE cana-1623 117 1 + + PROPN cana-1623 117 2 ∞ ∞ PROPN cana-1623 117 3 0 0 NUM cana-1623 117 4 π‘‘βˆ’πœ‚ π‘‘βˆ’πœ‚ PROPN cana-1623 117 5 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 117 6 ; ; PUNCT cana-1623 117 7 πœ† πœ† X cana-1623 117 8 , , PUNCT cana-1623 117 9 πœ‚ πœ‚ NOUN cana-1623 117 10 ) ) PUNCT cana-1623 117 11 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 117 12 , , PUNCT cana-1623 117 13 πœ‚ πœ‚ PROPN cana-1623 117 14 ∣ ∣ PROPN cana-1623 117 15 οΏ½ οΏ½ PROPN cana-1623 117 16 Μƒ Μƒ PROPN cana-1623 117 17 οΏ½ οΏ½ NOUN cana-1623 117 18 𝑖 𝑖 NUM cana-1623 117 19 ) ) PUNCT cana-1623 117 20 𝑑𝑑 𝑑𝑑 ADP cana-1623 117 21 βˆ‚π»(πœ† βˆ‚π»(πœ† PROPN cana-1623 117 22 , , PUNCT cana-1623 117 23 πœ‚ πœ‚ PROPN cana-1623 117 24 ∣ ∣ PROPN cana-1623 117 25 οΏ½ οΏ½ PROPN cana-1623 117 26 Μƒ Μƒ PROPN cana-1623 117 27 οΏ½ οΏ½ PROPN cana-1623 117 28 ) ) PUNCT cana-1623 117 29 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 118 1 = = PRON cana-1623 118 2 βˆ‘ βˆ‘ NOUN cana-1623 118 3 β€Š β€Š SPACE cana-1623 118 4 𝑛 𝑛 PRON cana-1623 118 5 𝑖=1 𝑖=1 PROPN cana-1623 118 6 β€Š β€Š SPACE cana-1623 118 7 1 1 NUM cana-1623 118 8 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 118 9 , , PUNCT cana-1623 118 10 πœ‚ πœ‚ PROPN cana-1623 118 11 ∣ ∣ PROPN cana-1623 118 12 οΏ½ οΏ½ PROPN cana-1623 118 13 Μƒ Μƒ PROPN cana-1623 118 14 οΏ½ οΏ½ PROPN cana-1623 118 15 𝑖)Μ…Μ… 𝑖)Μ…Μ… NOUN cana-1623 118 16 Μ…Μ… Μ…Μ… PROPN cana-1623 118 17 Μ…Μ… Μ…Μ… PROPN cana-1623 118 18 Μ…Μ… Μ…Μ… PROPN cana-1623 118 19 Μ…Μ… Μ…Μ… PROPN cana-1623 118 20 Μ…Μ… Μ…Μ… PROPN cana-1623 118 21 Μ…Μ… Μ…Μ… PROPN cana-1623 118 22 ∫ ∫ PROPN cana-1623 118 23 β€Š β€Š SPACE cana-1623 119 1 + + PROPN cana-1623 119 2 ∞ ∞ PROPN cana-1623 119 3 0 0 NUM cana-1623 119 4 β€Š β€Š SPACE cana-1623 119 5 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 119 6 ) ) PUNCT cana-1623 119 7 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 119 8 ; ; PUNCT cana-1623 119 9 πœ† πœ† X cana-1623 119 10 , , PUNCT cana-1623 119 11 πœ‚ πœ‚ NOUN cana-1623 119 12 ) ) PUNCT cana-1623 119 13 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 119 14 𝑑𝑑 𝑑𝑑 ADP cana-1623 119 15 = = NOUN cana-1623 119 16 𝑛 𝑛 PROPN cana-1623 119 17 1 1 NUM cana-1623 119 18 πœ‚ πœ‚ PROPN cana-1623 119 19 βˆ’βˆ‘ βˆ’βˆ‘ PROPN cana-1623 119 20 β€Š β€Š SPACE cana-1623 119 21 𝑛 𝑛 DET cana-1623 119 22 𝑖=1 𝑖=1 PROPN cana-1623 119 23 β€Š β€Š SPACE cana-1623 119 24 𝐸2𝑖 𝐸2𝑖 NOUN cana-1623 120 1 + + CCONJ cana-1623 120 2 πœ†βˆ‘ πœ†βˆ‘ VERB cana-1623 120 3 β€Š β€Š SPACE cana-1623 120 4 𝑛 𝑛 PRON cana-1623 120 5 𝑖=1 𝑖=1 PROPN cana-1623 120 6 β€Š β€Š SPACE cana-1623 120 7 𝐸3𝑖 𝐸3𝑖 PROPN cana-1623 120 8 let let VERB cana-1623 120 9 βˆ‚π»(πœ† βˆ‚π»(πœ† NOUN cana-1623 120 10 , , PUNCT cana-1623 120 11 πœ‚ πœ‚ PROPN cana-1623 120 12 ∣ ∣ PROPN cana-1623 120 13 οΏ½ οΏ½ PROPN cana-1623 120 14 Μƒ Μƒ PROPN cana-1623 120 15 οΏ½ οΏ½ PROPN cana-1623 120 16 ) ) PUNCT cana-1623 120 17 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 120 18 = = SYM cana-1623 120 19 0 0 PROPN cana-1623 120 20 , , PUNCT cana-1623 120 21 where where SCONJ cana-1623 120 22 𝐸2𝑖 𝐸2𝑖 NOUN cana-1623 120 23 = = SYM cana-1623 120 24 𝐸(ln 𝐸(ln X cana-1623 120 25 𝑇 𝑇 PROPN cana-1623 120 26 ∣ ∣ PROPN cana-1623 120 27 οΏ½ οΏ½ PROPN cana-1623 120 28 Μƒ Μƒ PROPN cana-1623 120 29 οΏ½ οΏ½ NOUN cana-1623 120 30 𝑖 𝑖 NUM cana-1623 120 31 ) ) PUNCT cana-1623 120 32 = = SYM cana-1623 121 1 ∫ ∫ PROPN cana-1623 121 2 β€Š β€Š SPACE cana-1623 122 1 + + PROPN cana-1623 122 2 ∞ ∞ PROPN cana-1623 122 3 0 0 PUNCT cana-1623 123 1 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 ADJ cana-1623 123 2 ; ; PUNCT cana-1623 123 3 πœ† πœ† X cana-1623 123 4 , , PUNCT cana-1623 123 5 πœ‚ πœ‚ NOUN cana-1623 123 6 ) ) PUNCT cana-1623 123 7 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 123 8 , , PUNCT cana-1623 123 9 πœ‚ πœ‚ PROPN cana-1623 123 10 ∣ ∣ PROPN cana-1623 123 11 οΏ½ οΏ½ PROPN cana-1623 123 12 Μƒ Μƒ PROPN cana-1623 123 13 οΏ½ οΏ½ NOUN cana-1623 123 14 𝑖 𝑖 NUM cana-1623 123 15 ) ) PUNCT cana-1623 123 16 ( ( PUNCT cana-1623 123 17 ln ln PROPN cana-1623 123 18 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN cana-1623 123 19 and and CCONJ cana-1623 123 20 communications communication NOUN cana-1623 123 21 on on ADP cana-1623 123 22 applied apply VERB cana-1623 123 23 nonlinear nonlinear ADJ cana-1623 123 24 analysis analysis NOUN cana-1623 123 25 issn issn NOUN cana-1623 123 26 : : PUNCT cana-1623 123 27 1074 1074 NUM cana-1623 123 28 - - PUNCT cana-1623 123 29 133x 133x NUM cana-1623 123 30 vol vol NOUN cana-1623 123 31 32 32 NUM cana-1623 123 32 no no NOUN cana-1623 123 33 . . NOUN cana-1623 123 34 1 1 NUM cana-1623 123 35 ( ( PUNCT cana-1623 123 36 2025 2025 NUM cana-1623 123 37 ) ) PUNCT cana-1623 123 38 96 96 NUM cana-1623 124 1 https://internationalpubls.com https://internationalpubls.com X cana-1623 124 2 𝐸3𝑖 𝐸3𝑖 PROPN cana-1623 124 3 = = PUNCT cana-1623 124 4 𝐸(π‘‡βˆ’πœ‚ln 𝐸(π‘‡βˆ’πœ‚ln PROPN cana-1623 124 5 𝑇 𝑇 PROPN cana-1623 124 6 ∣ ∣ PROPN cana-1623 124 7 οΏ½ οΏ½ PROPN cana-1623 124 8 Μƒ Μƒ PROPN cana-1623 124 9 οΏ½ οΏ½ NOUN cana-1623 124 10 𝑖 𝑖 NUM cana-1623 124 11 ) ) PUNCT cana-1623 124 12 = = SYM cana-1623 124 13 ∫ ∫ PROPN cana-1623 124 14 β€Š β€Š SPACE cana-1623 124 15 + + PROPN cana-1623 124 16 ∞ ∞ PROPN cana-1623 124 17 0 0 PUNCT cana-1623 125 1 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 ADJ cana-1623 125 2 ; ; PUNCT cana-1623 125 3 πœ† πœ† X cana-1623 125 4 , , PUNCT cana-1623 125 5 πœ‚ πœ‚ NOUN cana-1623 125 6 ) ) PUNCT cana-1623 125 7 β„Ž(πœ† β„Ž(πœ† NOUN cana-1623 125 8 , , PUNCT cana-1623 125 9 πœ‚ πœ‚ PROPN cana-1623 125 10 ∣ ∣ PROPN cana-1623 125 11 οΏ½ οΏ½ PROPN cana-1623 125 12 Μƒ Μƒ PROPN cana-1623 125 13 οΏ½ οΏ½ NOUN cana-1623 125 14 𝑖 𝑖 NUM cana-1623 125 15 ) ) PUNCT cana-1623 125 16 ( ( PUNCT cana-1623 125 17 π‘‘βˆ’πœ‚ln π‘‘βˆ’πœ‚ln VERB cana-1623 126 1 𝑑)𝑑𝑑 𝑑)𝑑𝑑 ADP cana-1623 126 2 the the DET cana-1623 126 3 iterative iterative NOUN cana-1623 126 4 processes process NOUN cana-1623 126 5 for for ADP cana-1623 126 6 obtaining obtain VERB cana-1623 126 7 mles mle NOUN cana-1623 126 8 with with ADP cana-1623 126 9 the the DET cana-1623 126 10 em em PROPN cana-1623 126 11 method method NOUN cana-1623 126 12 are be AUX cana-1623 126 13 as as SCONJ cana-1623 126 14 follows follow VERB cana-1623 126 15 : : PUNCT cana-1623 126 16 step step NOUN cana-1623 126 17 1 1 NUM cana-1623 126 18 : : PUNCT cana-1623 126 19 let let VERB cana-1623 126 20 the the DET cana-1623 126 21 initial initial ADJ cana-1623 126 22 value value NOUN cana-1623 126 23 be be AUX cana-1623 126 24 πœƒ(0 πœƒ(0 VERB cana-1623 126 25 ) ) PUNCT cana-1623 126 26 = = SYM cana-1623 126 27 ( ( PUNCT cana-1623 126 28 πœ†(0 πœ†(0 PROPN cana-1623 126 29 ) ) PUNCT cana-1623 126 30 , , PUNCT cana-1623 126 31 πœ‚(0 πœ‚(0 PROPN cana-1623 126 32 ) ) PUNCT cana-1623 126 33 ) ) PUNCT cana-1623 126 34 , , PUNCT cana-1623 126 35 and and CCONJ cana-1623 126 36 set set VERB cana-1623 126 37 𝑗 𝑗 PROPN cana-1623 126 38 = = SYM cana-1623 126 39 0 0 X cana-1623 126 40 . . PUNCT cana-1623 126 41 give give VERB cana-1623 126 42 the the DET cana-1623 126 43 accuracy accuracy NOUN cana-1623 126 44 Ξ΅ Ξ΅ PROPN cana-1623 126 45 > > X cana-1623 126 46 0 0 PROPN cana-1623 126 47 . . PUNCT cana-1623 127 1 step step NOUN cana-1623 127 2 2 2 NUM cana-1623 127 3 : : PUNCT cana-1623 127 4 at at ADP cana-1623 127 5 the the DET cana-1623 127 6 ( ( PUNCT cana-1623 127 7 𝑗 𝑗 PROPN cana-1623 127 8 + + CCONJ cana-1623 127 9 1)th 1)th NUM cana-1623 127 10 iteration iteration NOUN cana-1623 127 11 , , PUNCT cana-1623 127 12 compute compute VERB cana-1623 127 13 the the DET cana-1623 127 14 intuitionistic intuitionistic ADJ cana-1623 127 15 fuzzy fuzzy ADJ cana-1623 127 16 conditional conditional ADJ cana-1623 127 17 expectations expectation NOUN cana-1623 127 18 shown show VERB cana-1623 127 19 below below ADV cana-1623 127 20 . . PUNCT cana-1623 128 1 𝐸1𝑖 𝐸1𝑖 PROPN cana-1623 128 2 = = SYM cana-1623 128 3 ∫ ∫ PROPN cana-1623 128 4 π‘‘βˆ’πœ‚ π‘‘βˆ’πœ‚ PROPN cana-1623 128 5 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 128 6 ; ; PUNCT cana-1623 128 7 πœ† πœ† X cana-1623 128 8 , , PUNCT cana-1623 128 9 πœ‚ πœ‚ NOUN cana-1623 128 10 ) ) PUNCT cana-1623 128 11 β„Ž β„Ž PROPN cana-1623 128 12 ( ( PUNCT cana-1623 128 13 πœ† πœ† NOUN cana-1623 128 14 , , PUNCT cana-1623 128 15 πœ‚ πœ‚ X cana-1623 128 16 ∣∣ ∣∣ NUM cana-1623 128 17 οΏ½ οΏ½ PROPN cana-1623 128 18 Μƒ Μƒ PROPN cana-1623 128 19 οΏ½ οΏ½ NOUN cana-1623 128 20 𝑖 𝑖 X cana-1623 128 21 ) ) PUNCT cana-1623 129 1 + + VERB cana-1623 129 2 ∞ ∞ NUM cana-1623 129 3 0 0 NUM cana-1623 129 4 β€Šβ€Š β€Šβ€Š SPACE cana-1623 129 5 | | ADV cana-1623 129 6 πœƒ(𝑗+1)=πœƒ(𝑗 πœƒ(𝑗+1)=πœƒ(𝑗 ADJ cana-1623 129 7 ) ) PUNCT cana-1623 129 8 𝑑𝑑 𝑑𝑑 ADP cana-1623 129 9 , , PUNCT cana-1623 129 10 𝐸2𝑖 𝐸2𝑖 PROPN cana-1623 129 11 = = SYM cana-1623 129 12 ∫ ∫ PROPN cana-1623 130 1 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 130 2 ; ; PUNCT cana-1623 130 3 πœ† πœ† X cana-1623 130 4 , , PUNCT cana-1623 130 5 πœ‚ πœ‚ NOUN cana-1623 130 6 ) ) PUNCT cana-1623 130 7 β„Ž β„Ž PROPN cana-1623 130 8 ( ( PUNCT cana-1623 130 9 πœ† πœ† NOUN cana-1623 130 10 , , PUNCT cana-1623 130 11 πœ‚ πœ‚ X cana-1623 130 12 ∣∣ ∣∣ NUM cana-1623 130 13 οΏ½ οΏ½ PROPN cana-1623 130 14 Μƒ Μƒ PROPN cana-1623 130 15 οΏ½ οΏ½ NOUN cana-1623 130 16 𝑖 𝑖 X cana-1623 130 17 ) ) PUNCT cana-1623 130 18 ( ( PUNCT cana-1623 130 19 ln ln NOUN cana-1623 130 20 𝑑 𝑑 NOUN cana-1623 130 21 ) ) PUNCT cana-1623 131 1 + + NOUN cana-1623 131 2 ∞ ∞ NOUN cana-1623 131 3 0 0 NUM cana-1623 131 4 β€Šβ€Š β€Šβ€Š SPACE cana-1623 131 5 | | ADV cana-1623 131 6 πœƒ(𝑗+1)=πœƒ(𝑗 πœƒ(𝑗+1)=πœƒ(𝑗 ADJ cana-1623 131 7 ) ) PUNCT cana-1623 131 8 𝑑𝑑 𝑑𝑑 ADP cana-1623 131 9 , , PUNCT cana-1623 131 10 𝐸3𝑖 𝐸3𝑖 PROPN cana-1623 131 11 = = PUNCT cana-1623 131 12 ∫ ∫ PROPN cana-1623 132 1 𝑠𝑖(𝑑)𝑦(𝑑 𝑠𝑖(𝑑)𝑦(𝑑 PROPN cana-1623 132 2 ; ; PUNCT cana-1623 132 3 πœ† πœ† X cana-1623 132 4 , , PUNCT cana-1623 132 5 πœ‚ πœ‚ NOUN cana-1623 132 6 ) ) PUNCT cana-1623 132 7 β„Ž β„Ž PROPN cana-1623 132 8 ( ( PUNCT cana-1623 132 9 πœ† πœ† NOUN cana-1623 132 10 , , PUNCT cana-1623 132 11 πœ‚ πœ‚ X cana-1623 132 12 ∣∣ ∣∣ NUM cana-1623 132 13 οΏ½ οΏ½ PROPN cana-1623 132 14 Μƒ Μƒ PROPN cana-1623 132 15 οΏ½ οΏ½ NOUN cana-1623 132 16 𝑖 𝑖 X cana-1623 132 17 ) ) PUNCT cana-1623 132 18 ( ( PUNCT cana-1623 132 19 π‘‘βˆ’πœ‚ π‘‘βˆ’πœ‚ PROPN cana-1623 132 20 ln ln ADJ cana-1623 132 21 𝑑 𝑑 PROPN cana-1623 132 22 ) ) PUNCT cana-1623 133 1 + + NOUN cana-1623 133 2 ∞ ∞ NUM cana-1623 133 3 0 0 NUM cana-1623 133 4 β€Šβ€Š β€Šβ€Š SPACE cana-1623 133 5 | | ADV cana-1623 133 6 πœƒ(𝑗+1)&=πœƒ(𝑗 πœƒ(𝑗+1)&=πœƒ(𝑗 NOUN cana-1623 133 7 ) ) PUNCT cana-1623 133 8 𝑑𝑑. 𝑑𝑑. VERB cana-1623 133 9 step step NOUN cana-1623 133 10 3 3 NUM cana-1623 133 11 . . PUNCT cana-1623 133 12 πœ†(𝑗+1 πœ†(𝑗+1 PUNCT cana-1623 133 13 ) ) PUNCT cana-1623 134 1 = = PRON cana-1623 134 2 𝑛(βˆ‘ 𝑛(βˆ‘ NOUN cana-1623 134 3 β€Š β€Š SPACE cana-1623 134 4 𝑛 𝑛 PRON cana-1623 134 5 𝑖=1 𝑖=1 PROPN cana-1623 134 6 β€Š β€Š SPACE cana-1623 134 7 𝐸1𝑖 𝐸1𝑖 PROPN cana-1623 134 8 ) ) PUNCT cana-1623 134 9 βˆ’1 βˆ’1 NOUN cana-1623 134 10 from from ADP cana-1623 134 11 above above ADP cana-1623 134 12 equations equation NOUN cana-1623 134 13 we we PRON cana-1623 134 14 get get VERB cana-1623 134 15 , , PUNCT cana-1623 134 16 πœ‚(𝑗+1 πœ‚(𝑗+1 PUNCT cana-1623 134 17 ) ) PUNCT cana-1623 134 18 = = SYM cana-1623 134 19 𝑛(βˆ‘ 𝑛(βˆ‘ NOUN cana-1623 134 20 β€Š β€Š SPACE cana-1623 134 21 𝑛 𝑛 PRON cana-1623 134 22 𝑖=1 𝑖=1 PROPN cana-1623 134 23 β€Š β€Š SPACE cana-1623 134 24 𝐸2𝑖 𝐸2𝑖 PROPN cana-1623 135 1 βˆ’ βˆ’ VERB cana-1623 135 2 πœ† πœ† SYM cana-1623 135 3 ( ( PUNCT cana-1623 135 4 𝑗)βˆ‘ 𝑗)βˆ‘ ADJ cana-1623 135 5 β€Š β€Š SPACE cana-1623 135 6 𝑛 𝑛 PRON cana-1623 135 7 𝑖=1 𝑖=1 PROPN cana-1623 135 8 β€Š β€Š SPACE cana-1623 135 9 𝐸3𝑖 𝐸3𝑖 PROPN cana-1623 135 10 ) ) PUNCT cana-1623 135 11 βˆ’1 βˆ’1 NOUN cana-1623 136 1 step step NOUN cana-1623 136 2 4 4 NUM cana-1623 136 3 : : PUNCT cana-1623 136 4 if if SCONJ cana-1623 136 5 |πœƒ(𝑗+1 |πœƒ(𝑗+1 NUM cana-1623 136 6 ) ) PUNCT cana-1623 136 7 βˆ’ βˆ’ NOUN cana-1623 137 1 πœƒ(𝑗)| πœƒ(𝑗)| CCONJ cana-1623 137 2 < < X cana-1623 137 3 πœ€ πœ€ PROPN cana-1623 137 4 , , PUNCT cana-1623 137 5 the the DET cana-1623 137 6 mles mle NOUN cana-1623 137 7 are be AUX cana-1623 137 8 produced produce VERB cana-1623 137 9 by by ADP cana-1623 137 10 οΏ½ οΏ½ PROPN cana-1623 137 11 Μ‚ Μ‚ NOUN cana-1623 137 12 οΏ½ οΏ½ NOUN cana-1623 137 13 𝑀𝐿 𝑀𝐿 NOUN cana-1623 137 14 = = SYM cana-1623 137 15 πœ† πœ† PROPN cana-1623 137 16 ( ( PUNCT cana-1623 137 17 𝑗 𝑗 NOUN cana-1623 137 18 ) ) PUNCT cana-1623 137 19 and and CCONJ cana-1623 137 20 οΏ½ οΏ½ PROPN cana-1623 137 21 Μ‚ Μ‚ NOUN cana-1623 137 22 οΏ½ οΏ½ NOUN cana-1623 137 23 𝑀𝐿 𝑀𝐿 NOUN cana-1623 137 24 = = SYM cana-1623 137 25 πœ‚ πœ‚ PROPN cana-1623 137 26 ( ( PUNCT cana-1623 137 27 𝑗 𝑗 NOUN cana-1623 137 28 ) ) PUNCT cana-1623 137 29 . . PUNCT cana-1623 138 1 if if SCONJ cana-1623 138 2 not not PART cana-1623 138 3 , , PUNCT cana-1623 138 4 set set VERB cana-1623 138 5 𝑗 𝑗 NOUN cana-1623 138 6 = = X cana-1623 138 7 𝑗 𝑗 PROPN cana-1623 139 1 + + NUM cana-1623 139 2 1 1 NUM cana-1623 139 3 and and CCONJ cana-1623 139 4 go go VERB cana-1623 139 5 back back ADV cana-1623 139 6 to to PART cana-1623 139 7 step step NOUN cana-1623 139 8 2 2 NUM cana-1623 139 9 . . PUNCT cana-1623 140 1 the the DET cana-1623 140 2 mle⁑ mle⁑ PROPN cana-1623 140 3 mle mle PROPN cana-1623 140 4 οΏ½ οΏ½ PROPN cana-1623 140 5 Μ‚ Μ‚ VERB cana-1623 140 6 οΏ½ οΏ½ NOUN cana-1623 140 7 𝑀𝐿(𝑑)can 𝑀𝐿(𝑑)can NOUN cana-1623 140 8 be be AUX cana-1623 140 9 calculated calculate VERB cana-1623 140 10 using use VERB cana-1623 140 11 maximum maximum ADJ cana-1623 140 12 likelihood likelihood NOUN cana-1623 140 13 estimation estimation NOUN cana-1623 140 14 invariance invariance NOUN cana-1623 140 15 as as SCONJ cana-1623 140 16 follows follow VERB cana-1623 140 17 : : PUNCT cana-1623 140 18 οΏ½ οΏ½ NOUN cana-1623 140 19 Μ‚ Μ‚ NOUN cana-1623 140 20 οΏ½ οΏ½ NOUN cana-1623 140 21 𝑀𝐿(𝑑 𝑀𝐿(𝑑 NOUN cana-1623 140 22 ) ) PUNCT cana-1623 140 23 = = SYM cana-1623 140 24 1 1 NUM cana-1623 140 25 βˆ’ βˆ’ NOUN cana-1623 140 26 exp exp NOUN cana-1623 140 27 ( ( PUNCT cana-1623 140 28 βˆ’ βˆ’ PROPN cana-1623 140 29 οΏ½ οΏ½ PROPN cana-1623 140 30 Μ‚ Μ‚ NOUN cana-1623 140 31 οΏ½ οΏ½ NOUN cana-1623 140 32 𝑀𝐿𝑑 𝑀𝐿𝑑 NOUN cana-1623 140 33 βˆ’ βˆ’ NUM cana-1623 140 34 οΏ½ οΏ½ PROPN cana-1623 140 35 Μ‚ Μ‚ NOUN cana-1623 140 36 οΏ½ οΏ½ NOUN cana-1623 140 37 𝑀𝐿 𝑀𝐿 PROPN cana-1623 140 38 ) ) PUNCT cana-1623 140 39 2.5 2.5 NUM cana-1623 140 40 bayesian bayesian NOUN cana-1623 140 41 estimation estimation NOUN cana-1623 140 42 in in ADP cana-1623 140 43 bayesian bayesian NOUN cana-1623 140 44 statistical statistical ADJ cana-1623 140 45 inference inference NOUN cana-1623 140 46 , , PUNCT cana-1623 140 47 the the DET cana-1623 140 48 prior prior ADJ cana-1623 140 49 distribution distribution NOUN cana-1623 140 50 is be AUX cana-1623 140 51 important important ADJ cana-1623 140 52 . . PUNCT cana-1623 141 1 it it PRON cana-1623 141 2 indicates indicate VERB cana-1623 141 3 our our PRON cana-1623 141 4 prior prior ADJ cana-1623 141 5 knowledge knowledge NOUN cana-1623 141 6 or or CCONJ cana-1623 141 7 assumption assumption NOUN cana-1623 141 8 about about ADP cana-1623 141 9 the the DET cana-1623 141 10 parameters parameter NOUN cana-1623 141 11 and and CCONJ cana-1623 141 12 can can AUX cana-1623 141 13 be be AUX cana-1623 141 14 used use VERB cana-1623 141 15 to to PART cana-1623 141 16 better well ADV cana-1623 141 17 precisely precisely ADV cana-1623 141 18 predict predict VERB cana-1623 141 19 the the DET cana-1623 141 20 posterior posterior ADJ cana-1623 141 21 distribution distribution NOUN cana-1623 141 22 .choosing .choose VERB cana-1623 141 23 an an DET cana-1623 141 24 appropriate appropriate ADJ cana-1623 141 25 prior prior ADJ cana-1623 141 26 distribution distribution NOUN cana-1623 141 27 is be AUX cana-1623 141 28 critical critical ADJ cana-1623 141 29 since since SCONJ cana-1623 141 30 it it PRON cana-1623 141 31 influences influence VERB cana-1623 141 32 the the DET cana-1623 141 33 final final ADJ cana-1623 141 34 inference inference NOUN cana-1623 141 35 results result NOUN cana-1623 141 36 . . PUNCT cana-1623 142 1 the the DET cana-1623 142 2 gamma gamma NOUN cana-1623 142 3 distribution distribution NOUN cana-1623 142 4 is be AUX cana-1623 142 5 a a DET cana-1623 142 6 versatile versatile ADV cana-1623 142 7 continuous continuous ADJ cana-1623 142 8 probability probability NOUN cana-1623 142 9 distribution distribution NOUN cana-1623 142 10 with with ADP cana-1623 142 11 numerous numerous ADJ cana-1623 142 12 desirable desirable ADJ cana-1623 142 13 qualities quality NOUN cana-1623 142 14 , , PUNCT cana-1623 142 15 making make VERB cana-1623 142 16 it it PRON cana-1623 142 17 a a DET cana-1623 142 18 popular popular ADJ cana-1623 142 19 candidate candidate NOUN cana-1623 142 20 for for ADP cana-1623 142 21 the the DET cana-1623 142 22 prior prior ADJ cana-1623 142 23 distribution distribution NOUN cana-1623 142 24 of of ADP cana-1623 142 25 parameters parameter NOUN cana-1623 142 26 in in ADP cana-1623 142 27 bayesian bayesian NOUN cana-1623 142 28 statistics statistic NOUN cana-1623 142 29 . . PUNCT cana-1623 143 1 the the DET cana-1623 143 2 parameters parameter NOUN cana-1623 143 3 of of ADP cana-1623 143 4 the the DET cana-1623 143 5 gamma gamma NOUN cana-1623 143 6 distribution distribution NOUN cana-1623 143 7 can can AUX cana-1623 143 8 be be AUX cana-1623 143 9 changed change VERB cana-1623 143 10 to to PART cana-1623 143 11 fit fit VERB cana-1623 143 12 various various ADJ cana-1623 143 13 prior prior ADJ cana-1623 143 14 beliefs belief NOUN cana-1623 143 15 . . PUNCT cana-1623 144 1 furthermore furthermore ADV cana-1623 144 2 , , PUNCT cana-1623 144 3 the the DET cana-1623 144 4 gamma gamma NOUN cana-1623 144 5 distribution distribution NOUN cana-1623 144 6 is be AUX cana-1623 144 7 conjugate conjugate ADJ cana-1623 144 8 , , PUNCT cana-1623 144 9 which which PRON cana-1623 144 10 means mean VERB cana-1623 144 11 that that SCONJ cana-1623 144 12 when when SCONJ cana-1623 144 13 employed employ VERB cana-1623 144 14 as as ADP cana-1623 144 15 a a DET cana-1623 144 16 prior prior ADJ cana-1623 144 17 distribution distribution NOUN cana-1623 144 18 , , PUNCT cana-1623 144 19 the the DET cana-1623 144 20 communications communication NOUN cana-1623 144 21 on on ADP cana-1623 144 22 applied apply VERB cana-1623 144 23 nonlinear nonlinear ADJ cana-1623 144 24 analysis analysis NOUN cana-1623 144 25 issn issn NOUN cana-1623 144 26 : : PUNCT cana-1623 144 27 1074 1074 NUM cana-1623 144 28 - - PUNCT cana-1623 144 29 133x 133x NUM cana-1623 144 30 vol vol NOUN cana-1623 144 31 32 32 NUM cana-1623 144 32 no no NOUN cana-1623 144 33 . . NOUN cana-1623 144 34 1 1 NUM cana-1623 144 35 ( ( PUNCT cana-1623 144 36 2025 2025 NUM cana-1623 144 37 ) ) PUNCT cana-1623 144 38 97 97 NUM cana-1623 144 39 https://internationalpubls.com https://internationalpubls.com NOUN cana-1623 144 40 product product NOUN cana-1623 144 41 with with ADP cana-1623 144 42 the the DET cana-1623 144 43 likelihood likelihood NOUN cana-1623 144 44 function function NOUN cana-1623 144 45 remains remain VERB cana-1623 144 46 a a DET cana-1623 144 47 gamma gamma NOUN cana-1623 144 48 distribution distribution NOUN cana-1623 144 49 ; ; PUNCT cana-1623 144 50 simplifying simplify VERB cana-1623 144 51 posterior posterior ADJ cana-1623 144 52 distribution distribution NOUN cana-1623 144 53 computations computation NOUN cana-1623 144 54 .the .the X cana-1623 145 1 pdf pdf NOUN cana-1623 145 2 for for ADP cana-1623 145 3 the the DET cana-1623 145 4 gamma gamma NOUN cana-1623 145 5 distribution distribution NOUN cana-1623 145 6 is be AUX cana-1623 145 7 [ [ X cana-1623 145 8 11 11 NUM cana-1623 145 9 ] ] PUNCT cana-1623 145 10 πœ‹(πœ” πœ‹(πœ” NOUN cana-1623 145 11 ) ) PUNCT cana-1623 145 12 = = PRON cana-1623 145 13 π‘π‘Ž π‘π‘Ž X cana-1623 145 14 Ξ³(π‘Ž Ξ³(π‘Ž PROPN cana-1623 145 15 ) ) PUNCT cana-1623 145 16 πœ”π‘Žβˆ’1π‘’βˆ’π‘πœ” πœ”π‘Žβˆ’1π‘’βˆ’π‘πœ” ADP cana-1623 145 17 , , PUNCT cana-1623 145 18 πœ” πœ” X cana-1623 145 19 > > X cana-1623 145 20 0 0 NUM cana-1623 145 21 , , PUNCT cana-1623 145 22 π‘Ž π‘Ž NOUN cana-1623 145 23 , , PUNCT cana-1623 145 24 𝑏 𝑏 PROPN cana-1623 145 25 > > X cana-1623 145 26 0 0 PUNCT cana-1623 145 27 in in ADP cana-1623 145 28 this this DET cana-1623 145 29 section section NOUN cana-1623 145 30 , , PUNCT cana-1623 145 31 we we PRON cana-1623 145 32 assume assume VERB cana-1623 145 33 that that SCONJ cana-1623 145 34 Ξ» Ξ» PROPN cana-1623 145 35 and and CCONJ cana-1623 145 36 Ξ· Ξ· PROPN cana-1623 145 37 are be AUX cana-1623 145 38 independent independent ADJ cana-1623 145 39 random random ADJ cana-1623 145 40 variables variable NOUN cana-1623 145 41 . . PUNCT cana-1623 146 1 Ξ» Ξ» NOUN cana-1623 146 2 follows follow VERB cana-1623 146 3 gamma gamma NOUN cana-1623 146 4 ( ( PUNCT cana-1623 146 5 𝑐1 𝑐1 NOUN cana-1623 146 6 , , PUNCT cana-1623 146 7 𝑑1 𝑑1 NOUN cana-1623 146 8 ) ) PUNCT cana-1623 146 9 and and CCONJ cana-1623 146 10 Ξ· Ξ· PROPN cana-1623 146 11 follows follow VERB cana-1623 146 12 gamma gamma NOUN cana-1623 146 13 ( ( PUNCT cana-1623 146 14 𝑐2 𝑐2 PROPN cana-1623 146 15 , , PUNCT cana-1623 146 16 𝑑2 𝑑2 NOUN cana-1623 146 17 ) ) PUNCT cana-1623 146 18 . . PUNCT cana-1623 147 1 that that PRON cana-1623 147 2 means mean VERB cana-1623 147 3 : : PUNCT cana-1623 147 4 πœ‹1(πœ† πœ‹1(πœ† X cana-1623 147 5 ) ) PUNCT cana-1623 147 6 ∝ ∝ PROPN cana-1623 148 1 πœ† πœ† ADP cana-1623 148 2 𝑑1βˆ’1π‘’βˆ’π‘1πœ†πœ† 𝑑1βˆ’1π‘’βˆ’π‘1πœ†πœ† PROPN cana-1623 148 3 > > X cana-1623 148 4 0 0 PROPN cana-1623 148 5 , , PUNCT cana-1623 148 6 𝑐1 𝑐1 NOUN cana-1623 148 7 > > X cana-1623 148 8 0 0 NUM cana-1623 148 9 , , PUNCT cana-1623 148 10 𝑑1 𝑑1 NOUN cana-1623 148 11 > > X cana-1623 148 12 0 0 PUNCT cana-1623 148 13 πœ‹2(πœ‚ πœ‹2(πœ‚ NUM cana-1623 148 14 ) ) PUNCT cana-1623 148 15 ∝ ∝ PROPN cana-1623 148 16 πœ‚ πœ‚ X cana-1623 148 17 𝑑2βˆ’1π‘’βˆ’π‘2πœ‚πœ‚ 𝑑2βˆ’1π‘’βˆ’π‘2πœ‚πœ‚ PROPN cana-1623 148 18 > > X cana-1623 148 19 0 0 NUM cana-1623 148 20 , , PUNCT cana-1623 148 21 𝑐2 𝑐2 NOUN cana-1623 148 22 > > X cana-1623 148 23 0 0 NUM cana-1623 148 24 , , PUNCT cana-1623 148 25 𝑑2 𝑑2 VERB cana-1623 148 26 > > X cana-1623 148 27 0 0 X cana-1623 148 28 . . PUNCT cana-1623 149 1 thus thus ADV cana-1623 149 2 , , PUNCT cana-1623 149 3 the the DET cana-1623 149 4 joint joint ADJ cana-1623 149 5 prior prior ADJ cana-1623 149 6 distribution distribution NOUN cana-1623 149 7 of of ADP cana-1623 149 8 πœ† πœ† PRON cana-1623 149 9 and and CCONJ cana-1623 149 10 πœ‚ πœ‚ NOUN cana-1623 149 11 is be AUX cana-1623 149 12 : : PUNCT cana-1623 149 13 πœ‹(πœ† πœ‹(πœ† NOUN cana-1623 149 14 , , PUNCT cana-1623 149 15 πœ‚ πœ‚ NOUN cana-1623 149 16 ) ) PUNCT cana-1623 149 17 = = SYM cana-1623 149 18 πœ‹1(πœ† πœ‹1(πœ† PROPN cana-1623 149 19 ) ) PUNCT cana-1623 149 20 Γ— Γ— NOUN cana-1623 149 21 πœ‹2(πœ‚ πœ‹2(πœ‚ PROPN cana-1623 149 22 ) ) PUNCT cana-1623 149 23 ∝ ∝ PROPN cana-1623 149 24 πœ† πœ† DET cana-1623 149 25 𝑑1βˆ’1πœ‚π‘‘2βˆ’1π‘’βˆ’π‘1πœ†βˆ’π‘2πœ‚ 𝑑1βˆ’1πœ‚π‘‘2βˆ’1π‘’βˆ’π‘1πœ†βˆ’π‘2πœ‚ NOUN cana-1623 149 26 with with ADP cana-1623 149 27 reference reference NOUN cana-1623 149 28 to to ADP cana-1623 149 29 the the DET cana-1623 149 30 bayesian bayesian NOUN cana-1623 149 31 formulation formulation NOUN cana-1623 149 32 , , PUNCT cana-1623 149 33 the the DET cana-1623 149 34 posterior posterior ADJ cana-1623 149 35 distribution distribution NOUN cana-1623 149 36 of of ADP cana-1623 149 37 πœ† πœ† PRON cana-1623 149 38 and and CCONJ cana-1623 149 39 πœ‚ πœ‚ NOUN cana-1623 149 40 is be AUX cana-1623 149 41 πœ‹(πœ† πœ‹(πœ† PROPN cana-1623 149 42 , , PUNCT cana-1623 149 43 πœ‚ πœ‚ PROPN cana-1623 149 44 ∣ ∣ PROPN cana-1623 149 45 οΏ½ οΏ½ PROPN cana-1623 149 46 Μƒ Μƒ PROPN cana-1623 149 47 οΏ½ οΏ½ PROPN cana-1623 149 48 )∝ )∝ PUNCT cana-1623 149 49 β„Ž(πœ† β„Ž(πœ† PROPN cana-1623 149 50 , , PUNCT cana-1623 149 51 πœ‚ πœ‚ PROPN cana-1623 149 52 ∣ ∣ PROPN cana-1623 149 53 οΏ½ οΏ½ PROPN cana-1623 149 54 Μƒ Μƒ PROPN cana-1623 149 55 οΏ½ οΏ½ PROPN cana-1623 149 56 ) ) PUNCT cana-1623 149 57 Γ— Γ— NOUN cana-1623 149 58 πœ‹(πœ† πœ‹(πœ† PROPN cana-1623 149 59 , , PUNCT cana-1623 149 60 πœ‚ πœ‚ NOUN cana-1623 149 61 ) ) PUNCT cana-1623 149 62 the the DET cana-1623 149 63 posterior posterior ADJ cana-1623 149 64 expectation expectation NOUN cana-1623 149 65 of of ADP cana-1623 149 66 the the DET cana-1623 149 67 function function NOUN cana-1623 149 68 𝑔(πœ† 𝑔(πœ† NOUN cana-1623 149 69 , , PUNCT cana-1623 149 70 πœ‚ πœ‚ NOUN cana-1623 149 71 ) ) PUNCT cana-1623 149 72 of of ADP cana-1623 149 73 πœ† πœ† PRON cana-1623 149 74 and and CCONJ cana-1623 149 75 πœ‚ πœ‚ NOUN cana-1623 149 76 is be AUX cana-1623 149 77 : : PUNCT cana-1623 149 78 𝐸[𝑔(πœ† 𝐸[𝑔(πœ† NOUN cana-1623 149 79 , , PUNCT cana-1623 149 80 πœ‚ πœ‚ NOUN cana-1623 149 81 ) ) PUNCT cana-1623 149 82 ∣ ∣ PROPN cana-1623 149 83 οΏ½ οΏ½ PROPN cana-1623 149 84 Μƒ Μƒ PROPN cana-1623 149 85 οΏ½ οΏ½ NOUN cana-1623 149 86 ]= ]= NUM cana-1623 149 87 ∫ ∫ NOUN cana-1623 149 88 β€Š β€Š SPACE cana-1623 150 1 + + PROPN cana-1623 150 2 ∞ ∞ NOUN cana-1623 150 3 0 0 NUM cana-1623 150 4 β€Š β€Š SPACE cana-1623 150 5 ∫ ∫ PROPN cana-1623 150 6 β€Š β€Š SPACE cana-1623 151 1 + + PROPN cana-1623 151 2 ∞ ∞ PROPN cana-1623 151 3 0 0 NUM cana-1623 151 4 β€Š β€Š SPACE cana-1623 151 5 𝑔(πœ† 𝑔(πœ† NOUN cana-1623 151 6 , , PUNCT cana-1623 151 7 πœ‚ πœ‚ NOUN cana-1623 151 8 ) ) PUNCT cana-1623 151 9 πœ‹(πœ† πœ‹(πœ† PROPN cana-1623 151 10 , , PUNCT cana-1623 151 11 πœ‚ πœ‚ PROPN cana-1623 151 12 ∣ ∣ PROPN cana-1623 151 13 οΏ½ οΏ½ PROPN cana-1623 151 14 Μƒ Μƒ PROPN cana-1623 151 15 οΏ½ οΏ½ PROPN cana-1623 151 16 ) ) PUNCT cana-1623 151 17 ∫ ∫ PROPN cana-1623 151 18 β€Š β€Š SPACE cana-1623 152 1 + + NOUN cana-1623 152 2 ∞ ∞ NOUN cana-1623 152 3 0 0 NUM cana-1623 152 4 β€Š β€Š SPACE cana-1623 152 5 ∫ ∫ PROPN cana-1623 152 6 β€Š β€Š SPACE cana-1623 153 1 + + PROPN cana-1623 153 2 ∞ ∞ PROPN cana-1623 153 3 0 0 NUM cana-1623 153 4 β€Š β€Š SPACE cana-1623 153 5 πœ‹(πœ† πœ‹(πœ† PROPN cana-1623 153 6 , , PUNCT cana-1623 153 7 πœ‚ πœ‚ PROPN cana-1623 153 8 ∣ ∣ PROPN cana-1623 153 9 οΏ½ οΏ½ PROPN cana-1623 153 10 Μƒ Μƒ PROPN cana-1623 153 11 οΏ½ οΏ½ PROPN cana-1623 153 12 )π‘‘πœ†π‘‘πœ‚ )π‘‘πœ†π‘‘πœ‚ PUNCT cana-1623 153 13 π‘‘πœ†π‘‘πœ‚ π‘‘πœ†π‘‘πœ‚ VERB cana-1623 153 14 𝐸[𝑔(πœ† 𝐸[𝑔(πœ† NOUN cana-1623 153 15 , , PUNCT cana-1623 153 16 πœ‚ πœ‚ NOUN cana-1623 153 17 ) ) PUNCT cana-1623 153 18 ∣ ∣ PROPN cana-1623 153 19 οΏ½ οΏ½ PROPN cana-1623 153 20 Μƒ Μƒ PROPN cana-1623 153 21 οΏ½ οΏ½ NOUN cana-1623 153 22 ] ] X cana-1623 153 23 = = SYM cana-1623 153 24 βˆ«π‘”(πœ† βˆ«π‘”(πœ† NOUN cana-1623 153 25 , , PUNCT cana-1623 153 26 πœ‚)𝑒𝐻(πœ†,πœ‚βˆ£ πœ‚)𝑒𝐻(πœ†,πœ‚βˆ£ PROPN cana-1623 153 27 οΏ½ οΏ½ PROPN cana-1623 153 28 Μƒ Μƒ PROPN cana-1623 153 29 οΏ½ οΏ½ NOUN cana-1623 153 30 )+𝐺(πœ†,πœ‚)𝑑(πœ† )+𝐺(πœ†,πœ‚)𝑑(πœ† PROPN cana-1623 153 31 , , PUNCT cana-1623 153 32 πœ‚ πœ‚ NOUN cana-1623 153 33 ) ) PUNCT cana-1623 153 34 ∫ ∫ PROPN cana-1623 153 35 𝑒𝐻(πœ†,πœ‚βˆ£ 𝑒𝐻(πœ†,πœ‚βˆ£ PROPN cana-1623 153 36 οΏ½ οΏ½ PROPN cana-1623 153 37 Μƒ Μƒ PROPN cana-1623 153 38 οΏ½ οΏ½ NOUN cana-1623 153 39 )+𝐺(πœ†,πœ‚)𝑑(πœ† )+𝐺(πœ†,πœ‚)𝑑(πœ† PROPN cana-1623 153 40 , , PUNCT cana-1623 153 41 πœ‚ πœ‚ NOUN cana-1623 153 42 ) ) PUNCT cana-1623 153 43 where where SCONJ cana-1623 153 44 𝐺(πœ† 𝐺(πœ† NOUN cana-1623 153 45 , , PUNCT cana-1623 153 46 πœ‚ πœ‚ NOUN cana-1623 153 47 ) ) PUNCT cana-1623 153 48 = = PUNCT cana-1623 153 49 ln ln ADJ cana-1623 153 50 πœ‹(πœ† πœ‹(πœ† PROPN cana-1623 153 51 , , PUNCT cana-1623 153 52 πœ‚ πœ‚ NOUN cana-1623 153 53 ) ) PUNCT cana-1623 153 54 . . PUNCT cana-1623 154 1 𝐸[𝑔(πœ† 𝐸[𝑔(πœ† NOUN cana-1623 154 2 , , PUNCT cana-1623 154 3 πœ‚ πœ‚ NOUN cana-1623 154 4 ) ) PUNCT cana-1623 154 5 ∣∣ ∣∣ NUM cana-1623 154 6 οΏ½ οΏ½ PROPN cana-1623 154 7 Μƒ Μƒ NOUN cana-1623 154 8 οΏ½ οΏ½ NOUN cana-1623 154 9 ] ] PUNCT cana-1623 154 10 = = SYM cana-1623 154 11 𝑔(πœ† 𝑔(πœ† NOUN cana-1623 154 12 ˆ𝑀𝐿 ˆ𝑀𝐿 NOUN cana-1623 154 13 , , PUNCT cana-1623 154 14 πœ‚ πœ‚ DET cana-1623 154 15 ˆ𝑀𝐿 ˆ𝑀𝐿 NUM cana-1623 154 16 ) ) PUNCT cana-1623 154 17 + + CCONJ cana-1623 154 18 1 1 NUM cana-1623 154 19 2(𝐴 2(𝐴 NOUN cana-1623 154 20 + + CCONJ cana-1623 154 21 𝐡 𝐡 NOUN cana-1623 154 22 + + CCONJ cana-1623 154 23 𝐢 𝐢 PROPN cana-1623 154 24 + + CCONJ cana-1623 154 25 𝐷 𝐷 NOUN cana-1623 154 26 ) ) PUNCT cana-1623 154 27 𝐴 𝐴 NOUN cana-1623 154 28 = = PUNCT cana-1623 154 29 ( ( PUNCT cana-1623 154 30 𝑔 𝑔 PROPN cana-1623 154 31 Λ†πœ†πœ† Λ†πœ†πœ† NOUN cana-1623 154 32 + + CCONJ cana-1623 154 33 2𝑔 2𝑔 NUM cana-1623 154 34 Λ†πœ†πΊ Λ†πœ†πΊ PROPN cana-1623 154 35 Λ†πœ†)πœ™ Λ†πœ†)πœ™ PROPN cana-1623 154 36 Λ†πœ†πœ† Λ†πœ†πœ† NOUN cana-1623 154 37 + + CCONJ cana-1623 154 38 ( ( PUNCT cana-1623 154 39 𝑔 𝑔 PROPN cana-1623 154 40 Λ†πœ‚πœ† Λ†πœ‚πœ† NOUN cana-1623 154 41 + + CCONJ cana-1623 154 42 2𝑔 2𝑔 NUM cana-1623 154 43 Λ†πœ‚πΊ Λ†πœ‚πΊ PROPN cana-1623 154 44 Λ†πœ†)πœ™ Λ†πœ†)πœ™ PROPN cana-1623 154 45 Λ†πœ‚πœ† Λ†πœ‚πœ† NOUN cana-1623 154 46 𝐡 𝐡 NOUN cana-1623 154 47 = = SYM cana-1623 154 48 ( ( PUNCT cana-1623 154 49 𝑔 𝑔 PROPN cana-1623 154 50 Λ†πœ†πœ‚ Λ†πœ†πœ‚ NOUN cana-1623 154 51 + + CCONJ cana-1623 154 52 2𝑔 2𝑔 NUM cana-1623 154 53 Λ†πœ†πΊ Λ†πœ†πΊ PROPN cana-1623 154 54 Λ†πœ‚)πœ™ Λ†πœ‚)πœ™ PROPN cana-1623 154 55 Λ†πœ†πœ‚ Λ†πœ†πœ‚ NOUN cana-1623 154 56 + + CCONJ cana-1623 154 57 ( ( PUNCT cana-1623 154 58 𝑔 𝑔 PROPN cana-1623 154 59 Λ†πœ‚πœ‚ Λ†πœ‚πœ‚ PROPN cana-1623 154 60 + + CCONJ cana-1623 154 61 2𝑔 2𝑔 NUM cana-1623 154 62 Λ†πœ‚πΊ Λ†πœ‚πΊ PROPN cana-1623 154 63 Λ†πœ‚)πœ™ Λ†πœ‚)πœ™ PROPN cana-1623 154 64 Λ†πœ‚πœ‚ Λ†πœ‚πœ‚ PROPN cana-1623 154 65 𝐢 𝐢 PROPN cana-1623 154 66 = = SYM cana-1623 154 67 ( ( PUNCT cana-1623 154 68 𝑔 𝑔 NOUN cana-1623 154 69 Λ†πœ†πœ™ Λ†πœ†πœ™ NOUN cana-1623 154 70 Λ†πœ†πœ† Λ†πœ†πœ† NOUN cana-1623 154 71 + + CCONJ cana-1623 154 72 𝑔 𝑔 NUM cana-1623 154 73 Λ†πœ‚πœ™ Λ†πœ‚πœ™ DET cana-1623 154 74 Λ†πœ†πœ‚)(𝐻 Λ†πœ†πœ‚)(𝐻 NOUN cana-1623 154 75 Λ†πœ†πœ†πœ†πœ™ Λ†πœ†πœ†πœ†πœ™ NOUN cana-1623 154 76 Λ†πœ†πœ† Λ†πœ†πœ† NOUN cana-1623 154 77 + + CCONJ cana-1623 154 78 𝐻 𝐻 NOUN cana-1623 154 79 Λ†πœ‚πœ†πœ†πœ™ Λ†πœ‚πœ†πœ†πœ™ ADJ cana-1623 154 80 Λ†πœ‚πœ† Λ†πœ‚πœ† NOUN cana-1623 155 1 + + CCONJ cana-1623 155 2 𝐻 𝐻 PROPN cana-1623 155 3 Λ†πœ†πœ‚πœ†πœ™ Λ†πœ†πœ‚πœ†πœ™ ADJ cana-1623 155 4 Λ†πœ†πœ‚ Λ†πœ†πœ‚ NOUN cana-1623 155 5 + + CCONJ cana-1623 155 6 𝐻 𝐻 PROPN cana-1623 155 7 Λ†πœ‚πœ‚πœ†πœ™ Λ†πœ‚πœ‚πœ†πœ™ ADJ cana-1623 155 8 Λ†πœ‚πœ‚ Λ†πœ‚πœ‚ NOUN cana-1623 155 9 ) ) PUNCT cana-1623 155 10 𝐷 𝐷 NOUN cana-1623 155 11 = = SYM cana-1623 155 12 ( ( PUNCT cana-1623 155 13 𝑔 𝑔 NOUN cana-1623 155 14 Λ†πœ†πœ™ Λ†πœ†πœ™ NOUN cana-1623 155 15 Λ†πœ‚πœ† Λ†πœ‚πœ† NOUN cana-1623 156 1 + + CCONJ cana-1623 156 2 𝑔 𝑔 PROPN cana-1623 156 3 Λ†πœ‚πœ™ Λ†πœ‚πœ™ PRON cana-1623 156 4 Λ†πœ‚πœ‚)(𝐻 Λ†πœ‚πœ‚)(𝐻 NOUN cana-1623 156 5 Λ†πœ†πœ†πœ‚πœ™ Λ†πœ†πœ†πœ‚πœ™ NOUN cana-1623 156 6 Λ†πœ†πœ† Λ†πœ†πœ† NOUN cana-1623 156 7 + + NOUN cana-1623 156 8 𝐻 𝐻 PROPN cana-1623 156 9 Λ†πœ‚πœ†πœ‚πœ™ Λ†πœ‚πœ†πœ‚πœ™ NOUN cana-1623 156 10 Λ†πœ‚πœ† Λ†πœ‚πœ† NOUN cana-1623 157 1 + + CCONJ cana-1623 157 2 𝐻 𝐻 PROPN cana-1623 157 3 Λ†πœ†πœ‚πœ‚πœ™ Λ†πœ†πœ‚πœ‚πœ™ NOUN cana-1623 157 4 Λ†πœ†πœ‚ Λ†πœ†πœ‚ NOUN cana-1623 157 5 + + CCONJ cana-1623 157 6 𝐻 𝐻 PROPN cana-1623 157 7 Λ†πœ‚πœ‚πœ‚πœ™ Λ†πœ‚πœ‚πœ‚πœ™ NOUN cana-1623 157 8 Λ†πœ‚πœ‚ Λ†πœ‚πœ‚ NOUN cana-1623 157 9 ) ) PUNCT cana-1623 157 10 the the DET cana-1623 157 11 element element NOUN cana-1623 157 12 πœ™π‘–π‘—(𝑖 πœ™π‘–π‘—(𝑖 PROPN cana-1623 157 13 , , PUNCT cana-1623 157 14 𝑗 𝑗 PROPN cana-1623 157 15 = = SYM cana-1623 157 16 πœ† πœ† NOUN cana-1623 157 17 , , PUNCT cana-1623 157 18 πœ‚)represents πœ‚)represent VERB cana-1623 157 19 the the DET cana-1623 157 20 inverse inverse NOUN cana-1623 157 21 matrix matrix NOUN cana-1623 157 22 of of ADP cana-1623 157 23 βˆ’π»π‘–π‘— βˆ’π»π‘–π‘— NUM cana-1623 157 24 .. .. PUNCT cana-1623 157 25 the the DET cana-1623 157 26 symbol symbol NOUN cana-1623 157 27 οΏ½ οΏ½ PROPN cana-1623 157 28 Μ‚ Μ‚ NOUN cana-1623 157 29 οΏ½ οΏ½ NOUN cana-1623 157 30 πœ†πœ† πœ†πœ† NOUN cana-1623 157 31 signifies signifie NOUN cana-1623 157 32 taking take VERB cana-1623 157 33 the the DET cana-1623 157 34 second second ADJ cana-1623 157 35 derivative derivative NOUN cana-1623 157 36 of of ADP cana-1623 157 37 𝑔(πœ† 𝑔(πœ† NOUN cana-1623 157 38 , , PUNCT cana-1623 157 39 πœ‚ πœ‚ NOUN cana-1623 157 40 ) ) PUNCT cana-1623 157 41 with with ADP cana-1623 157 42 regard regard NOUN cana-1623 157 43 to to ADP cana-1623 157 44 Ξ» Ξ» PROPN cana-1623 157 45 and and CCONJ cana-1623 157 46 putting put VERB cana-1623 157 47 οΏ½ οΏ½ PROPN cana-1623 157 48 Μ‚ Μ‚ NUM cana-1623 157 49 οΏ½ οΏ½ NOUN cana-1623 157 50 𝑀𝐿 𝑀𝐿 PROPN cana-1623 157 51 into into ADP cana-1623 157 52 it it PRON cana-1623 157 53 . . PUNCT cana-1623 158 1 similarly similarly ADV cana-1623 158 2 , , PUNCT cana-1623 158 3 the the DET cana-1623 158 4 rest rest NOUN cana-1623 158 5 can can AUX cana-1623 158 6 be be AUX cana-1623 158 7 illustrated illustrate VERB cana-1623 158 8 as as SCONJ cana-1623 158 9 follows follow VERB cana-1623 158 10 : : PUNCT cana-1623 158 11 π»πœ†πœ†πœ† π»πœ†πœ†πœ† PROPN cana-1623 158 12 = = PROPN cana-1623 158 13 βˆ‘ βˆ‘ NOUN cana-1623 158 14 β€Š β€Š SPACE cana-1623 158 15 𝑛 𝑛 PRON cana-1623 158 16 𝑖=1 𝑖=1 PROPN cana-1623 158 17 β€Š β€Š SPACE cana-1623 159 1 [ [ X cana-1623 159 2 2β„Žβˆ’3(πœ† 2β„Žβˆ’3(πœ† NUM cana-1623 159 3 , , PUNCT cana-1623 159 4 πœ‚ πœ‚ PROPN cana-1623 159 5 ∣ ∣ PROPN cana-1623 159 6 οΏ½ οΏ½ PROPN cana-1623 159 7 Μƒ Μƒ PROPN cana-1623 159 8 οΏ½ οΏ½ NOUN cana-1623 159 9 𝑖 𝑖 NUM cana-1623 159 10 ) ) PUNCT cana-1623 159 11 ( ( PUNCT cana-1623 159 12 ∫ ∫ PROPN cana-1623 159 13 β€Š β€Š SPACE cana-1623 160 1 + + PROPN cana-1623 160 2 ∞ ∞ PROPN cana-1623 160 3 0 0 NUM cana-1623 160 4 β€Š β€Š SPACE cana-1623 160 5 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 160 6 ) ) PUNCT cana-1623 160 7 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 160 8 ; ; PUNCT cana-1623 160 9 πœ† πœ† X cana-1623 160 10 , , PUNCT cana-1623 160 11 πœ‚ πœ‚ NOUN cana-1623 160 12 ) ) PUNCT cana-1623 160 13 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 160 14 𝑑𝑑 𝑑𝑑 ADP cana-1623 160 15 ) ) PUNCT cana-1623 160 16 3 3 NUM cana-1623 160 17 βˆ’ βˆ’ NOUN cana-1623 160 18 β„Žβˆ’1(πœ† β„Žβˆ’1(πœ† NOUN cana-1623 160 19 , , PUNCT cana-1623 160 20 πœ‚ πœ‚ PROPN cana-1623 160 21 ∣ ∣ PROPN cana-1623 160 22 οΏ½ οΏ½ PROPN cana-1623 160 23 Μƒ Μƒ PROPN cana-1623 160 24 οΏ½ οΏ½ NOUN cana-1623 160 25 𝑖)∫ 𝑖)∫ PROPN cana-1623 160 26 β€Š β€Š SPACE cana-1623 160 27 + + PROPN cana-1623 160 28 ∞ ∞ PROPN cana-1623 160 29 0 0 NUM cana-1623 160 30 β€Š β€Š SPACE cana-1623 160 31 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 160 32 ) ) PUNCT cana-1623 160 33 βˆ‚3𝑦(𝑑 βˆ‚3𝑦(𝑑 NUM cana-1623 160 34 ; ; PUNCT cana-1623 160 35 πœ† πœ† X cana-1623 160 36 , , PUNCT cana-1623 160 37 πœ‚ πœ‚ NOUN cana-1623 160 38 ) ) PUNCT cana-1623 160 39 βˆ‚πœ†3 βˆ‚πœ†3 PROPN cana-1623 160 40 𝑑𝑑 𝑑𝑑 ADP cana-1623 160 41 ] ] X cana-1623 160 42 π»πœ†πœ†πœ‚ π»πœ†πœ†πœ‚ PROPN cana-1623 160 43 = = SYM cana-1623 160 44 π»πœ†πœ‚πœ† π»πœ†πœ‚πœ† PROPN cana-1623 160 45 = = SYM cana-1623 160 46 π»πœ‚πœ†πœ† π»πœ‚πœ†πœ† PROPN cana-1623 160 47 communications communication NOUN cana-1623 160 48 on on ADP cana-1623 160 49 applied apply VERB cana-1623 160 50 nonlinear nonlinear ADJ cana-1623 160 51 analysis analysis NOUN cana-1623 160 52 issn issn NOUN cana-1623 160 53 : : PUNCT cana-1623 160 54 1074 1074 NUM cana-1623 160 55 - - PUNCT cana-1623 160 56 133x 133x NUM cana-1623 160 57 vol vol NOUN cana-1623 160 58 32 32 NUM cana-1623 160 59 no no NOUN cana-1623 160 60 . . NOUN cana-1623 160 61 1 1 NUM cana-1623 160 62 ( ( PUNCT cana-1623 160 63 2025 2025 NUM cana-1623 160 64 ) ) PUNCT cana-1623 160 65 98 98 NUM cana-1623 160 66 https://internationalpubls.com https://internationalpubls.com X cana-1623 160 67 = = PUNCT cana-1623 160 68 βˆ‘ βˆ‘ NOUN cana-1623 160 69 β€Š β€Š SPACE cana-1623 160 70 𝑛 𝑛 PRON cana-1623 160 71 𝑖=1 𝑖=1 PROPN cana-1623 160 72 β€Š β€Š SPACE cana-1623 161 1 [ [ X cana-1623 161 2 2β„Žβˆ’3(πœ† 2β„Žβˆ’3(πœ† NUM cana-1623 161 3 , , PUNCT cana-1623 161 4 πœ‚ πœ‚ PROPN cana-1623 161 5 ∣ ∣ PROPN cana-1623 161 6 οΏ½ οΏ½ PROPN cana-1623 161 7 Μƒ Μƒ PROPN cana-1623 161 8 οΏ½ οΏ½ NOUN cana-1623 161 9 𝑖)∫ 𝑖)∫ PROPN cana-1623 161 10 β€Š β€Š SPACE cana-1623 161 11 + + PROPN cana-1623 161 12 ∞ ∞ PROPN cana-1623 161 13 0 0 NUM cana-1623 161 14 β€Š β€Š SPACE cana-1623 161 15 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 161 16 ) ) PUNCT cana-1623 161 17 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 161 18 ; ; PUNCT cana-1623 161 19 πœ† πœ† X cana-1623 161 20 , , PUNCT cana-1623 161 21 πœ‚ πœ‚ NOUN cana-1623 161 22 ) ) PUNCT cana-1623 161 23 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 161 24 𝑑𝑑 𝑑𝑑 ADP cana-1623 161 25 ( ( PUNCT cana-1623 161 26 ∫ ∫ PROPN cana-1623 161 27 β€Š β€Š SPACE cana-1623 161 28 + + PROPN cana-1623 161 29 ∞ ∞ PROPN cana-1623 161 30 0 0 NUM cana-1623 161 31 β€Š β€Š SPACE cana-1623 161 32 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 161 33 ) ) PUNCT cana-1623 161 34 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 161 35 ; ; PUNCT cana-1623 161 36 πœ† πœ† X cana-1623 161 37 , , PUNCT cana-1623 161 38 πœ‚ πœ‚ NOUN cana-1623 161 39 ) ) PUNCT cana-1623 161 40 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 161 41 𝑑𝑑 𝑑𝑑 ADP cana-1623 161 42 ) ) PUNCT cana-1623 161 43 2 2 NUM cana-1623 161 44 ] ] PUNCT cana-1623 161 45 βˆ’βˆ‘ βˆ’βˆ‘ PROPN cana-1623 161 46 β€Š β€Š SPACE cana-1623 161 47 𝑛 𝑛 PRON cana-1623 161 48 𝑖=1 𝑖=1 PROPN cana-1623 161 49 β€Š β€Š SPACE cana-1623 162 1 [ [ X cana-1623 162 2 β„Žβˆ’2(πœ† β„Žβˆ’2(πœ† PROPN cana-1623 162 3 , , PUNCT cana-1623 162 4 πœ‚ πœ‚ PROPN cana-1623 162 5 ∣ ∣ PROPN cana-1623 162 6 οΏ½ οΏ½ PROPN cana-1623 162 7 Μƒ Μƒ PROPN cana-1623 162 8 οΏ½ οΏ½ NOUN cana-1623 162 9 𝑖)∫ 𝑖)∫ PROPN cana-1623 162 10 β€Š β€Š SPACE cana-1623 162 11 + + PROPN cana-1623 162 12 ∞ ∞ PROPN cana-1623 162 13 0 0 NUM cana-1623 162 14 β€Š β€Š SPACE cana-1623 162 15 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 162 16 ) ) PUNCT cana-1623 162 17 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 162 18 ; ; PUNCT cana-1623 162 19 πœ† πœ† X cana-1623 162 20 , , PUNCT cana-1623 162 21 πœ‚ πœ‚ NOUN cana-1623 162 22 ) ) PUNCT cana-1623 162 23 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 162 24 π‘‘π‘‘βˆ« π‘‘π‘‘βˆ« NOUN cana-1623 162 25 β€Š β€Š SPACE cana-1623 162 26 + + PROPN cana-1623 162 27 ∞ ∞ PROPN cana-1623 162 28 0 0 NUM cana-1623 162 29 β€Š β€Š SPACE cana-1623 162 30 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 162 31 ) ) PUNCT cana-1623 162 32 βˆ‚2𝑦(𝑑 βˆ‚2𝑦(𝑑 ADV cana-1623 162 33 ; ; PUNCT cana-1623 162 34 πœ† πœ† X cana-1623 162 35 , , PUNCT cana-1623 162 36 πœ‚ πœ‚ NOUN cana-1623 162 37 ) ) PUNCT cana-1623 162 38 βˆ‚πœ†2 βˆ‚πœ†2 NOUN cana-1623 162 39 𝑑𝑑 𝑑𝑑 ADP cana-1623 162 40 ] ] X cana-1623 162 41 + + ADJ cana-1623 162 42 βˆ‘ βˆ‘ PROPN cana-1623 162 43 β€Š β€Š SPACE cana-1623 162 44 𝑛 𝑛 PRON cana-1623 162 45 𝑖=1 𝑖=1 PROPN cana-1623 162 46 β€Š β€Š SPACE cana-1623 162 47 β„Žβˆ’1(πœ† β„Žβˆ’1(πœ† NOUN cana-1623 162 48 , , PUNCT cana-1623 162 49 πœ‚ πœ‚ PROPN cana-1623 162 50 ∣ ∣ PROPN cana-1623 162 51 οΏ½ οΏ½ PROPN cana-1623 162 52 Μƒ Μƒ PROPN cana-1623 162 53 οΏ½ οΏ½ NOUN cana-1623 162 54 𝑖)∫ 𝑖)∫ PROPN cana-1623 162 55 β€Š β€Š SPACE cana-1623 162 56 + + PROPN cana-1623 162 57 ∞ ∞ PROPN cana-1623 162 58 0 0 NUM cana-1623 162 59 β€Š β€Š SPACE cana-1623 162 60 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 162 61 ) ) PUNCT cana-1623 162 62 βˆ‚3𝑦(𝑑 βˆ‚3𝑦(𝑑 NUM cana-1623 162 63 ; ; PUNCT cana-1623 162 64 πœ† πœ† X cana-1623 162 65 , , PUNCT cana-1623 162 66 πœ‚ πœ‚ NOUN cana-1623 162 67 ) ) PUNCT cana-1623 162 68 βˆ‚πœ†2 βˆ‚πœ†2 NOUN cana-1623 162 69 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 162 70 𝑑𝑑 𝑑𝑑 ADP cana-1623 162 71 π»πœ‚πœ‚πœ† π»πœ‚πœ‚πœ† PROPN cana-1623 163 1 = = SYM cana-1623 163 2 π»πœ‚πœ†πœ‚ π»πœ‚πœ†πœ‚ PROPN cana-1623 163 3 = = SYM cana-1623 164 1 π»πœ†πœ‚πœ‚ π»πœ†πœ‚πœ‚ PROPN cana-1623 164 2 = = PROPN cana-1623 164 3 βˆ‘ βˆ‘ NOUN cana-1623 164 4 β€Š β€Š SPACE cana-1623 164 5 𝑛 𝑛 PRON cana-1623 164 6 𝑖=1 𝑖=1 PROPN cana-1623 164 7 β€Š β€Š SPACE cana-1623 165 1 [ [ X cana-1623 165 2 2β„Žβˆ’3(πœ† 2β„Žβˆ’3(πœ† NUM cana-1623 165 3 , , PUNCT cana-1623 165 4 πœ‚ πœ‚ PROPN cana-1623 165 5 ∣ ∣ PROPN cana-1623 165 6 οΏ½ οΏ½ PROPN cana-1623 165 7 Μƒ Μƒ PROPN cana-1623 165 8 οΏ½ οΏ½ NOUN cana-1623 165 9 𝑖)∫ 𝑖)∫ PROPN cana-1623 165 10 β€Š β€Š SPACE cana-1623 165 11 + + PROPN cana-1623 165 12 ∞ ∞ PROPN cana-1623 165 13 0 0 NUM cana-1623 165 14 β€Š β€Š SPACE cana-1623 165 15 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 165 16 ) ) PUNCT cana-1623 165 17 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 165 18 ; ; PUNCT cana-1623 165 19 πœ† πœ† X cana-1623 165 20 , , PUNCT cana-1623 165 21 πœ‚ πœ‚ NOUN cana-1623 165 22 ) ) PUNCT cana-1623 165 23 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 165 24 𝑑𝑑 𝑑𝑑 ADP cana-1623 165 25 ( ( PUNCT cana-1623 165 26 ∫ ∫ PROPN cana-1623 165 27 β€Š β€Š SPACE cana-1623 165 28 + + PROPN cana-1623 165 29 ∞ ∞ PROPN cana-1623 165 30 0 0 NUM cana-1623 165 31 β€Š β€Š SPACE cana-1623 165 32 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 165 33 ) ) PUNCT cana-1623 165 34 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 165 35 ; ; PUNCT cana-1623 165 36 πœ† πœ† X cana-1623 165 37 , , PUNCT cana-1623 165 38 πœ‚ πœ‚ NOUN cana-1623 165 39 ) ) PUNCT cana-1623 165 40 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 165 41 𝑑𝑑 𝑑𝑑 ADP cana-1623 165 42 ) ) PUNCT cana-1623 165 43 2 2 NUM cana-1623 165 44 ] ] PUNCT cana-1623 165 45 βˆ’βˆ‘ βˆ’βˆ‘ PROPN cana-1623 165 46 β€Š β€Š SPACE cana-1623 165 47 𝑛 𝑛 PRON cana-1623 165 48 𝑖=1 𝑖=1 PROPN cana-1623 165 49 β€Š β€Š SPACE cana-1623 166 1 [ [ X cana-1623 166 2 β„Žβˆ’2(πœ† β„Žβˆ’2(πœ† PROPN cana-1623 166 3 , , PUNCT cana-1623 166 4 πœ‚ πœ‚ PROPN cana-1623 166 5 ∣ ∣ PROPN cana-1623 166 6 οΏ½ οΏ½ PROPN cana-1623 166 7 Μƒ Μƒ PROPN cana-1623 166 8 οΏ½ οΏ½ NOUN cana-1623 166 9 𝑖)∫ 𝑖)∫ PROPN cana-1623 166 10 β€Š β€Š SPACE cana-1623 166 11 + + PROPN cana-1623 166 12 ∞ ∞ PROPN cana-1623 166 13 0 0 NUM cana-1623 166 14 β€Š β€Š SPACE cana-1623 166 15 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 166 16 ) ) PUNCT cana-1623 166 17 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 166 18 ; ; PUNCT cana-1623 166 19 πœ† πœ† X cana-1623 166 20 , , PUNCT cana-1623 166 21 πœ‚ πœ‚ NOUN cana-1623 166 22 ) ) PUNCT cana-1623 166 23 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 166 24 π‘‘π‘‘βˆ« π‘‘π‘‘βˆ« NOUN cana-1623 166 25 β€Š β€Š SPACE cana-1623 166 26 + + PROPN cana-1623 166 27 ∞ ∞ PROPN cana-1623 166 28 0 0 NUM cana-1623 166 29 β€Š β€Š SPACE cana-1623 166 30 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 166 31 ) ) PUNCT cana-1623 166 32 βˆ‚2𝑦(𝑑 βˆ‚2𝑦(𝑑 ADV cana-1623 166 33 ; ; PUNCT cana-1623 166 34 πœ† πœ† X cana-1623 166 35 , , PUNCT cana-1623 166 36 πœ‚ πœ‚ NOUN cana-1623 166 37 ) ) PUNCT cana-1623 166 38 βˆ‚πœ‚2 βˆ‚πœ‚2 NOUN cana-1623 166 39 𝑑𝑑 𝑑𝑑 ADP cana-1623 166 40 ] ] X cana-1623 166 41 + + PROPN cana-1623 166 42 βˆ‘ βˆ‘ PROPN cana-1623 166 43 β€Š β€Š SPACE cana-1623 166 44 𝑛 𝑛 PRON cana-1623 166 45 𝑖=1 𝑖=1 PROPN cana-1623 166 46 β€Š β€Š SPACE cana-1623 167 1 [ [ X cana-1623 167 2 β„Žβˆ’1(πœ† β„Žβˆ’1(πœ† NOUN cana-1623 167 3 , , PUNCT cana-1623 167 4 πœ‚ πœ‚ PROPN cana-1623 167 5 ∣ ∣ PROPN cana-1623 167 6 οΏ½ οΏ½ PROPN cana-1623 167 7 Μƒ Μƒ PROPN cana-1623 167 8 οΏ½ οΏ½ NOUN cana-1623 167 9 𝑖)∫ 𝑖)∫ PROPN cana-1623 167 10 β€Š β€Š SPACE cana-1623 167 11 + + PROPN cana-1623 167 12 ∞ ∞ PROPN cana-1623 167 13 0 0 NUM cana-1623 167 14 β€Š β€Š SPACE cana-1623 167 15 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 167 16 ) ) PUNCT cana-1623 167 17 βˆ‚3𝑦(𝑑 βˆ‚3𝑦(𝑑 NUM cana-1623 167 18 ; ; PUNCT cana-1623 167 19 πœ† πœ† X cana-1623 167 20 , , PUNCT cana-1623 167 21 πœ‚ πœ‚ NOUN cana-1623 167 22 ) ) PUNCT cana-1623 167 23 βˆ‚πœ‚2 βˆ‚πœ‚2 PROPN cana-1623 167 24 βˆ‚πœ† βˆ‚πœ† PROPN cana-1623 167 25 𝑑𝑑 𝑑𝑑 ADP cana-1623 167 26 ] ] PUNCT cana-1623 167 27 π»πœ‚πœ‚πœ‚ π»πœ‚πœ‚πœ‚ PROPN cana-1623 167 28 = = PROPN cana-1623 167 29 βˆ‘ βˆ‘ NOUN cana-1623 167 30 β€Š β€Š SPACE cana-1623 167 31 𝑛 𝑛 PRON cana-1623 167 32 𝑖=1 𝑖=1 PROPN cana-1623 167 33 β€Š β€Š SPACE cana-1623 168 1 [ [ X cana-1623 168 2 2β„Žβˆ’3(πœ† 2β„Žβˆ’3(πœ† NUM cana-1623 168 3 , , PUNCT cana-1623 168 4 πœ‚ πœ‚ PROPN cana-1623 168 5 ∣ ∣ PROPN cana-1623 168 6 οΏ½ οΏ½ PROPN cana-1623 168 7 Μƒ Μƒ PROPN cana-1623 168 8 οΏ½ οΏ½ NOUN cana-1623 168 9 𝑖 𝑖 NUM cana-1623 168 10 ) ) PUNCT cana-1623 168 11 ( ( PUNCT cana-1623 168 12 ∫ ∫ PROPN cana-1623 168 13 β€Š β€Š SPACE cana-1623 169 1 + + PROPN cana-1623 169 2 ∞ ∞ PROPN cana-1623 169 3 0 0 NUM cana-1623 169 4 β€Š β€Š SPACE cana-1623 169 5 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 169 6 ) ) PUNCT cana-1623 169 7 βˆ‚π‘¦(𝑑 βˆ‚π‘¦(𝑑 PROPN cana-1623 169 8 ; ; PUNCT cana-1623 169 9 πœ† πœ† X cana-1623 169 10 , , PUNCT cana-1623 169 11 πœ‚ πœ‚ NOUN cana-1623 169 12 ) ) PUNCT cana-1623 169 13 βˆ‚πœ‚ βˆ‚πœ‚ PROPN cana-1623 169 14 𝑑𝑑 𝑑𝑑 ADP cana-1623 169 15 ) ) PUNCT cana-1623 169 16 3 3 NUM cana-1623 169 17 + + SYM cana-1623 169 18 β„Žβˆ’1(πœ† β„Žβˆ’1(πœ† NOUN cana-1623 169 19 , , PUNCT cana-1623 169 20 πœ‚ πœ‚ PROPN cana-1623 169 21 ∣ ∣ PROPN cana-1623 169 22 οΏ½ οΏ½ PROPN cana-1623 169 23 Μƒ Μƒ PROPN cana-1623 169 24 οΏ½ οΏ½ NOUN cana-1623 169 25 𝑖)∫ 𝑖)∫ PROPN cana-1623 169 26 β€Š β€Š SPACE cana-1623 169 27 + + PROPN cana-1623 169 28 ∞ ∞ PROPN cana-1623 169 29 0 0 NUM cana-1623 169 30 β€Š β€Š SPACE cana-1623 169 31 𝑠𝑖(𝑑 𝑠𝑖(𝑑 NOUN cana-1623 169 32 ) ) PUNCT cana-1623 169 33 βˆ‚3𝑦(𝑑 βˆ‚3𝑦(𝑑 NOUN cana-1623 169 34 , , PUNCT cana-1623 169 35 πœ† πœ† NOUN cana-1623 169 36 , , PUNCT cana-1623 169 37 πœ‚ πœ‚ NOUN cana-1623 169 38 ) ) PUNCT cana-1623 169 39 βˆ‚πœ‚3 βˆ‚πœ‚3 NOUN cana-1623 169 40 𝑑𝑑 𝑑𝑑 ADP cana-1623 169 41 ] ] PUNCT cana-1623 169 42 the the DET cana-1623 169 43 loss loss NOUN cana-1623 169 44 function function NOUN cana-1623 169 45 plays play VERB cana-1623 169 46 an an DET cana-1623 169 47 important important ADJ cana-1623 169 48 role role NOUN cana-1623 169 49 in in ADP cana-1623 169 50 bayesian bayesian NOUN cana-1623 169 51 statistical statistical ADJ cana-1623 169 52 inference inference NOUN cana-1623 169 53 since since SCONJ cana-1623 169 54 it it PRON cana-1623 169 55 evaluates evaluate VERB cana-1623 169 56 the the DET cana-1623 169 57 difference difference NOUN cana-1623 169 58 between between ADP cana-1623 169 59 model model NOUN cana-1623 169 60 predictions prediction NOUN cana-1623 169 61 and and CCONJ cana-1623 169 62 actual actual ADJ cana-1623 169 63 outcomes outcome NOUN cana-1623 169 64 . . PUNCT cana-1623 170 1 in in ADP cana-1623 170 2 the the DET cana-1623 170 3 bayesian bayesian NOUN cana-1623 170 4 framework framework NOUN cana-1623 170 5 , , PUNCT cana-1623 170 6 we we PRON cana-1623 170 7 used use VERB cana-1623 170 8 the the DET cana-1623 170 9 posterior posterior ADJ cana-1623 170 10 distribution distribution NOUN cana-1623 170 11 to to PART cana-1623 170 12 represent represent VERB cana-1623 170 13 uncertainty uncertainty NOUN cana-1623 170 14 and and CCONJ cana-1623 170 15 the the DET cana-1623 170 16 loss loss NOUN cana-1623 170 17 function function NOUN cana-1623 170 18 to to PART cana-1623 170 19 select select VERB cana-1623 170 20 the the DET cana-1623 170 21 best good ADJ cana-1623 170 22 decision decision NOUN cana-1623 170 23 or or CCONJ cana-1623 170 24 prediction prediction NOUN cana-1623 170 25 . . PUNCT cana-1623 171 1 different different ADJ cana-1623 171 2 loss loss NOUN cana-1623 171 3 functions function NOUN cana-1623 171 4 produce produce VERB cana-1623 171 5 different different ADJ cana-1623 171 6 conclusions conclusion NOUN cana-1623 171 7 or or CCONJ cana-1623 171 8 predictions prediction NOUN cana-1623 171 9 ; ; PUNCT cana-1623 171 10 thus thus ADV cana-1623 171 11 , , PUNCT cana-1623 171 12 choosing choose VERB cana-1623 171 13 an an DET cana-1623 171 14 appropriate appropriate ADJ cana-1623 171 15 loss loss NOUN cana-1623 171 16 function function NOUN cana-1623 171 17 is be AUX cana-1623 171 18 critical critical ADJ cana-1623 171 19 to to ADP cana-1623 171 20 the the DET cana-1623 171 21 precision precision NOUN cana-1623 171 22 and and CCONJ cana-1623 171 23 reliability reliability NOUN cana-1623 171 24 of of ADP cana-1623 171 25 bayesian bayesian NOUN cana-1623 171 26 inference inference NOUN cana-1623 171 27 . . PUNCT cana-1623 172 1 then then ADV cana-1623 172 2 , , PUNCT cana-1623 172 3 we we PRON cana-1623 172 4 investigate investigate VERB cana-1623 172 5 bayesian bayesian NOUN cana-1623 172 6 estimate estimate NOUN cana-1623 172 7 of of ADP cana-1623 172 8 unknown unknown ADJ cana-1623 172 9 parameters parameter NOUN cana-1623 172 10 using use VERB cana-1623 172 11 the the DET cana-1623 172 12 se se PROPN cana-1623 172 13 and and CCONJ cana-1623 172 14 sse sse PROPN cana-1623 172 15 loss loss NOUN cana-1623 172 16 functions function NOUN cana-1623 172 17 . . PUNCT cana-1623 173 1 2.6 2.6 NUM cana-1623 173 2 bayesian bayesian NOUN cana-1623 173 3 estimation estimation NOUN cana-1623 173 4 under under ADP cana-1623 173 5 the the DET cana-1623 173 6 se se PROPN cana-1623 173 7 loss loss PROPN cana-1623 173 8 function function NOUN cana-1623 173 9 the the DET cana-1623 173 10 se se PROPN cana-1623 173 11 loss loss NOUN cana-1623 173 12 function function NOUN cana-1623 173 13 is be AUX cana-1623 173 14 defined define VERB cana-1623 173 15 as as ADP cana-1623 173 16 follows follow VERB cana-1623 173 17 , , PUNCT cana-1623 173 18 𝐿1(πœƒ 𝐿1(πœƒ PROPN cana-1623 173 19 , , PUNCT cana-1623 173 20 οΏ½ οΏ½ PROPN cana-1623 173 21 Μ‚ Μ‚ NOUN cana-1623 173 22 οΏ½ οΏ½ NOUN cana-1623 173 23 ) ) PUNCT cana-1623 173 24 = = SYM cana-1623 173 25 οΏ½ οΏ½ PROPN cana-1623 173 26 Μ‚ Μ‚ PROPN cana-1623 173 27 οΏ½ οΏ½ NOUN cana-1623 173 28 πœƒ πœƒ NOUN cana-1623 173 29 + + NUM cana-1623 173 30 πœƒ πœƒ PRON cana-1623 173 31 οΏ½ οΏ½ NOUN cana-1623 173 32 Μ‚ Μ‚ SYM cana-1623 173 33 οΏ½ οΏ½ NOUN cana-1623 173 34 βˆ’ βˆ’ PROPN cana-1623 173 35 2 2 NUM cana-1623 173 36 where where SCONJ cana-1623 173 37 οΏ½ οΏ½ PROPN cana-1623 173 38 Μ‚ Μ‚ SYM cana-1623 173 39 οΏ½ οΏ½ NOUN cana-1623 173 40 is be AUX cana-1623 173 41 the the DET cana-1623 173 42 estimator estimator NOUN cana-1623 173 43 of of ADP cana-1623 173 44 unknown unknown ADJ cana-1623 173 45 parameter parameter NOUN cana-1623 173 46 πœƒ. πœƒ. PROPN cana-1623 173 47 3 3 X cana-1623 173 48 . . PUNCT cana-1623 174 1 real real ADJ cana-1623 174 2 data datum NOUN cana-1623 174 3 analysis analysis NOUN cana-1623 174 4 in in ADP cana-1623 174 5 this this DET cana-1623 174 6 application application NOUN cana-1623 174 7 , , PUNCT cana-1623 174 8 we we PRON cana-1623 174 9 used use VERB cana-1623 174 10 real real ADJ cana-1623 174 11 - - PUNCT cana-1623 174 12 time time NOUN cana-1623 174 13 agriculture agriculture NOUN cana-1623 174 14 data datum NOUN cana-1623 174 15 from from ADP cana-1623 174 16 kaggle.com kaggle.com X cana-1623 174 17 [ [ X cana-1623 174 18 12 12 NUM cana-1623 174 19 ] ] PUNCT cana-1623 174 20 to to PART cana-1623 174 21 analyze analyze VERB cana-1623 174 22 the the DET cana-1623 174 23 andra andra PROPN cana-1623 174 24 agriculture agriculture PROPN cana-1623 174 25 data datum NOUN cana-1623 174 26 set set VERB cana-1623 174 27 in in ADP cana-1623 174 28 2019 2019 NUM cana-1623 174 29 . . PUNCT cana-1623 175 1 we we PRON cana-1623 175 2 evaluated evaluate VERB cana-1623 175 3 the the DET cana-1623 175 4 data datum NOUN cana-1623 175 5 using use VERB cana-1623 175 6 an an DET cana-1623 175 7 inverse inverse ADJ cana-1623 175 8 weibull weibull NOUN cana-1623 175 9 distribution distribution NOUN cana-1623 175 10 with with ADP cana-1623 175 11 intuitionistic intuitionistic ADJ cana-1623 175 12 fuzzy fuzzy ADJ cana-1623 175 13 data datum NOUN cana-1623 175 14 , , PUNCT cana-1623 175 15 as as SCONJ cana-1623 175 16 shown show VERB cana-1623 175 17 in in ADP cana-1623 175 18 tables table NOUN cana-1623 175 19 1 1 NUM cana-1623 175 20 and and CCONJ cana-1623 175 21 2 2 NUM cana-1623 175 22 . . PUNCT cana-1623 175 23 mean mean ADJ cana-1623 175 24 square square ADJ cana-1623 175 25 error error NOUN cana-1623 175 26 for for ADP cana-1623 175 27 each each DET cana-1623 175 28 crop crop NOUN cana-1623 175 29 1.0551 1.0551 NUM cana-1623 175 30 , , PUNCT cana-1623 175 31 0.0419 0.0419 NUM cana-1623 175 32 , , PUNCT cana-1623 175 33 0.2632 0.2632 NUM cana-1623 175 34 , , PUNCT cana-1623 175 35 28.5692 28.5692 NUM cana-1623 175 36 , , PUNCT cana-1623 175 37 0.0126 0.0126 NUM cana-1623 175 38 , , PUNCT cana-1623 175 39 0.0507 0.0507 NUM cana-1623 175 40 , , PUNCT cana-1623 175 41 0.0915 0.0915 NUM cana-1623 175 42 , , PUNCT cana-1623 175 43 0.0125 0.0125 NUM cana-1623 175 44 , , PUNCT cana-1623 175 45 1.0093 1.0093 NUM cana-1623 175 46 , , PUNCT cana-1623 175 47 0.0397 0.0397 NUM cana-1623 175 48 and and CCONJ cana-1623 175 49 bayesian bayesian NOUN cana-1623 175 50 estimates estimate NOUN cana-1623 175 51 and and CCONJ cana-1623 175 52 reliability reliability NOUN cana-1623 175 53 ( ( PUNCT cana-1623 175 54 mse mse NOUN cana-1623 175 55 ) ) PUNCT cana-1623 175 56 for for ADP cana-1623 175 57 each each DET cana-1623 175 58 crop crop NOUN cana-1623 175 59 0.0172 0.0172 NUM cana-1623 175 60 , , PUNCT cana-1623 175 61 0.0173 0.0173 NUM cana-1623 175 62 , , PUNCT cana-1623 175 63 0.0129 0.0129 NUM cana-1623 175 64 , , PUNCT cana-1623 175 65 0.0241 0.0241 NUM cana-1623 175 66 , , PUNCT cana-1623 175 67 0.0075 0.0075 NUM cana-1623 175 68 , , PUNCT cana-1623 175 69 0.0212 0.0212 NUM cana-1623 175 70 , , PUNCT cana-1623 175 71 0.0139 0.0139 NUM cana-1623 175 72 , , PUNCT cana-1623 175 73 0.0151 0.0151 NUM cana-1623 175 74 , , PUNCT cana-1623 175 75 communications communication NOUN cana-1623 175 76 on on ADP cana-1623 175 77 applied apply VERB cana-1623 175 78 nonlinear nonlinear ADJ cana-1623 175 79 analysis analysis NOUN cana-1623 175 80 issn issn NOUN cana-1623 175 81 : : PUNCT cana-1623 175 82 1074 1074 NUM cana-1623 175 83 - - PUNCT cana-1623 175 84 133x 133x NUM cana-1623 175 85 vol vol NOUN cana-1623 175 86 32 32 NUM cana-1623 175 87 no no NOUN cana-1623 175 88 . . NOUN cana-1623 175 89 1 1 NUM cana-1623 175 90 ( ( PUNCT cana-1623 175 91 2025 2025 NUM cana-1623 175 92 ) ) PUNCT cana-1623 175 93 99 99 NUM cana-1623 175 94 https://internationalpubls.com https://internationalpubls.com X cana-1623 175 95 0.0372 0.0372 NUM cana-1623 175 96 , , PUNCT cana-1623 175 97 and and CCONJ cana-1623 175 98 0.0073 0.0073 NUM cana-1623 175 99 respectively respectively ADV cana-1623 175 100 , , PUNCT cana-1623 175 101 estimated estimate VERB cana-1623 175 102 fuzzy fuzzy ADJ cana-1623 175 103 parameters parameter NOUN cana-1623 175 104 for for ADP cana-1623 175 105 the the DET cana-1623 175 106 πœ† πœ† NOUN cana-1623 175 107 are be AUX cana-1623 175 108 2.5554 2.5554 NUM cana-1623 175 109 , , PUNCT cana-1623 175 110 2.8394 2.8394 NUM cana-1623 175 111 and and CCONJ cana-1623 175 112 3.1233 3.1233 NUM cana-1623 175 113 for for ADP cana-1623 175 114 the the DET cana-1623 175 115 πœ‚ πœ‚ NOUN cana-1623 175 116 are be AUX cana-1623 175 117 3.6139 3.6139 NUM cana-1623 175 118 , , PUNCT cana-1623 175 119 4.0155 4.0155 NUM cana-1623 175 120 and and CCONJ cana-1623 175 121 4.4170 4.4170 NUM cana-1623 175 122 . . PUNCT cana-1623 176 1 table.1 table.1 NOUN cana-1623 176 2 . . PUNCT cana-1623 177 1 agriculture agriculture NOUN cana-1623 177 2 data datum NOUN cana-1623 177 3 of of ADP cana-1623 177 4 andra andra NOUN cana-1623 177 5 in in ADP cana-1623 177 6 the the DET cana-1623 177 7 year year NOUN cana-1623 177 8 of of ADP cana-1623 177 9 2019 2019 NUM cana-1623 177 10 . . PUNCT cana-1623 178 1 crop crop NOUN cana-1623 178 2 season season NOUN cana-1623 178 3 membership membership NOUN cana-1623 178 4 degree degree NOUN cana-1623 178 5 ( ( PUNCT cana-1623 178 6 ΞΌ\muΞΌ ΞΌ\muΞΌ NOUN cana-1623 178 7 ) ) PUNCT cana-1623 178 8 non non ADJ cana-1623 178 9 - - ADJ cana-1623 178 10 membership membership ADJ cana-1623 178 11 degree degree NOUN cana-1623 178 12 ( ( PUNCT cana-1623 178 13 Ξ½\nuΞ½ Ξ½\nuΞ½ NOUN cana-1623 178 14 ) ) PUNCT cana-1623 178 15 degree degree NOUN cana-1623 178 16 of of ADP cana-1623 178 17 uncertainty uncertainty NOUN cana-1623 178 18 ( ( PUNCT cana-1623 178 19 Ο€\piΟ€ Ο€\piΟ€ NOUN cana-1623 178 20 ) ) PUNCT cana-1623 178 21 arecanut arecanut NOUN cana-1623 178 22 kharif kharif NOUN cana-1623 178 23 0.70 0.70 NUM cana-1623 178 24 0.20 0.20 NUM cana-1623 178 25 0.10 0.10 NUM cana-1623 178 26 arhar arhar ADJ cana-1623 178 27 / / SYM cana-1623 178 28 tur tur NOUN cana-1623 178 29 kharif kharif NOUN cana-1623 178 30 0.80 0.80 NUM cana-1623 178 31 0.10 0.10 NUM cana-1623 178 32 0.10 0.10 NUM cana-1623 178 33 arhar arhar ADJ cana-1623 178 34 / / SYM cana-1623 178 35 tur tur NOUN cana-1623 178 36 rabi rabi NOUN cana-1623 178 37 0.60 0.60 NUM cana-1623 178 38 0.30 0.30 NUM cana-1623 178 39 0.10 0.10 NUM cana-1623 178 40 bajra bajra NOUN cana-1623 178 41 kharif kharif NOUN cana-1623 178 42 0.65 0.65 NUM cana-1623 178 43 0.25 0.25 NUM cana-1623 178 44 0.10 0.10 NUM cana-1623 178 45 bajra bajra NOUN cana-1623 178 46 rabi rabi NOUN cana-1623 178 47 0.55 0.55 NUM cana-1623 178 48 0.35 0.35 NUM cana-1623 178 49 0.10 0.10 NUM cana-1623 178 50 banana banana NOUN cana-1623 178 51 whole whole ADJ cana-1623 178 52 year year NOUN cana-1623 178 53 0.90 0.90 NUM cana-1623 178 54 0.05 0.05 NUM cana-1623 178 55 0.05 0.05 NUM cana-1623 178 56 black black ADJ cana-1623 178 57 pepper pepper NOUN cana-1623 178 58 whole whole ADJ cana-1623 178 59 year year NOUN cana-1623 178 60 0.85 0.85 NUM cana-1623 178 61 0.10 0.10 NUM cana-1623 178 62 0.05 0.05 NUM cana-1623 178 63 cashewnut cashewnut NOUN cana-1623 178 64 kharif kharif NOUN cana-1623 178 65 0.75 0.75 NUM cana-1623 178 66 0.20 0.20 NUM cana-1623 178 67 0.05 0.05 NUM cana-1623 178 68 castor castor NOUN cana-1623 178 69 seed seed NOUN cana-1623 178 70 kharif kharif NOUN cana-1623 178 71 0.60 0.60 NUM cana-1623 178 72 0.30 0.30 NUM cana-1623 178 73 0.10 0.10 NUM cana-1623 178 74 castor castor NOUN cana-1623 178 75 seed seed NOUN cana-1623 178 76 rabi rabi NOUN cana-1623 178 77 0.50 0.50 NUM cana-1623 178 78 0.40 0.40 NUM cana-1623 178 79 0.10 0.10 NUM cana-1623 178 80 table.2 table.2 NOUN cana-1623 178 81 . . PUNCT cana-1623 179 1 intuitionistic intuitionistic ADJ cana-1623 179 2 fuzzy fuzzy ADJ cana-1623 179 3 data datum NOUN cana-1623 179 4 values value NOUN cana-1623 179 5 of of ADP cana-1623 179 6 andra andra PRON cana-1623 179 7 in in ADP cana-1623 179 8 the the DET cana-1623 179 9 year year NOUN cana-1623 179 10 of of ADP cana-1623 179 11 2019 2019 NUM cana-1623 179 12 . . PUNCT cana-1623 180 1 maximum maximum ADJ cana-1623 180 2 likelihood likelihood NOUN cana-1623 180 3 estimator estimator NOUN cana-1623 180 4 ( ( PUNCT cana-1623 180 5 mle mle PROPN cana-1623 180 6 ) ) PUNCT cana-1623 180 7 table table NOUN cana-1623 180 8 πœ† πœ† ADP cana-1623 180 9 = = PUNCT cana-1623 180 10 4.3956 4.3956 NUM cana-1623 180 11 and and CCONJ cana-1623 180 12 πœ‚ πœ‚ NOUN cana-1623 180 13 = = SYM cana-1623 180 14 7.3543 7.3543 NUM cana-1623 180 15 . . PUNCT cana-1623 181 1 s.no s.no AUX cana-1623 181 2 observed observe VERB cana-1623 181 3 yield(kg yield(kg ADV cana-1623 181 4 / / SYM cana-1623 181 5 ha ha INTJ cana-1623 181 6 ) ) PUNCT cana-1623 181 7 predicted predict VERB cana-1623 181 8 yield(kg yield(kg PROPN cana-1623 181 9 / / SYM cana-1623 181 10 ha ha NOUN cana-1623 181 11 ) ) PUNCT cana-1623 181 12 1 1 NUM cana-1623 181 13 5.00 5.00 NUM cana-1623 181 14 5.00 5.00 NUM cana-1623 181 15 2 2 NUM cana-1623 181 16 4.67 4.67 NUM cana-1623 181 17 4.67 4.67 NUM cana-1623 181 18 3 3 NUM cana-1623 181 19 4.00 4.00 NUM cana-1623 181 20 4.00 4.00 NUM cana-1623 181 21 4 4 NUM cana-1623 181 22 3.60 3.60 NUM cana-1623 181 23 3.60 3.60 NUM cana-1623 181 24 5 5 NUM cana-1623 181 25 3.33 3.33 NUM cana-1623 181 26 3.33 3.33 NUM cana-1623 181 27 crop crop NOUN cana-1623 181 28 season season NOUN cana-1623 181 29 area(ha area(ha NOUN cana-1623 181 30 ) ) PUNCT cana-1623 181 31 ( ( PUNCT cana-1623 181 32 mt mt PROPN cana-1623 181 33 ) ) PUNCT cana-1623 181 34 ( ( PUNCT cana-1623 181 35 kg kg X cana-1623 181 36 / / SYM cana-1623 181 37 ha ha INTJ cana-1623 181 38 ) ) PUNCT cana-1623 181 39 value(β‚Ή value(β‚Ή PROPN cana-1623 181 40 ) ) PUNCT cana-1623 181 41 ( ( PUNCT cana-1623 181 42 β‚Ή β‚Ή NOUN cana-1623 181 43 /kg /kg NOUN cana-1623 181 44 ) ) PUNCT cana-1623 181 45 crop crop NOUN cana-1623 181 46 arecanut arecanut PROPN cana-1623 181 47 kharif kharif PROPN cana-1623 181 48 1096 1096 NUM cana-1623 181 49 10418 10418 NUM cana-1623 181 50 899.2 899.2 NUM cana-1623 181 51 188249 188249 NUM cana-1623 181 52 405.52 405.52 NUM cana-1623 181 53 7.253333 7.253333 NUM cana-1623 181 54 arhar arhar ADJ cana-1623 181 55 / / SYM cana-1623 181 56 tur tur X cana-1623 181 57 kharif kharif NOUN cana-1623 181 58 237647 237647 NUM cana-1623 181 59 114451 114451 NUM cana-1623 181 60 899.2 899.2 NUM cana-1623 181 61 40818249 40818249 NUM cana-1623 181 62 87929.39 87929.39 NUM cana-1623 181 63 0.44 0.44 NUM cana-1623 181 64 arhar arhar ADJ cana-1623 181 65 / / SYM cana-1623 181 66 tur tur NOUN cana-1623 181 67 rabi rabi NOUN cana-1623 181 68 5940 5940 NUM cana-1623 181 69 3747 3747 NUM cana-1623 181 70 899.2 899.2 NUM cana-1623 181 71 1020254 1020254 NUM cana-1623 181 72 2197.8 2197.8 NUM cana-1623 181 73 0.43 0.43 NUM cana-1623 181 74 bajra bajra NOUN cana-1623 181 75 kharif kharif NOUN cana-1623 181 76 20484 20484 NUM cana-1623 181 77 47045 47045 NUM cana-1623 181 78 899.2 899.2 NUM cana-1623 181 79 3518332 3518332 NUM cana-1623 181 80 7579.08 7579.08 NUM cana-1623 181 81 2.004545 2.004545 NUM cana-1623 181 82 bajra bajra NOUN cana-1623 181 83 rabi rabi NOUN cana-1623 181 84 4592 4592 NUM cana-1623 181 85 11322 11322 NUM cana-1623 181 86 899.2 899.2 NUM cana-1623 181 87 788721.9 788721.9 NUM cana-1623 181 88 1699.04 1699.04 NUM cana-1623 181 89 2.48 2.48 NUM cana-1623 181 90 banana banana NOUN cana-1623 181 91 whole whole ADJ cana-1623 181 92 year year NOUN cana-1623 181 93 97695 97695 NUM cana-1623 181 94 5861700 5861700 NUM cana-1623 181 95 899.2 899.2 NUM cana-1623 181 96 16780093 16780093 NUM cana-1623 181 97 36147.15 36147.15 NUM cana-1623 181 98 60 60 NUM cana-1623 181 99 black black ADJ cana-1623 181 100 pepper pepper NOUN cana-1623 181 101 whole whole ADJ cana-1623 181 102 year year NOUN cana-1623 181 103 17645 17645 NUM cana-1623 181 104 17645 17645 NUM cana-1623 181 105 899.2 899.2 NUM cana-1623 181 106 3030705 3030705 NUM cana-1623 181 107 6528.65 6528.65 NUM cana-1623 181 108 1 1 NUM cana-1623 181 109 cashewnut cashewnut NOUN cana-1623 181 110 kharif kharif NOUN cana-1623 181 111 115785 115785 NUM cana-1623 181 112 115785 115785 NUM cana-1623 181 113 899.2 899.2 NUM cana-1623 181 114 19887232 19887232 NUM cana-1623 181 115 42840.45 42840.45 NUM cana-1623 181 116 1 1 NUM cana-1623 181 117 castor castor NOUN cana-1623 181 118 seed seed NOUN cana-1623 181 119 kharif kharif NOUN cana-1623 181 120 36827 36827 NUM cana-1623 181 121 25270 25270 NUM cana-1623 181 122 899.2 899.2 NUM cana-1623 181 123 6325406 6325406 NUM cana-1623 181 124 13625.99 13625.99 NUM cana-1623 181 125 0.7625 0.7625 NUM cana-1623 181 126 castor castor NOUN cana-1623 181 127 seed seed NOUN cana-1623 181 128 rabi rabi NOUN cana-1623 181 129 1056 1056 NUM cana-1623 181 130 637 637 NUM cana-1623 181 131 899.2 899.2 NUM cana-1623 181 132 181378.6 181378.6 NUM cana-1623 181 133 390.72 390.72 NUM cana-1623 181 134 0.684 0.684 NUM cana-1623 181 135 communications communication NOUN cana-1623 181 136 on on ADP cana-1623 181 137 applied apply VERB cana-1623 181 138 nonlinear nonlinear ADJ cana-1623 181 139 analysis analysis NOUN cana-1623 181 140 issn issn NOUN cana-1623 181 141 : : PUNCT cana-1623 181 142 1074 1074 NUM cana-1623 181 143 - - PUNCT cana-1623 181 144 133x 133x NUM cana-1623 181 145 vol vol NOUN cana-1623 181 146 32 32 NUM cana-1623 181 147 no no NOUN cana-1623 181 148 . . NOUN cana-1623 181 149 1 1 NUM cana-1623 181 150 ( ( PUNCT cana-1623 181 151 2025 2025 NUM cana-1623 181 152 ) ) PUNCT cana-1623 181 153 100 100 NUM cana-1623 181 154 https://internationalpubls.com https://internationalpubls.com X cana-1623 181 155 mathematical mathematical ADJ cana-1623 181 156 results result NOUN cana-1623 181 157 of of ADP cana-1623 181 158 the the DET cana-1623 181 159 inverse inverse ADJ cana-1623 181 160 weibull weibull NOUN cana-1623 181 161 distribution distribution NOUN cana-1623 181 162 . . PUNCT cana-1623 182 1 fig fig NOUN cana-1623 182 2 . . PUNCT cana-1623 183 1 1 1 NUM cana-1623 183 2 : : PUNCT cana-1623 183 3 pdf pdf NOUN cana-1623 183 4 and and CCONJ cana-1623 183 5 empirical empirical ADJ cana-1623 183 6 pdf pdf NOUN cana-1623 183 7 of of ADP cana-1623 183 8 inverse inverse ADJ cana-1623 183 9 weibull weibull NOUN cana-1623 183 10 distribution distribution NOUN cana-1623 183 11 using use VERB cana-1623 183 12 intuitionistic intuitionistic ADJ cana-1623 183 13 fuzzy fuzzy ADJ cana-1623 183 14 set set NOUN cana-1623 183 15 . . PUNCT cana-1623 184 1 fig fig NOUN cana-1623 184 2 . . PUNCT cana-1623 185 1 2 2 NUM cana-1623 185 2 : : PUNCT cana-1623 186 1 cdf cdf NOUN cana-1623 186 2 and and CCONJ cana-1623 186 3 empirical empirical ADJ cana-1623 186 4 cdf cdf NOUN cana-1623 186 5 of of ADP cana-1623 186 6 inverse inverse ADJ cana-1623 186 7 weibull weibull NOUN cana-1623 186 8 distribution distribution NOUN cana-1623 186 9 using use VERB cana-1623 186 10 intuitionistic intuitionistic ADJ cana-1623 186 11 fuzzy fuzzy ADJ cana-1623 186 12 set set NOUN cana-1623 186 13 . . PUNCT cana-1623 187 1 fig.3 fig.3 PROPN cana-1623 187 2 : : PUNCT cana-1623 187 3 reliability reliability NOUN cana-1623 187 4 estimation estimation NOUN cana-1623 187 5 of of ADP cana-1623 187 6 inverse inverse ADJ cana-1623 187 7 weibull weibull NOUN cana-1623 187 8 distribution distribution NOUN cana-1623 187 9 with with ADP cana-1623 187 10 intuitionistic intuitionistic ADJ cana-1623 187 11 fuzzy fuzzy ADJ cana-1623 187 12 set set NOUN cana-1623 187 13 . . PUNCT cana-1623 188 1 4 4 X cana-1623 188 2 . . NOUN cana-1623 188 3 results result NOUN cana-1623 188 4 and and CCONJ cana-1623 188 5 discussion discussion NOUN cana-1623 188 6 fuzzy fuzzy ADJ cana-1623 188 7 lifetime lifetime NOUN cana-1623 188 8 data datum NOUN cana-1623 188 9 can can AUX cana-1623 188 10 be be AUX cana-1623 188 11 used use VERB cana-1623 188 12 to to PART cana-1623 188 13 estimate estimate VERB cana-1623 188 14 the the DET cana-1623 188 15 reliability reliability NOUN cana-1623 188 16 of of ADP cana-1623 188 17 iwd iwd PROPN cana-1623 188 18 in in ADP cana-1623 188 19 real real ADJ cana-1623 188 20 - - PUNCT cana-1623 188 21 life life NOUN cana-1623 188 22 scenarios scenario NOUN cana-1623 188 23 due due ADJ cana-1623 188 24 to to ADP cana-1623 188 25 uncontrollable uncontrollable ADJ cana-1623 188 26 factors factor NOUN cana-1623 188 27 . . PUNCT cana-1623 189 1 however however ADV cana-1623 189 2 , , PUNCT cana-1623 189 3 fuzzy fuzzy ADJ cana-1623 189 4 sets set NOUN cana-1623 189 5 only only ADV cana-1623 189 6 have have VERB cana-1623 189 7 one one NUM cana-1623 189 8 membership membership NOUN cana-1623 189 9 degree degree NOUN cana-1623 189 10 parameter parameter NOUN cana-1623 189 11 , , PUNCT cana-1623 189 12 resulting result VERB cana-1623 189 13 in in ADP cana-1623 189 14 a a DET cana-1623 189 15 less less ADV cana-1623 189 16 precise precise ADJ cana-1623 189 17 description description NOUN cana-1623 189 18 of of ADP cana-1623 189 19 the the DET cana-1623 189 20 objective objective ADJ cana-1623 189 21 world world NOUN cana-1623 189 22 . . PUNCT cana-1623 190 1 in in ADP cana-1623 190 2 contrast contrast NOUN cana-1623 190 3 , , PUNCT cana-1623 190 4 intuitionistic intuitionistic ADJ cana-1623 190 5 fuzzy fuzzy ADJ cana-1623 190 6 sets set NOUN cana-1623 190 7 can can AUX cana-1623 190 8 better well ADV cana-1623 190 9 express express VERB cana-1623 190 10 uncertainty uncertainty NOUN cana-1623 190 11 and and CCONJ cana-1623 190 12 fuzziness fuzziness NOUN cana-1623 190 13 when when SCONJ cana-1623 190 14 dealing deal VERB cana-1623 190 15 with with ADP cana-1623 190 16 fuzzy fuzzy ADJ cana-1623 190 17 information information NOUN cana-1623 190 18 . . PUNCT cana-1623 191 1 the the DET cana-1623 191 2 em em PROPN cana-1623 191 3 algorithm algorithm NOUN cana-1623 191 4 was be AUX cana-1623 191 5 used use VERB cana-1623 191 6 to to PART cana-1623 191 7 obtain obtain VERB cana-1623 191 8 mles mle NOUN cana-1623 191 9 , , PUNCT cana-1623 191 10 followed follow VERB cana-1623 191 11 by by ADP cana-1623 191 12 the the DET cana-1623 191 13 lindley lindley NOUN cana-1623 191 14 approximation approximation NOUN cana-1623 191 15 to to PART cana-1623 191 16 obtain obtain VERB cana-1623 191 17 bes bes NOUN cana-1623 191 18 under under ADP cana-1623 191 19 se se PROPN cana-1623 191 20 and and CCONJ cana-1623 191 21 sse sse PROPN cana-1623 191 22 loss loss NOUN cana-1623 191 23 functions function NOUN cana-1623 191 24 . . PUNCT cana-1623 192 1 results result NOUN cana-1623 192 2 showed show VERB cana-1623 192 3 that that SCONJ cana-1623 192 4 changing change VERB cana-1623 192 5 the the DET cana-1623 192 6 true true ADJ cana-1623 192 7 values value NOUN cana-1623 192 8 of of ADP cana-1623 192 9 multiple multiple ADJ cana-1623 192 10 sets set NOUN cana-1623 192 11 of of ADP cana-1623 192 12 communications communication NOUN cana-1623 192 13 on on ADP cana-1623 192 14 applied apply VERB cana-1623 192 15 nonlinear nonlinear ADJ cana-1623 192 16 analysis analysis NOUN cana-1623 192 17 issn issn NOUN cana-1623 192 18 : : PUNCT cana-1623 192 19 1074 1074 NUM cana-1623 192 20 - - PUNCT cana-1623 192 21 133x 133x NUM cana-1623 192 22 vol vol NOUN cana-1623 192 23 32 32 NUM cana-1623 192 24 no no NOUN cana-1623 192 25 . . NOUN cana-1623 192 26 1 1 NUM cana-1623 192 27 ( ( PUNCT cana-1623 192 28 2025 2025 NUM cana-1623 192 29 ) ) PUNCT cana-1623 192 30 101 101 NUM cana-1623 192 31 https://internationalpubls.com https://internationalpubls.com X cana-1623 192 32 parameters parameter NOUN cana-1623 192 33 resulted result VERB cana-1623 192 34 in in ADP cana-1623 192 35 a a DET cana-1623 192 36 significantly significantly ADV cana-1623 192 37 smaller small ADJ cana-1623 192 38 mean mean ADJ cana-1623 192 39 square square ADJ cana-1623 192 40 error error NOUN cana-1623 192 41 under under ADP cana-1623 192 42 bayesian bayesian NOUN cana-1623 192 43 estimation estimation NOUN cana-1623 192 44 compared compare VERB cana-1623 192 45 to to ADP cana-1623 192 46 the the DET cana-1623 192 47 maximum maximum ADJ cana-1623 192 48 likelihood likelihood NOUN cana-1623 192 49 estimator estimator NOUN cana-1623 192 50 . . PUNCT cana-1623 193 1 kaggle.com kaggle.com X cana-1623 193 2 supports support VERB cana-1623 193 3 the the DET cana-1623 193 4 current current ADJ cana-1623 193 5 research research NOUN cana-1623 193 6 findings finding NOUN cana-1623 193 7 [ [ X cana-1623 193 8 11 11 NUM cana-1623 193 9 ] ] PUNCT cana-1623 193 10 . . PUNCT cana-1623 194 1 we we PRON cana-1623 194 2 discovered discover VERB cana-1623 194 3 results result NOUN cana-1623 194 4 for for ADP cana-1623 194 5 the the DET cana-1623 194 6 probability probability NOUN cana-1623 194 7 density density NOUN cana-1623 194 8 function function NOUN cana-1623 194 9 as as ADV cana-1623 194 10 well well ADV cana-1623 194 11 as as ADP cana-1623 194 12 pdf pdf NOUN cana-1623 194 13 and and CCONJ cana-1623 194 14 empirical empirical ADJ cana-1623 194 15 pdf pdf NOUN cana-1623 194 16 ( ( PUNCT cana-1623 194 17 fig.1 fig.1 PROPN cana-1623 194 18 ) ) PUNCT cana-1623 194 19 , , PUNCT cana-1623 194 20 cumulative cumulative ADJ cana-1623 194 21 density density NOUN cana-1623 194 22 function function NOUN cana-1623 194 23 as as ADV cana-1623 194 24 well well ADV cana-1623 194 25 as as ADP cana-1623 194 26 cdf cdf NOUN cana-1623 194 27 and and CCONJ cana-1623 194 28 empirical empirical ADJ cana-1623 194 29 cdf cdf PROPN cana-1623 194 30 ( ( PUNCT cana-1623 194 31 fig.2 fig.2 PROPN cana-1623 194 32 ) ) PUNCT cana-1623 194 33 , , PUNCT cana-1623 194 34 and and CCONJ cana-1623 194 35 reliability reliability NOUN cana-1623 194 36 estimation estimation NOUN cana-1623 194 37 ( ( PUNCT cana-1623 194 38 fig.3 fig.3 PROPN cana-1623 194 39 ) ) PUNCT cana-1623 194 40 in in ADP cana-1623 194 41 the the DET cana-1623 194 42 inverse inverse NOUN cana-1623 194 43 weibull weibull NOUN cana-1623 194 44 distribution distribution NOUN cana-1623 194 45 intuitionistic intuitionistic ADJ cana-1623 194 46 fuzzy fuzzy ADJ cana-1623 194 47 set set NOUN cana-1623 194 48 to to ADP cana-1623 194 49 the the DET cana-1623 194 50 agriculture agriculture NOUN cana-1623 194 51 problem problem NOUN cana-1623 194 52 of of ADP cana-1623 194 53 andra andra NOUN cana-1623 194 54 in in ADP cana-1623 194 55 the the DET cana-1623 194 56 year year NOUN cana-1623 194 57 of of ADP cana-1623 194 58 2019 2019 NUM cana-1623 194 59 with with ADP cana-1623 194 60 fuzzy fuzzy ADJ cana-1623 194 61 parameters parameter NOUN cana-1623 194 62 and and CCONJ cana-1623 194 63 supporting support VERB cana-1623 194 64 matlab matlab PROPN cana-1623 194 65 tool tool PROPN cana-1623 194 66 , , PUNCT cana-1623 194 67 which which PRON cana-1623 194 68 shows show VERB cana-1623 194 69 how how SCONJ cana-1623 194 70 well well ADV cana-1623 194 71 the the DET cana-1623 194 72 suggested suggest VERB cana-1623 194 73 technique technique NOUN cana-1623 194 74 performs perform VERB cana-1623 194 75 in in ADP cana-1623 194 76 predicting predict VERB cana-1623 194 77 crop crop NOUN cana-1623 194 78 production production NOUN cana-1623 194 79 for for ADP cana-1623 194 80 all all DET cana-1623 194 81 seasons season NOUN cana-1623 194 82 . . PUNCT cana-1623 195 1 5 5 X cana-1623 195 2 . . X cana-1623 195 3 conclusion conclusion NOUN cana-1623 195 4 in in ADP cana-1623 195 5 this this DET cana-1623 195 6 study study NOUN cana-1623 195 7 , , PUNCT cana-1623 195 8 the the DET cana-1623 195 9 inverse inverse ADJ cana-1623 195 10 weibull weibull NOUN cana-1623 195 11 distribution distribution NOUN cana-1623 195 12 model model NOUN cana-1623 195 13 is be AUX cana-1623 195 14 applied apply VERB cana-1623 195 15 to to ADP cana-1623 195 16 real real ADJ cana-1623 195 17 - - PUNCT cana-1623 195 18 time time NOUN cana-1623 195 19 data datum NOUN cana-1623 195 20 in in ADP cana-1623 195 21 a a DET cana-1623 195 22 fuzzy fuzzy ADJ cana-1623 195 23 environment environment NOUN cana-1623 195 24 . . PUNCT cana-1623 196 1 this this DET cana-1623 196 2 value value NOUN cana-1623 196 3 is be AUX cana-1623 196 4 generated generate VERB cana-1623 196 5 by by ADP cana-1623 196 6 combining combine VERB cana-1623 196 7 the the DET cana-1623 196 8 inverse inverse NOUN cana-1623 196 9 weibull weibull NOUN cana-1623 196 10 distribution distribution NOUN cana-1623 196 11 with with ADP cana-1623 196 12 the the DET cana-1623 196 13 intuitionistic intuitionistic ADJ cana-1623 196 14 fuzzy fuzzy ADJ cana-1623 196 15 set set NOUN cana-1623 196 16 , , PUNCT cana-1623 196 17 and and CCONJ cana-1623 196 18 the the DET cana-1623 196 19 resulting result VERB cana-1623 196 20 curve curve NOUN cana-1623 196 21 is be AUX cana-1623 196 22 used use VERB cana-1623 196 23 to to PART cana-1623 196 24 assess assess VERB cana-1623 196 25 the the DET cana-1623 196 26 performance performance NOUN cana-1623 196 27 of of ADP cana-1623 196 28 the the DET cana-1623 196 29 given give VERB cana-1623 196 30 data datum NOUN cana-1623 196 31 . . PUNCT cana-1623 197 1 the the DET cana-1623 197 2 calculated calculate VERB cana-1623 197 3 mean mean NOUN cana-1623 197 4 squared square VERB cana-1623 197 5 error error NOUN cana-1623 197 6 ( ( PUNCT cana-1623 197 7 mse mse NOUN cana-1623 197 8 ) ) PUNCT cana-1623 197 9 , , PUNCT cana-1623 197 10 maximum maximum ADJ cana-1623 197 11 likelihood likelihood NOUN cana-1623 197 12 estimator estimator NOUN cana-1623 197 13 ( ( PUNCT cana-1623 197 14 mle mle PROPN cana-1623 197 15 ) ) PUNCT cana-1623 197 16 and and CCONJ cana-1623 197 17 fuzzy fuzzy ADJ cana-1623 197 18 operating operating NOUN cana-1623 197 19 characteristic characteristic ADJ cana-1623 197 20 curves curve NOUN cana-1623 197 21 for for ADP cana-1623 197 22 several several ADJ cana-1623 197 23 functions function NOUN cana-1623 197 24 are be AUX cana-1623 197 25 examined examine VERB cana-1623 197 26 . . PUNCT cana-1623 198 1 this this PRON cana-1623 198 2 includes include VERB cana-1623 198 3 the the DET cana-1623 198 4 probability probability NOUN cana-1623 198 5 density density NOUN cana-1623 198 6 function function NOUN cana-1623 198 7 , , PUNCT cana-1623 198 8 empirical empirical ADJ cana-1623 198 9 pdf pdf NOUN cana-1623 198 10 , , PUNCT cana-1623 198 11 cumulative cumulative ADJ cana-1623 198 12 density density NOUN cana-1623 198 13 function function NOUN cana-1623 198 14 , , PUNCT cana-1623 198 15 empirical empirical ADJ cana-1623 198 16 cdf cdf NOUN cana-1623 198 17 , , PUNCT cana-1623 198 18 and and CCONJ cana-1623 198 19 reliability reliability NOUN cana-1623 198 20 estimation estimation NOUN cana-1623 198 21 for for ADP cana-1623 198 22 the the DET cana-1623 198 23 inverse inverse ADJ cana-1623 198 24 weibull weibull NOUN cana-1623 198 25 distribution distribution NOUN cana-1623 198 26 . . PUNCT cana-1623 199 1 this this DET cana-1623 199 2 study study NOUN cana-1623 199 3 determined determine VERB cana-1623 199 4 that that SCONJ cana-1623 199 5 the the DET cana-1623 199 6 proposed propose VERB cana-1623 199 7 approach approach NOUN cana-1623 199 8 can can AUX cana-1623 199 9 be be AUX cana-1623 199 10 implemented implement VERB cana-1623 199 11 if if SCONJ cana-1623 199 12 the the DET cana-1623 199 13 product product NOUN cana-1623 199 14 's 's PART cana-1623 199 15 quality quality NOUN cana-1623 199 16 is be AUX cana-1623 199 17 uncertain uncertain ADJ cana-1623 199 18 . . PUNCT cana-1623 200 1 the the DET cana-1623 200 2 study study NOUN cana-1623 200 3 discovered discover VERB cana-1623 200 4 that that SCONJ cana-1623 200 5 the the DET cana-1623 200 6 strategy strategy NOUN cana-1623 200 7 is be AUX cana-1623 200 8 quite quite ADV cana-1623 200 9 efficient efficient ADJ cana-1623 200 10 in in ADP cana-1623 200 11 unpredictable unpredictable ADJ cana-1623 200 12 agriculture agriculture NOUN cana-1623 200 13 and and CCONJ cana-1623 200 14 situations situation NOUN cana-1623 200 15 . . PUNCT cana-1623 201 1 references reference NOUN cana-1623 201 2 [ [ X cana-1623 201 3 1 1 NUM cana-1623 201 4 ] ] X cana-1623 201 5 zadeh zadeh PROPN cana-1623 201 6 , , PUNCT cana-1623 201 7 lotfi lotfi PROPN cana-1623 201 8 a. a. NOUN cana-1623 201 9 " " PUNCT cana-1623 201 10 fuzzy fuzzy ADJ cana-1623 201 11 sets set NOUN cana-1623 201 12 . . PUNCT cana-1623 201 13 " " PUNCT cana-1623 202 1 information information NOUN cana-1623 202 2 and and CCONJ cana-1623 202 3 control control NOUN cana-1623 202 4 8 8 NUM cana-1623 202 5 , , PUNCT cana-1623 202 6 no no INTJ cana-1623 202 7 . . NOUN cana-1623 202 8 3 3 NUM cana-1623 202 9 ( ( PUNCT cana-1623 202 10 1965 1965 NUM cana-1623 202 11 ): ): PUNCT cana-1623 202 12 338 338 NUM cana-1623 202 13 - - SYM cana-1623 202 14 353 353 NUM cana-1623 202 15 . . PUNCT cana-1623 203 1 [ [ X cana-1623 203 2 2 2 NUM cana-1623 203 3 ] ] X cana-1623 203 4 kumar kumar PROPN cana-1623 203 5 , , PUNCT cana-1623 203 6 pawan pawan PROPN cana-1623 203 7 , , PUNCT cana-1623 203 8 and and CCONJ cana-1623 203 9 s. s. PROPN cana-1623 203 10 b. b. PROPN cana-1623 203 11 singh singh PROPN cana-1623 203 12 . . PUNCT cana-1623 204 1 " " PUNCT cana-1623 204 2 fuzzy fuzzy ADJ cana-1623 204 3 system system NOUN cana-1623 204 4 reliability reliability NOUN cana-1623 204 5 using use VERB cana-1623 204 6 intuitionistic intuitionistic ADJ cana-1623 204 7 fuzzy fuzzy ADJ cana-1623 204 8 weibull weibull NOUN cana-1623 204 9 lifetime lifetime NOUN cana-1623 204 10 distribution distribution NOUN cana-1623 204 11 . . PUNCT cana-1623 204 12 " " PUNCT cana-1623 205 1 international international ADJ cana-1623 205 2 journal journal NOUN cana-1623 205 3 of of ADP cana-1623 205 4 reliability reliability NOUN cana-1623 205 5 and and CCONJ cana-1623 205 6 applications application NOUN cana-1623 205 7 16 16 NUM cana-1623 205 8 , , PUNCT cana-1623 205 9 no no INTJ cana-1623 205 10 . . NOUN cana-1623 205 11 1 1 NUM cana-1623 205 12 ( ( PUNCT cana-1623 205 13 2015 2015 NUM cana-1623 205 14 ): ): PUNCT cana-1623 205 15 15 15 NUM cana-1623 205 16 - - SYM cana-1623 205 17 26 26 NUM cana-1623 205 18 . . PUNCT cana-1623 206 1 [ [ X cana-1623 206 2 3 3 NUM cana-1623 206 3 ] ] X cana-1623 206 4 ebrahimnejad ebrahimnejad PROPN cana-1623 206 5 , , PUNCT cana-1623 206 6 ali ali PROPN cana-1623 206 7 , , PUNCT cana-1623 206 8 and and CCONJ cana-1623 206 9 ezzatallah ezzatallah PROPN cana-1623 206 10 b. b. PROPN cana-1623 206 11 jamkhaneh jamkhaneh PROPN cana-1623 206 12 . . PUNCT cana-1623 207 1 " " PUNCT cana-1623 207 2 system system NOUN cana-1623 207 3 reliability reliability NOUN cana-1623 207 4 using use VERB cana-1623 207 5 generalized generalized ADJ cana-1623 207 6 intuitionistic intuitionistic ADJ cana-1623 207 7 fuzzy fuzzy ADJ cana-1623 207 8 rayleigh rayleigh NOUN cana-1623 207 9 lifetime lifetime NOUN cana-1623 207 10 distribution distribution NOUN cana-1623 207 11 . . PUNCT cana-1623 207 12 " " PUNCT cana-1623 208 1 applications application NOUN cana-1623 208 2 and and CCONJ cana-1623 208 3 applied apply VERB cana-1623 208 4 mathematics mathematic NOUN cana-1623 208 5 : : PUNCT cana-1623 208 6 an an DET cana-1623 208 7 international international ADJ cana-1623 208 8 journal journal NOUN cana-1623 208 9 ( ( PUNCT cana-1623 208 10 aam aam PROPN cana-1623 208 11 ) ) PUNCT cana-1623 208 12 13 13 NUM cana-1623 208 13 , , PUNCT cana-1623 208 14 no no INTJ cana-1623 208 15 . . NOUN cana-1623 208 16 1 1 NUM cana-1623 208 17 ( ( PUNCT cana-1623 208 18 2018 2018 NUM cana-1623 208 19 ): ): PUNCT cana-1623 208 20 7 7 NUM cana-1623 208 21 . . PUNCT cana-1623 209 1 [ [ X cana-1623 209 2 4 4 NUM cana-1623 209 3 ] ] X cana-1623 209 4 akbari akbari PROPN cana-1623 209 5 , , PUNCT cana-1623 209 6 mohammad mohammad PROPN cana-1623 209 7 ghasem ghasem PROPN cana-1623 209 8 , , PUNCT cana-1623 209 9 and and CCONJ cana-1623 209 10 gholamreza gholamreza PROPN cana-1623 209 11 hesamian hesamian NOUN cana-1623 209 12 . . PUNCT cana-1623 210 1 " " PUNCT cana-1623 210 2 time time NOUN cana-1623 210 3 - - PUNCT cana-1623 210 4 dependent dependent ADJ cana-1623 210 5 intuitionistic intuitionistic ADJ cana-1623 210 6 fuzzy fuzzy ADJ cana-1623 210 7 system system NOUN cana-1623 210 8 reliability reliability NOUN cana-1623 210 9 analysis analysis NOUN cana-1623 210 10 . . PUNCT cana-1623 210 11 " " PUNCT cana-1623 210 12 soft soft ADJ cana-1623 210 13 computing computing NOUN cana-1623 210 14 24 24 NUM cana-1623 210 15 ( ( PUNCT cana-1623 210 16 2020 2020 NUM cana-1623 210 17 ): ): PUNCT cana-1623 210 18 14441 14441 NUM cana-1623 210 19 - - SYM cana-1623 210 20 14448 14448 NUM cana-1623 210 21 . . PUNCT cana-1623 211 1 [ [ X cana-1623 211 2 5 5 NUM cana-1623 211 3 ] ] X cana-1623 211 4 roohanizadeh roohanizadeh PROPN cana-1623 211 5 , , PUNCT cana-1623 211 6 zahra zahra PROPN cana-1623 211 7 , , PUNCT cana-1623 211 8 ezzatallah ezzatallah PROPN cana-1623 211 9 baloui baloui PROPN cana-1623 211 10 jamkhaneh jamkhaneh PROPN cana-1623 211 11 , , PUNCT cana-1623 211 12 and and CCONJ cana-1623 211 13 einolah einolah PROPN cana-1623 211 14 deiri deiri NOUN cana-1623 211 15 . . PUNCT cana-1623 212 1 " " PUNCT cana-1623 212 2 a a DET cana-1623 212 3 novel novel ADJ cana-1623 212 4 approach approach NOUN cana-1623 212 5 for for ADP cana-1623 212 6 analyzing analyze VERB cana-1623 212 7 system system NOUN cana-1623 212 8 reliability reliability NOUN cana-1623 212 9 using use VERB cana-1623 212 10 generalized generalized ADJ cana-1623 212 11 intuitionistic intuitionistic ADJ cana-1623 212 12 fuzzy fuzzy ADJ cana-1623 212 13 pareto pareto ADJ cana-1623 212 14 lifetime lifetime NOUN cana-1623 212 15 distribution distribution NOUN cana-1623 212 16 . . PUNCT cana-1623 212 17 " " PUNCT cana-1623 213 1 journal journal NOUN cana-1623 213 2 of of ADP cana-1623 213 3 mathematical mathematical ADJ cana-1623 213 4 extension extension NOUN cana-1623 213 5 16 16 NUM cana-1623 213 6 ( ( PUNCT cana-1623 213 7 2021 2021 NUM cana-1623 213 8 ) ) PUNCT cana-1623 213 9 . . PUNCT cana-1623 214 1 [ [ X cana-1623 214 2 6 6 NUM cana-1623 214 3 ] ] X cana-1623 214 4 bhandari bhandari PROPN cana-1623 214 5 , , PUNCT cana-1623 214 6 ashok ashok PROPN cana-1623 214 7 singh singh PROPN cana-1623 214 8 , , PUNCT cana-1623 214 9 akshay akshay PROPN cana-1623 214 10 kumar kumar PROPN cana-1623 214 11 , , PUNCT cana-1623 214 12 and and CCONJ cana-1623 214 13 mangey mangey PROPN cana-1623 214 14 ram ram NOUN cana-1623 214 15 . . PUNCT cana-1623 215 1 " " PUNCT cana-1623 215 2 fuzzy fuzzy ADJ cana-1623 215 3 reliability reliability NOUN cana-1623 215 4 evaluation evaluation NOUN cana-1623 215 5 of of ADP cana-1623 215 6 complex complex ADJ cana-1623 215 7 systems system NOUN cana-1623 215 8 using use VERB cana-1623 215 9 intuitionistic intuitionistic ADJ cana-1623 215 10 fuzzy fuzzy ADJ cana-1623 215 11 sets set NOUN cana-1623 215 12 . . PUNCT cana-1623 215 13 " " PUNCT cana-1623 216 1 in in ADP cana-1623 216 2 advancements advancement NOUN cana-1623 216 3 in in ADP cana-1623 216 4 fuzzy fuzzy ADJ cana-1623 216 5 reliability reliability NOUN cana-1623 216 6 theory theory NOUN cana-1623 216 7 , , PUNCT cana-1623 216 8 pp pp ADJ cana-1623 216 9 . . PUNCT cana-1623 216 10 166 166 NUM cana-1623 216 11 - - SYM cana-1623 216 12 180 180 NUM cana-1623 216 13 . . PUNCT cana-1623 216 14 igi igi PROPN cana-1623 216 15 global global PROPN cana-1623 216 16 , , PUNCT cana-1623 216 17 2021 2021 NUM cana-1623 216 18 . . PUNCT cana-1623 217 1 [ [ X cana-1623 217 2 7 7 NUM cana-1623 217 3 ] ] X cana-1623 217 4 taha taha PROPN cana-1623 217 5 , , PUNCT cana-1623 217 6 taha taha PROPN cana-1623 217 7 anwar anwar PROPN cana-1623 217 8 , , PUNCT cana-1623 217 9 and and CCONJ cana-1623 217 10 abbas abbas PROPN cana-1623 217 11 najim najim PROPN cana-1623 217 12 salman salman PROPN cana-1623 217 13 . . PUNCT cana-1623 218 1 " " PUNCT cana-1623 218 2 comparison comparison VERB cana-1623 218 3 different different ADJ cana-1623 218 4 estimation estimation NOUN cana-1623 218 5 method method NOUN cana-1623 218 6 for for ADP cana-1623 218 7 reliability reliability NOUN cana-1623 218 8 function function NOUN cana-1623 218 9 of of ADP cana-1623 218 10 rayleigh rayleigh ADJ cana-1623 218 11 distribution distribution NOUN cana-1623 218 12 based base VERB cana-1623 218 13 on on ADP cana-1623 218 14 fuzzy fuzzy ADJ cana-1623 218 15 lifetime lifetime NOUN cana-1623 218 16 data datum NOUN cana-1623 218 17 . . PUNCT cana-1623 218 18 " " PUNCT cana-1623 219 1 iraqi iraqi ADJ cana-1623 219 2 journal journal NOUN cana-1623 219 3 of of ADP cana-1623 219 4 science science NOUN cana-1623 219 5 ( ( PUNCT cana-1623 219 6 2022 2022 NUM cana-1623 219 7 ): ): PUNCT cana-1623 219 8 1707 1707 NUM cana-1623 219 9 - - SYM cana-1623 219 10 1719 1719 NUM cana-1623 219 11 . . PUNCT cana-1623 220 1 [ [ X cana-1623 220 2 8 8 NUM cana-1623 220 3 ] ] X cana-1623 220 4 bhadauria bhadauria NOUN cana-1623 220 5 , , PUNCT cana-1623 220 6 jaya jaya PROPN cana-1623 220 7 , , PUNCT cana-1623 220 8 sudha sudha PROPN cana-1623 220 9 rana rana PROPN cana-1623 220 10 , , PUNCT cana-1623 220 11 anita anita PROPN cana-1623 220 12 kumari kumari PROPN cana-1623 220 13 , , PUNCT cana-1623 220 14 and and CCONJ cana-1623 220 15 deepak deepak PROPN cana-1623 220 16 kumar kumar PROPN cana-1623 220 17 . . PUNCT cana-1623 221 1 " " PUNCT cana-1623 221 2 reliability reliability NOUN cana-1623 221 3 analysis analysis NOUN cana-1623 221 4 of of ADP cana-1623 221 5 different different ADJ cana-1623 221 6 complex complex ADJ cana-1623 221 7 systems system NOUN cana-1623 221 8 using use VERB cana-1623 221 9 intuitionistic intuitionistic ADJ cana-1623 221 10 trapezoidal trapezoidal ADJ cana-1623 221 11 fuzzy fuzzy ADJ cana-1623 221 12 number number NOUN cana-1623 221 13 . . PUNCT cana-1623 221 14 " " PUNCT cana-1623 222 1 in in ADP cana-1623 222 2 2022 2022 NUM cana-1623 222 3 7th 7th ADJ cana-1623 222 4 international international ADJ cana-1623 222 5 conference conference NOUN cana-1623 222 6 on on ADP cana-1623 222 7 computing computing NOUN cana-1623 222 8 , , PUNCT cana-1623 222 9 communication communication NOUN cana-1623 222 10 and and CCONJ cana-1623 222 11 security security NOUN cana-1623 222 12 ( ( PUNCT cana-1623 222 13 icccs icccs PROPN cana-1623 222 14 ) ) PUNCT cana-1623 222 15 , , PUNCT cana-1623 222 16 pp pp PROPN cana-1623 222 17 . . PUNCT cana-1623 223 1 1 1 NUM cana-1623 223 2 - - SYM cana-1623 223 3 6 6 NUM cana-1623 223 4 . . PUNCT cana-1623 223 5 ieee ieee NOUN cana-1623 223 6 , , PUNCT cana-1623 223 7 2022 2022 NUM cana-1623 223 8 . . PUNCT cana-1623 224 1 [ [ X cana-1623 224 2 9 9 NUM cana-1623 224 3 ] ] X cana-1623 224 4 chachra chachra NOUN cana-1623 224 5 , , PUNCT cana-1623 224 6 aayushi aayushi PROPN cana-1623 224 7 , , PUNCT cana-1623 224 8 akshay akshay PROPN cana-1623 224 9 kumar kumar PROPN cana-1623 224 10 , , PUNCT cana-1623 224 11 and and CCONJ cana-1623 224 12 mangey mangey PROPN cana-1623 224 13 ram ram NOUN cana-1623 224 14 . . PUNCT cana-1623 225 1 " " PUNCT cana-1623 225 2 intuitionistic intuitionistic ADJ cana-1623 225 3 fuzzy fuzzy ADJ cana-1623 225 4 approach approach NOUN cana-1623 225 5 to to ADP cana-1623 225 6 reliability reliability NOUN cana-1623 225 7 assessment assessment NOUN cana-1623 225 8 of of ADP cana-1623 225 9 multi multi ADJ cana-1623 225 10 - - ADJ cana-1623 225 11 state state ADJ cana-1623 225 12 systems system NOUN cana-1623 225 13 . . PUNCT cana-1623 225 14 " " PUNCT cana-1623 226 1 mathematics mathematic NOUN cana-1623 226 2 and and CCONJ cana-1623 226 3 computers computer NOUN cana-1623 226 4 in in ADP cana-1623 226 5 simulation simulation NOUN cana-1623 226 6 212 212 NUM cana-1623 226 7 ( ( PUNCT cana-1623 226 8 2023 2023 NUM cana-1623 226 9 ): ): PUNCT cana-1623 226 10 489 489 NUM cana-1623 226 11 - - SYM cana-1623 226 12 503 503 NUM cana-1623 226 13 . . PUNCT cana-1623 227 1 [ [ X cana-1623 227 2 10 10 NUM cana-1623 227 3 ] ] X cana-1623 227 4 patrai patrai NOUN cana-1623 227 5 , , PUNCT cana-1623 227 6 kalika kalika NOUN cana-1623 227 7 , , PUNCT cana-1623 227 8 and and CCONJ cana-1623 227 9 surbhi surbhi PROPN cana-1623 227 10 gupta gupta PROPN cana-1623 227 11 . . PUNCT cana-1623 228 1 " " PUNCT cana-1623 228 2 reliability reliability NOUN cana-1623 228 3 estimation estimation NOUN cana-1623 228 4 of of ADP cana-1623 228 5 a a DET cana-1623 228 6 degradable degradable ADJ cana-1623 228 7 system system NOUN cana-1623 228 8 using use VERB cana-1623 228 9 intuitionistic intuitionistic ADJ cana-1623 228 10 fuzzy fuzzy ADJ cana-1623 228 11 weibull weibull NOUN cana-1623 228 12 lifetime lifetime NOUN cana-1623 228 13 distribution distribution NOUN cana-1623 228 14 . . PUNCT cana-1623 228 15 " " PUNCT cana-1623 229 1 ( ( PUNCT cana-1623 229 2 2023 2023 NUM cana-1623 229 3 ): ): PUNCT cana-1623 229 4 2317 2317 NUM cana-1623 229 5 - - SYM cana-1623 229 6 2324 2324 NUM cana-1623 229 7 . . PUNCT cana-1623 230 1 [ [ X cana-1623 230 2 11 11 NUM cana-1623 230 3 ] ] SYM cana-1623 230 4 hu hu PROPN cana-1623 230 5 , , PUNCT cana-1623 230 6 xue xue PROPN cana-1623 230 7 , , PUNCT cana-1623 230 8 and and CCONJ cana-1623 230 9 haiping haipe VERB cana-1623 230 10 ren ren PROPN cana-1623 230 11 . . PUNCT cana-1623 231 1 " " PUNCT cana-1623 231 2 reliability reliability NOUN cana-1623 231 3 estimation estimation NOUN cana-1623 231 4 of of ADP cana-1623 231 5 inverse inverse ADJ cana-1623 231 6 weibull weibull NOUN cana-1623 231 7 distribution distribution NOUN cana-1623 231 8 based base VERB cana-1623 231 9 on on ADP cana-1623 231 10 intuitionistic intuitionistic ADJ cana-1623 231 11 fuzzy fuzzy ADJ cana-1623 231 12 lifetime lifetime NOUN cana-1623 231 13 data datum NOUN cana-1623 231 14 . . PUNCT cana-1623 231 15 " " PUNCT cana-1623 231 16 axioms axiom VERB cana-1623 231 17 12 12 NUM cana-1623 231 18 , , PUNCT cana-1623 231 19 no no INTJ cana-1623 231 20 . . NOUN cana-1623 231 21 9 9 NUM cana-1623 231 22 ( ( PUNCT cana-1623 231 23 2023 2023 NUM cana-1623 231 24 ): ): PUNCT cana-1623 231 25 838 838 NUM cana-1623 231 26 . . PUNCT cana-1623 232 1 [ [ X cana-1623 232 2 12 12 NUM cana-1623 232 3 ] ] X cana-1623 232 4 https://www.kaggle.com/datasets/akshatgupta7/crop-yield-in-indian-states-dataset https://www.kaggle.com/datasets/akshatgupta7/crop-yield-in-indian-states-dataset NOUN