id sid tid token lemma pos cana-4954 1 1 communications communication NOUN cana-4954 1 2 on on ADP cana-4954 1 3 applied apply VERB cana-4954 1 4 nonlinear nonlinear ADJ cana-4954 1 5 analysis analysis NOUN cana-4954 1 6 issn issn NOUN cana-4954 1 7 : : PUNCT cana-4954 1 8 1074 1074 NUM cana-4954 1 9 - - PUNCT cana-4954 1 10 133x 133x NUM cana-4954 1 11 vol vol VERB cana-4954 1 12 32 32 NUM cana-4954 1 13 no no NOUN cana-4954 1 14 . . PUNCT cana-4954 2 1 10s 10 NOUN cana-4954 2 2 ( ( PUNCT cana-4954 2 3 2025 2025 NUM cana-4954 2 4 ) ) PUNCT cana-4954 2 5 1031 1031 NUM cana-4954 2 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 2 7 singularly singularly ADV cana-4954 2 8 perturbed perturb VERB cana-4954 2 9 initial initial ADJ cana-4954 2 10 value value NOUN cana-4954 2 11 problem problem NOUN cana-4954 2 12 for for ADP cana-4954 2 13 first first ADJ cana-4954 2 14 order order NOUN cana-4954 2 15 delay delay NOUN cana-4954 2 16 differential differential ADJ cana-4954 2 17 equation equation NOUN cana-4954 2 18 magdm magdm NOUN cana-4954 2 19 problem problem NOUN cana-4954 2 20 using use VERB cana-4954 2 21 a a DET cana-4954 2 22 magdm magdm NOUN cana-4954 2 23 problem problem NOUN cana-4954 2 24 manjumari manjumari ADJ cana-4954 2 25 m m VERB cana-4954 2 26 1 1 NUM cana-4954 2 27 1assistant 1assistant NUM cana-4954 2 28 professor professor NOUN cana-4954 2 29 , , PUNCT cana-4954 2 30 department department NOUN cana-4954 2 31 of of ADP cana-4954 2 32 mathematics mathematic NOUN cana-4954 2 33 , , PUNCT cana-4954 2 34 dhanalakshmi dhanalakshmi PROPN cana-4954 2 35 srinivasan srinivasan NOUN cana-4954 2 36 college college PROPN cana-4954 2 37 of of ADP cana-4954 2 38 arts art NOUN cana-4954 2 39 and and CCONJ cana-4954 2 40 science science NOUN cana-4954 2 41 for for ADP cana-4954 2 42 women(autonomous women(autonomous PROPN cana-4954 2 43 ) ) PUNCT cana-4954 2 44 , , PUNCT cana-4954 2 45 perambalur perambalur VERB cana-4954 2 46 , , PUNCT cana-4954 2 47 india india PROPN cana-4954 2 48 . . PUNCT cana-4954 3 1 manjumaths87@gmail.com manjumaths87@gmail.com X cana-4954 3 2 article article NOUN cana-4954 3 3 history history NOUN cana-4954 3 4 : : PUNCT cana-4954 3 5 received receive VERB cana-4954 3 6 : : PUNCT cana-4954 3 7 12 12 NUM cana-4954 3 8 - - SYM cana-4954 3 9 01 01 NUM cana-4954 3 10 - - PUNCT cana-4954 3 11 2025 2025 NUM cana-4954 3 12 revised revise VERB cana-4954 3 13 : : PUNCT cana-4954 3 14 15 15 NUM cana-4954 3 15 - - NUM cana-4954 3 16 02 02 NUM cana-4954 3 17 - - PUNCT cana-4954 3 18 2025 2025 NUM cana-4954 3 19 accepted accept VERB cana-4954 3 20 : : PUNCT cana-4954 3 21 01 01 NUM cana-4954 3 22 - - SYM cana-4954 3 23 03 03 NUM cana-4954 3 24 - - PUNCT cana-4954 3 25 2025 2025 NUM cana-4954 3 26 abstract abstract NOUN cana-4954 3 27 : : PUNCT cana-4954 3 28 this this DET cana-4954 3 29 paper paper NOUN cana-4954 3 30 presents present VERB cana-4954 3 31 a a DET cana-4954 3 32 novel novel ADJ cana-4954 3 33 approach approach NOUN cana-4954 3 34 to to ADP cana-4954 3 35 dynamic dynamic ADJ cana-4954 3 36 intuitionistic intuitionistic ADJ cana-4954 3 37 fuzzy fuzzy ADJ cana-4954 3 38 multiple multiple ADJ cana-4954 3 39 attribute attribute NOUN cana-4954 3 40 group group NOUN cana-4954 3 41 decision decision NOUN cana-4954 3 42 making making NOUN cana-4954 3 43 ( ( PUNCT cana-4954 3 44 dif dif X cana-4954 3 45 - - PUNCT cana-4954 3 46 magdm magdm NOUN cana-4954 3 47 ) ) PUNCT cana-4954 3 48 problems problem NOUN cana-4954 3 49 , , PUNCT cana-4954 3 50 where where SCONJ cana-4954 3 51 decision decision NOUN cana-4954 3 52 attributes attribute NOUN cana-4954 3 53 are be AUX cana-4954 3 54 represented represent VERB cana-4954 3 55 by by ADP cana-4954 3 56 intuitionistic intuitionistic ADJ cana-4954 3 57 fuzzy fuzzy ADJ cana-4954 3 58 numbers number NOUN cana-4954 3 59 collected collect VERB cana-4954 3 60 over over ADP cana-4954 3 61 multiple multiple ADJ cana-4954 3 62 time time NOUN cana-4954 3 63 periods period NOUN cana-4954 3 64 . . PUNCT cana-4954 4 1 to to PART cana-4954 4 2 determine determine VERB cana-4954 4 3 the the DET cana-4954 4 4 unknown unknown ADJ cana-4954 4 5 decision decision NOUN cana-4954 4 6 - - PUNCT cana-4954 4 7 maker maker NOUN cana-4954 4 8 weights weight NOUN cana-4954 4 9 , , PUNCT cana-4954 4 10 a a DET cana-4954 4 11 singularly singularly ADV cana-4954 4 12 perturbed perturb VERB cana-4954 4 13 initial initial ADJ cana-4954 4 14 value value NOUN cana-4954 4 15 problem problem NOUN cana-4954 4 16 is be AUX cana-4954 4 17 formulated formulate VERB cana-4954 4 18 , , PUNCT cana-4954 4 19 incorporating incorporate VERB cana-4954 4 20 a a DET cana-4954 4 21 transition transition NOUN cana-4954 4 22 parameter parameter NOUN cana-4954 4 23 Ο„ Ο„ PROPN cana-4954 4 24 for for ADP cana-4954 4 25 computing compute VERB cana-4954 4 26 the the DET cana-4954 4 27 weighting weight VERB cana-4954 4 28 vectors vector NOUN cana-4954 4 29 . . PUNCT cana-4954 5 1 the the DET cana-4954 5 2 proposed propose VERB cana-4954 5 3 method method NOUN cana-4954 5 4 employs employ VERB cana-4954 5 5 the the DET cana-4954 5 6 dynamic dynamic ADJ cana-4954 5 7 intuitionistic intuitionistic ADJ cana-4954 5 8 fuzzy fuzzy ADJ cana-4954 5 9 weighted weight VERB cana-4954 5 10 averaging average VERB cana-4954 5 11 ( ( PUNCT cana-4954 5 12 difwa difwa NOUN cana-4954 5 13 ) ) PUNCT cana-4954 5 14 operator operator NOUN cana-4954 5 15 to to PART cana-4954 5 16 transform transform VERB cana-4954 5 17 all all DET cana-4954 5 18 dynamic dynamic ADJ cana-4954 5 19 intuitionistic intuitionistic ADJ cana-4954 5 20 fuzzy fuzzy ADJ cana-4954 5 21 decision decision NOUN cana-4954 5 22 matrices matrix NOUN cana-4954 5 23 into into ADP cana-4954 5 24 a a DET cana-4954 5 25 column column NOUN cana-4954 5 26 matrix matrix NOUN cana-4954 5 27 . . PUNCT cana-4954 6 1 to to PART cana-4954 6 2 rank rank VERB cana-4954 6 3 and and CCONJ cana-4954 6 4 select select VERB cana-4954 6 5 the the DET cana-4954 6 6 most most ADV cana-4954 6 7 suitable suitable ADJ cana-4954 6 8 alternative alternative NOUN cana-4954 6 9 , , PUNCT cana-4954 6 10 a a DET cana-4954 6 11 proximity proximity NOUN cana-4954 6 12 coefficient coefficient NOUN cana-4954 6 13 function function NOUN cana-4954 6 14 is be AUX cana-4954 6 15 applied apply VERB cana-4954 6 16 . . PUNCT cana-4954 7 1 the the DET cana-4954 7 2 effectiveness effectiveness NOUN cana-4954 7 3 and and CCONJ cana-4954 7 4 practicality practicality NOUN cana-4954 7 5 of of ADP cana-4954 7 6 the the DET cana-4954 7 7 approach approach NOUN cana-4954 7 8 are be AUX cana-4954 7 9 demonstrated demonstrate VERB cana-4954 7 10 through through ADP cana-4954 7 11 a a DET cana-4954 7 12 numerical numerical ADJ cana-4954 7 13 case case NOUN cana-4954 7 14 study study NOUN cana-4954 7 15 on on ADP cana-4954 7 16 supplier supplier NOUN cana-4954 7 17 selection selection NOUN cana-4954 7 18 . . PUNCT cana-4954 8 1 the the DET cana-4954 8 2 results result NOUN cana-4954 8 3 validate validate VERB cana-4954 8 4 the the DET cana-4954 8 5 robustness robustness NOUN cana-4954 8 6 and and CCONJ cana-4954 8 7 applicability applicability NOUN cana-4954 8 8 of of ADP cana-4954 8 9 the the DET cana-4954 8 10 proposed propose VERB cana-4954 8 11 decision decision NOUN cana-4954 8 12 - - PUNCT cana-4954 8 13 making make VERB cana-4954 8 14 framework framework NOUN cana-4954 8 15 in in ADP cana-4954 8 16 dynamic dynamic ADJ cana-4954 8 17 and and CCONJ cana-4954 8 18 uncertain uncertain ADJ cana-4954 8 19 environments environment NOUN cana-4954 8 20 . . PUNCT cana-4954 9 1 keywords keyword NOUN cana-4954 9 2 : : PUNCT cana-4954 9 3 intuitionistic intuitionistic ADJ cana-4954 9 4 fuzzy fuzzy ADJ cana-4954 9 5 sets set NOUN cana-4954 9 6 ( ( PUNCT cana-4954 9 7 ifss ifss NOUN cana-4954 9 8 ) ) PUNCT cana-4954 9 9 , , PUNCT cana-4954 9 10 magdm magdm NOUN cana-4954 9 11 , , PUNCT cana-4954 9 12 dynamic dynamic ADJ cana-4954 9 13 intuitionistic intuitionistic ADJ cana-4954 9 14 fuzzy fuzzy ADJ cana-4954 9 15 weighted weight VERB cana-4954 9 16 averaging average VERB cana-4954 9 17 ( ( PUNCT cana-4954 9 18 difwa difwa NOUN cana-4954 9 19 ) ) PUNCT cana-4954 9 20 operator operator NOUN cana-4954 9 21 , , PUNCT cana-4954 9 22 singular singular ADJ cana-4954 9 23 perturbation perturbation NOUN cana-4954 9 24 problem problem NOUN cana-4954 9 25 . . PUNCT cana-4954 10 1 introduction introduction NOUN cana-4954 10 2 multi multi ADJ cana-4954 10 3 - - ADJ cana-4954 10 4 attribute attribute NOUN cana-4954 10 5 group group NOUN cana-4954 10 6 decision decision NOUN cana-4954 10 7 - - PUNCT cana-4954 10 8 making make VERB cana-4954 10 9 ( ( PUNCT cana-4954 10 10 magdm magdm NOUN cana-4954 10 11 ) ) PUNCT cana-4954 10 12 plays play VERB cana-4954 10 13 a a DET cana-4954 10 14 crucial crucial ADJ cana-4954 10 15 role role NOUN cana-4954 10 16 in in ADP cana-4954 10 17 modern modern ADJ cana-4954 10 18 decision decision NOUN cana-4954 10 19 theory theory NOUN cana-4954 10 20 , , PUNCT cana-4954 10 21 providing provide VERB cana-4954 10 22 a a DET cana-4954 10 23 framework framework NOUN cana-4954 10 24 for for ADP cana-4954 10 25 evaluating evaluate VERB cana-4954 10 26 multiple multiple ADJ cana-4954 10 27 alternatives alternative NOUN cana-4954 10 28 based base VERB cana-4954 10 29 on on ADP cana-4954 10 30 multiple multiple ADJ cana-4954 10 31 criteria criterion NOUN cana-4954 10 32 . . PUNCT cana-4954 11 1 when when SCONJ cana-4954 11 2 intuitionistic intuitionistic ADJ cana-4954 11 3 fuzzy fuzzy ADJ cana-4954 11 4 sets set NOUN cana-4954 11 5 ( ( PUNCT cana-4954 11 6 ifss ifss NOUN cana-4954 11 7 ) ) PUNCT cana-4954 11 8 are be AUX cana-4954 11 9 incorporated incorporate VERB cana-4954 11 10 into into ADP cana-4954 11 11 magdm magdm NOUN cana-4954 11 12 and and CCONJ cana-4954 11 13 extended extend VERB cana-4954 11 14 across across ADP cana-4954 11 15 multiple multiple ADJ cana-4954 11 16 time time NOUN cana-4954 11 17 periods period NOUN cana-4954 11 18 , , PUNCT cana-4954 11 19 the the DET cana-4954 11 20 process process NOUN cana-4954 11 21 is be AUX cana-4954 11 22 referred refer VERB cana-4954 11 23 to to ADP cana-4954 11 24 as as ADP cana-4954 11 25 dynamic dynamic ADJ cana-4954 11 26 intuitionistic intuitionistic ADJ cana-4954 11 27 fuzzy fuzzy ADJ cana-4954 11 28 multi multi ADJ cana-4954 11 29 - - ADJ cana-4954 11 30 attribute attribute NOUN cana-4954 11 31 group group NOUN cana-4954 11 32 decisionmaking decisionmaking NOUN cana-4954 11 33 ( ( PUNCT cana-4954 11 34 dif dif X cana-4954 11 35 - - PUNCT cana-4954 11 36 magdm magdm NOUN cana-4954 11 37 ) ) PUNCT cana-4954 11 38 . . PUNCT cana-4954 12 1 since since SCONJ cana-4954 12 2 atanassov atanassov PROPN cana-4954 12 3 [ [ X cana-4954 12 4 1 1 NUM cana-4954 12 5 ] ] PUNCT cana-4954 12 6 introduced introduce VERB cana-4954 12 7 the the DET cana-4954 12 8 concept concept NOUN cana-4954 12 9 of of ADP cana-4954 12 10 ifss ifss ADJ cana-4954 12 11 , , PUNCT cana-4954 12 12 significant significant ADJ cana-4954 12 13 advancements advancement NOUN cana-4954 12 14 have have AUX cana-4954 12 15 been be AUX cana-4954 12 16 made make VERB cana-4954 12 17 in in ADP cana-4954 12 18 their their PRON cana-4954 12 19 theoretical theoretical ADJ cana-4954 12 20 development development NOUN cana-4954 12 21 and and CCONJ cana-4954 12 22 practical practical ADJ cana-4954 12 23 applications application NOUN cana-4954 12 24 . . PUNCT cana-4954 13 1 intuitionistic intuitionistic ADJ cana-4954 13 2 fuzzy fuzzy ADJ cana-4954 13 3 sets set NOUN cana-4954 13 4 have have AUX cana-4954 13 5 been be AUX cana-4954 13 6 widely widely ADV cana-4954 13 7 utilized utilize VERB cana-4954 13 8 in in ADP cana-4954 13 9 various various ADJ cana-4954 13 10 real real ADJ cana-4954 13 11 - - PUNCT cana-4954 13 12 world world NOUN cana-4954 13 13 decision decision NOUN cana-4954 13 14 - - PUNCT cana-4954 13 15 making make VERB cana-4954 13 16 scenarios scenario NOUN cana-4954 13 17 [ [ X cana-4954 13 18 2 2 NUM cana-4954 13 19 ] ] PUNCT cana-4954 13 20 . . PUNCT cana-4954 14 1 atanassov atanassov PROPN cana-4954 14 2 et et PROPN cana-4954 14 3 al al PROPN cana-4954 14 4 . . PUNCT cana-4954 15 1 [ [ X cana-4954 15 2 3 3 X cana-4954 15 3 ] ] PUNCT cana-4954 15 4 explored explore VERB cana-4954 15 5 the the DET cana-4954 15 6 intuitionistic intuitionistic ADJ cana-4954 15 7 fuzzy fuzzy ADJ cana-4954 15 8 interpretations interpretation NOUN cana-4954 15 9 of of ADP cana-4954 15 10 multi multi ADJ cana-4954 15 11 - - NOUN cana-4954 15 12 criteria criterion NOUN cana-4954 15 13 and and CCONJ cana-4954 15 14 multi multi ADJ cana-4954 15 15 - - ADJ cana-4954 15 16 measurement measurement ADJ cana-4954 15 17 decision decision NOUN cana-4954 15 18 - - PUNCT cana-4954 15 19 making make VERB cana-4954 15 20 methods method NOUN cana-4954 15 21 , , PUNCT cana-4954 15 22 while while SCONJ cana-4954 15 23 bustine bustine VERB cana-4954 15 24 and and CCONJ cana-4954 15 25 burillo burillo VERB cana-4954 15 26 [ [ X cana-4954 15 27 4 4 X cana-4954 15 28 ] ] PUNCT cana-4954 15 29 extended extend VERB cana-4954 15 30 the the DET cana-4954 15 31 concept concept NOUN cana-4954 15 32 to to ADP cana-4954 15 33 vague vague ADJ cana-4954 15 34 sets set NOUN cana-4954 15 35 . . PUNCT cana-4954 16 1 several several ADJ cana-4954 16 2 operations operation NOUN cana-4954 16 3 on on ADP cana-4954 16 4 ifss ifss NOUN cana-4954 16 5 have have AUX cana-4954 16 6 been be AUX cana-4954 16 7 further far ADV cana-4954 16 8 refined refine VERB cana-4954 16 9 by by ADP cana-4954 16 10 biswas biswas PROPN cana-4954 16 11 and and CCONJ cana-4954 16 12 roy roy PROPN cana-4954 17 1 [ [ X cana-4954 17 2 5 5 NUM cana-4954 17 3 ] ] PUNCT cana-4954 17 4 . . PUNCT cana-4954 18 1 in in ADP cana-4954 18 2 parallel parallel NOUN cana-4954 18 3 , , PUNCT cana-4954 18 4 singular singular ADJ cana-4954 18 5 perturbation perturbation NOUN cana-4954 18 6 theory theory NOUN cana-4954 18 7 in in ADP cana-4954 18 8 ordinary ordinary ADJ cana-4954 18 9 differential differential ADJ cana-4954 18 10 equations equation NOUN cana-4954 18 11 has have AUX cana-4954 18 12 been be AUX cana-4954 18 13 a a DET cana-4954 18 14 subject subject NOUN cana-4954 18 15 of of ADP cana-4954 18 16 extensive extensive ADJ cana-4954 18 17 research research NOUN cana-4954 18 18 . . PUNCT cana-4954 19 1 doolan doolan PROPN cana-4954 19 2 et et PROPN cana-4954 19 3 al al PROPN cana-4954 19 4 . . PUNCT cana-4954 20 1 [ [ X cana-4954 20 2 6 6 NUM cana-4954 20 3 ] ] PUNCT cana-4954 20 4 introduced introduce VERB cana-4954 20 5 this this DET cana-4954 20 6 theory theory NOUN cana-4954 20 7 , , PUNCT cana-4954 20 8 and and CCONJ cana-4954 20 9 kadalbajoo kadalbajoo NOUN cana-4954 21 1 [ [ X cana-4954 21 2 7 7 NUM cana-4954 21 3 ] ] PUNCT cana-4954 21 4 expanded expand VERB cana-4954 21 5 its its PRON cana-4954 21 6 application application NOUN cana-4954 21 7 to to PART cana-4954 21 8 singularly singularly ADV cana-4954 21 9 perturbed perturb VERB cana-4954 21 10 differential differential ADJ cana-4954 21 11 equations equation NOUN cana-4954 21 12 , , PUNCT cana-4954 21 13 incorporating incorporate VERB cana-4954 21 14 both both CCONJ cana-4954 21 15 positive positive ADJ cana-4954 21 16 and and CCONJ cana-4954 21 17 negative negative ADJ cana-4954 21 18 communications communication NOUN cana-4954 21 19 on on ADP cana-4954 21 20 applied apply VERB cana-4954 21 21 nonlinear nonlinear ADJ cana-4954 21 22 analysis analysis NOUN cana-4954 21 23 issn issn NOUN cana-4954 21 24 : : PUNCT cana-4954 21 25 1074 1074 NUM cana-4954 21 26 - - PUNCT cana-4954 21 27 133x 133x NUM cana-4954 21 28 vol vol VERB cana-4954 21 29 32 32 NUM cana-4954 21 30 no no NOUN cana-4954 21 31 . . PUNCT cana-4954 22 1 10s 10 NOUN cana-4954 22 2 ( ( PUNCT cana-4954 22 3 2025 2025 NUM cana-4954 22 4 ) ) PUNCT cana-4954 22 5 1032 1032 NUM cana-4954 22 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 22 7 shifts shift NOUN cana-4954 22 8 . . PUNCT cana-4954 23 1 liu liu PROPN cana-4954 23 2 et et PROPN cana-4954 23 3 al al PROPN cana-4954 23 4 . . PUNCT cana-4954 24 1 [ [ X cana-4954 24 2 8 8 NUM cana-4954 24 3 ] ] PUNCT cana-4954 24 4 proposed propose VERB cana-4954 24 5 several several ADJ cana-4954 24 6 improvements improvement NOUN cana-4954 24 7 to to ADP cana-4954 24 8 magdm magdm NOUN cana-4954 24 9 and and CCONJ cana-4954 24 10 multiple multiple ADJ cana-4954 24 11 criteria criterion NOUN cana-4954 24 12 decisionmaking decisionmake VERB cana-4954 24 13 models model NOUN cana-4954 24 14 using use VERB cana-4954 24 15 ifss ifss NOUN cana-4954 24 16 . . PUNCT cana-4954 25 1 furthermore furthermore ADV cana-4954 25 2 , , PUNCT cana-4954 25 3 miller miller PROPN cana-4954 25 4 et et PROPN cana-4954 25 5 al al PROPN cana-4954 25 6 . . PUNCT cana-4954 26 1 [ [ X cana-4954 26 2 9 9 NUM cana-4954 26 3 ] ] PUNCT cana-4954 26 4 developed develop VERB cana-4954 26 5 fitted fit VERB cana-4954 26 6 numerical numerical ADJ cana-4954 26 7 techniques technique NOUN cana-4954 26 8 for for ADP cana-4954 26 9 singular singular ADJ cana-4954 26 10 perturbation perturbation NOUN cana-4954 26 11 problems problem NOUN cana-4954 26 12 in in ADP cana-4954 26 13 both both PRON cana-4954 26 14 one one NUM cana-4954 26 15 and and CCONJ cana-4954 26 16 two two NUM cana-4954 26 17 dimensions dimension NOUN cana-4954 26 18 . . PUNCT cana-4954 27 1 the the DET cana-4954 27 2 study study NOUN cana-4954 27 3 of of ADP cana-4954 27 4 distances distance NOUN cana-4954 27 5 between between ADP cana-4954 27 6 intuitionistic intuitionistic ADJ cana-4954 27 7 fuzzy fuzzy ADJ cana-4954 27 8 sets set NOUN cana-4954 27 9 for for ADP cana-4954 27 10 group group NOUN cana-4954 27 11 decision decision NOUN cana-4954 27 12 - - PUNCT cana-4954 27 13 making making NOUN cana-4954 27 14 was be AUX cana-4954 27 15 introduced introduce VERB cana-4954 27 16 by by ADP cana-4954 27 17 szmidt szmidt NOUN cana-4954 27 18 and and CCONJ cana-4954 27 19 kacprzyk kacprzyk VERB cana-4954 27 20 [ [ X cana-4954 27 21 10 10 NUM cana-4954 27 22 , , PUNCT cana-4954 27 23 11 11 NUM cana-4954 27 24 ] ] PUNCT cana-4954 27 25 , , PUNCT cana-4954 27 26 while while SCONJ cana-4954 27 27 xu xu PROPN cana-4954 27 28 and and CCONJ cana-4954 27 29 yager yager NOUN cana-4954 28 1 [ [ X cana-4954 28 2 12–15 12–15 NUM cana-4954 28 3 ] ] PUNCT cana-4954 28 4 developed develop VERB cana-4954 28 5 the the DET cana-4954 28 6 dynamic dynamic ADJ cana-4954 28 7 intuitionistic intuitionistic ADJ cana-4954 28 8 fuzzy fuzzy ADJ cana-4954 28 9 weighted weight VERB cana-4954 28 10 averaging average VERB cana-4954 28 11 ( ( PUNCT cana-4954 28 12 difwa difwa NOUN cana-4954 28 13 ) ) PUNCT cana-4954 28 14 operator operator NOUN cana-4954 28 15 to to PART cana-4954 28 16 enhance enhance VERB cana-4954 28 17 decision decision NOUN cana-4954 28 18 - - PUNCT cana-4954 28 19 making make VERB cana-4954 28 20 processes process NOUN cana-4954 28 21 . . PUNCT cana-4954 29 1 the the DET cana-4954 29 2 foundational foundational ADJ cana-4954 29 3 concept concept NOUN cana-4954 29 4 of of ADP cana-4954 29 5 fuzzy fuzzy ADJ cana-4954 29 6 sets set NOUN cana-4954 29 7 , , PUNCT cana-4954 29 8 which which PRON cana-4954 29 9 provides provide VERB cana-4954 29 10 a a DET cana-4954 29 11 powerful powerful ADJ cana-4954 29 12 approach approach NOUN cana-4954 29 13 to to ADP cana-4954 29 14 managing manage VERB cana-4954 29 15 uncertainty uncertainty NOUN cana-4954 29 16 , , PUNCT cana-4954 29 17 was be AUX cana-4954 29 18 first first ADV cana-4954 29 19 introduced introduce VERB cana-4954 29 20 by by ADP cana-4954 29 21 zadeh zadeh PROPN cana-4954 30 1 [ [ X cana-4954 30 2 16 16 NUM cana-4954 30 3 ] ] PUNCT cana-4954 30 4 . . PUNCT cana-4954 31 1 building build VERB cana-4954 31 2 upon upon SCONJ cana-4954 31 3 these these DET cana-4954 31 4 advancements advancement NOUN cana-4954 31 5 , , PUNCT cana-4954 31 6 this this DET cana-4954 31 7 paper paper NOUN cana-4954 31 8 presents present VERB cana-4954 31 9 an an DET cana-4954 31 10 approach approach NOUN cana-4954 31 11 for for ADP cana-4954 31 12 solving solve VERB cana-4954 31 13 dif dif ADJ cana-4954 31 14 - - PUNCT cana-4954 31 15 magdm magdm NOUN cana-4954 31 16 problems problem NOUN cana-4954 31 17 by by ADP cana-4954 31 18 incorporating incorporate VERB cana-4954 31 19 intuitionistic intuitionistic ADJ cana-4954 31 20 fuzzy fuzzy ADJ cana-4954 31 21 numbers number NOUN cana-4954 31 22 across across ADP cana-4954 31 23 various various ADJ cana-4954 31 24 time time NOUN cana-4954 31 25 periods period NOUN cana-4954 31 26 . . PUNCT cana-4954 32 1 the the DET cana-4954 32 2 proposed propose VERB cana-4954 32 3 method method NOUN cana-4954 32 4 leverages leverage VERB cana-4954 32 5 the the DET cana-4954 32 6 difwa difwa NOUN cana-4954 32 7 operator operator NOUN cana-4954 32 8 and and CCONJ cana-4954 32 9 a a DET cana-4954 32 10 proximity proximity NOUN cana-4954 32 11 coefficient coefficient NOUN cana-4954 32 12 function function NOUN cana-4954 32 13 to to PART cana-4954 32 14 facilitate facilitate VERB cana-4954 32 15 effective effective ADJ cana-4954 32 16 decision decision NOUN cana-4954 32 17 - - PUNCT cana-4954 32 18 making making NOUN cana-4954 32 19 , , PUNCT cana-4954 32 20 as as SCONJ cana-4954 32 21 demonstrated demonstrate VERB cana-4954 32 22 through through ADP cana-4954 32 23 a a DET cana-4954 32 24 numerical numerical ADJ cana-4954 32 25 case case NOUN cana-4954 32 26 study study NOUN cana-4954 32 27 on on ADP cana-4954 32 28 supplier supplier NOUN cana-4954 32 29 selection selection NOUN cana-4954 32 30 . . PUNCT cana-4954 33 1 preliminaries preliminary NOUN cana-4954 33 2 this this DET cana-4954 33 3 section section NOUN cana-4954 33 4 discusses discuss VERB cana-4954 33 5 key key ADJ cana-4954 33 6 concepts concept NOUN cana-4954 33 7 of of ADP cana-4954 33 8 dynamic dynamic ADJ cana-4954 33 9 intuitionistic intuitionistic ADJ cana-4954 33 10 fuzzy fuzzy ADJ cana-4954 33 11 multi multi ADJ cana-4954 33 12 - - ADJ cana-4954 33 13 attribute attribute NOUN cana-4954 33 14 group group NOUN cana-4954 33 15 decisionmaking decisionmaking NOUN cana-4954 33 16 ( ( PUNCT cana-4954 33 17 dif dif X cana-4954 33 18 - - PUNCT cana-4954 33 19 magdm magdm NOUN cana-4954 33 20 ) ) PUNCT cana-4954 33 21 and and CCONJ cana-4954 33 22 the the DET cana-4954 33 23 different different ADJ cana-4954 33 24 types type NOUN cana-4954 33 25 of of ADP cana-4954 33 26 aggregation aggregation NOUN cana-4954 33 27 operators operator NOUN cana-4954 33 28 . . PUNCT cana-4954 34 1 these these DET cana-4954 34 2 operators operator NOUN cana-4954 34 3 are be AUX cana-4954 34 4 essential essential ADJ cana-4954 34 5 for for ADP cana-4954 34 6 integrating integrate VERB cana-4954 34 7 intuitionistic intuitionistic ADJ cana-4954 34 8 fuzzy fuzzy ADJ cana-4954 34 9 information information NOUN cana-4954 34 10 from from ADP cana-4954 34 11 multiple multiple ADJ cana-4954 34 12 decision decision NOUN cana-4954 34 13 - - PUNCT cana-4954 34 14 makers maker NOUN cana-4954 34 15 over over ADP cana-4954 34 16 various various ADJ cana-4954 34 17 time time NOUN cana-4954 34 18 periods period NOUN cana-4954 34 19 , , PUNCT cana-4954 34 20 ensuring ensure VERB cana-4954 34 21 a a DET cana-4954 34 22 systematic systematic ADJ cana-4954 34 23 approach approach NOUN cana-4954 34 24 to to ADP cana-4954 34 25 decision decision NOUN cana-4954 34 26 - - PUNCT cana-4954 34 27 making making NOUN cana-4954 34 28 . . PUNCT cana-4954 35 1 the the DET cana-4954 35 2 section section NOUN cana-4954 35 3 highlights highlight VERB cana-4954 35 4 various various ADJ cana-4954 35 5 aggregation aggregation NOUN cana-4954 35 6 techniques technique NOUN cana-4954 35 7 , , PUNCT cana-4954 35 8 including include VERB cana-4954 35 9 the the DET cana-4954 35 10 dynamic dynamic ADJ cana-4954 35 11 intuitionistic intuitionistic ADJ cana-4954 35 12 fuzzy fuzzy ADJ cana-4954 35 13 weighted weight VERB cana-4954 35 14 averaging average VERB cana-4954 35 15 ( ( PUNCT cana-4954 35 16 difwa difwa NOUN cana-4954 35 17 ) ) PUNCT cana-4954 35 18 operator operator NOUN cana-4954 35 19 , , PUNCT cana-4954 35 20 which which PRON cana-4954 35 21 plays play VERB cana-4954 35 22 a a DET cana-4954 35 23 crucial crucial ADJ cana-4954 35 24 role role NOUN cana-4954 35 25 in in ADP cana-4954 35 26 managing manage VERB cana-4954 35 27 uncertainty uncertainty NOUN cana-4954 35 28 in in ADP cana-4954 35 29 group group NOUN cana-4954 35 30 decision decision NOUN cana-4954 35 31 - - PUNCT cana-4954 35 32 making make VERB cana-4954 35 33 processes process NOUN cana-4954 35 34 . . PUNCT cana-4954 36 1 definition definition NOUN cana-4954 36 2 let let VERB cana-4954 36 3 𝜎(𝑑1 𝜎(𝑑1 NOUN cana-4954 36 4 ) ) PUNCT cana-4954 36 5 , , PUNCT cana-4954 36 6 𝜎(𝑑2 𝜎(𝑑2 NOUN cana-4954 36 7 ) ) PUNCT cana-4954 36 8 , , PUNCT cana-4954 36 9 . . PUNCT cana-4954 36 10 . . PUNCT cana-4954 36 11 . . PUNCT cana-4954 36 12 . . PUNCT cana-4954 36 13 . . PUNCT cana-4954 36 14 . . PUNCT cana-4954 36 15 . . PUNCT cana-4954 36 16 . . PUNCT cana-4954 37 1 . . PUNCT cana-4954 38 1 , , PUNCT cana-4954 38 2 𝜎(𝑑𝑝)be 𝜎(𝑑𝑝)be AUX cana-4954 38 3 a a DET cana-4954 38 4 collection collection NOUN cana-4954 38 5 of of ADP cana-4954 38 6 ifns ifns NOUN cana-4954 38 7 collected collect VERB cana-4954 38 8 at at ADP cana-4954 38 9 p p X cana-4954 38 10 different different ADJ cana-4954 38 11 periods period NOUN cana-4954 38 12 π‘‘π‘˜(π‘˜ π‘‘π‘˜(π‘˜ PUNCT cana-4954 38 13 = = SYM cana-4954 38 14 1,2 1,2 NUM cana-4954 38 15 , , PUNCT cana-4954 38 16 . . PUNCT cana-4954 38 17 . . PUNCT cana-4954 38 18 . . PUNCT cana-4954 38 19 . . PUNCT cana-4954 39 1 . . PUNCT cana-4954 40 1 . . PUNCT cana-4954 41 1 , , PUNCT cana-4954 41 2 𝑝 𝑝 NOUN cana-4954 41 3 ) ) PUNCT cana-4954 41 4 , , PUNCT cana-4954 41 5 π‘Žπ‘›π‘‘πœ†(𝑑 π‘Žπ‘›π‘‘πœ†(𝑑 PROPN cana-4954 41 6 ) ) PUNCT cana-4954 41 7 = = SYM cana-4954 41 8 ( ( PUNCT cana-4954 41 9 πœ†(𝑑1 πœ†(𝑑1 NUM cana-4954 41 10 ) ) PUNCT cana-4954 41 11 , , PUNCT cana-4954 41 12 πœ†(𝑑2 πœ†(𝑑2 NUM cana-4954 41 13 ) ) PUNCT cana-4954 41 14 , , PUNCT cana-4954 41 15 . . PUNCT cana-4954 41 16 . . PUNCT cana-4954 41 17 . . PUNCT cana-4954 41 18 . . PUNCT cana-4954 42 1 . . PUNCT cana-4954 43 1 , , PUNCT cana-4954 43 2 πœ†(𝑑𝑝 πœ†(𝑑𝑝 NOUN cana-4954 43 3 ) ) PUNCT cana-4954 43 4 ) ) PUNCT cana-4954 44 1 𝑇 𝑇 PROPN cana-4954 44 2 be be VERB cana-4954 44 3 the the DET cana-4954 44 4 weight weight NOUN cana-4954 44 5 vector vector NOUN cana-4954 44 6 of of ADP cana-4954 44 7 the the DET cana-4954 44 8 periods period NOUN cana-4954 44 9 π‘‘π‘˜(π‘˜ π‘‘π‘˜(π‘˜ PUNCT cana-4954 44 10 = = SYM cana-4954 44 11 1,2 1,2 NUM cana-4954 44 12 , , PUNCT cana-4954 44 13 . . PUNCT cana-4954 44 14 . . PUNCT cana-4954 44 15 . . PUNCT cana-4954 44 16 . . PUNCT cana-4954 44 17 . . PUNCT cana-4954 45 1 . . PUNCT cana-4954 46 1 , , PUNCT cana-4954 46 2 𝑝 𝑝 NOUN cana-4954 46 3 ) ) PUNCT cana-4954 46 4 , , PUNCT cana-4954 46 5 then then ADV cana-4954 46 6 we we PRON cana-4954 46 7 call call VERB cana-4954 46 8 π·πΌπΉπ‘Šπ΄πœ†(𝑑 π·πΌπΉπ‘Šπ΄πœ†(𝑑 ADJ cana-4954 46 9 ) ) PUNCT cana-4954 46 10 ( ( PUNCT cana-4954 46 11 𝛼(𝑑1 𝛼(𝑑1 ADV cana-4954 46 12 ) ) PUNCT cana-4954 46 13 , , PUNCT cana-4954 46 14 𝛼(𝑑1 𝛼(𝑑1 NUM cana-4954 46 15 ) ) PUNCT cana-4954 46 16 , , PUNCT cana-4954 46 17 . . PUNCT cana-4954 46 18 . . PUNCT cana-4954 46 19 . . PUNCT cana-4954 46 20 . . PUNCT cana-4954 47 1 . . PUNCT cana-4954 48 1 , , PUNCT cana-4954 48 2 𝛼(𝑑𝑝 𝛼(𝑑𝑝 NOUN cana-4954 48 3 ) ) PUNCT cana-4954 48 4 ) ) PUNCT cana-4954 49 1 = = SYM cana-4954 49 2 πœ†(𝑑1)𝛼(𝑑1 πœ†(𝑑1)𝛼(𝑑1 PROPN cana-4954 49 3 ) ) PUNCT cana-4954 49 4 βŠ• βŠ• PROPN cana-4954 49 5 , , PUNCT cana-4954 49 6 πœ†(𝑑2)𝛼(𝑑2 πœ†(𝑑2)𝛼(𝑑2 PROPN cana-4954 49 7 ) ) PUNCT cana-4954 49 8 βŠ• βŠ• PROPN cana-4954 49 9 , , PUNCT cana-4954 49 10 . . PUNCT cana-4954 49 11 . . PUNCT cana-4954 49 12 . . PUNCT cana-4954 49 13 . . PUNCT cana-4954 49 14 . . PUNCT cana-4954 50 1 , , PUNCT cana-4954 50 2 πœ†(𝑑𝑝)𝛼(𝑑𝑝 πœ†(𝑑𝑝)𝛼(𝑑𝑝 X cana-4954 50 3 ) ) PUNCT cana-4954 50 4 a a DET cana-4954 50 5 dynamic dynamic ADJ cana-4954 50 6 intuitionistic intuitionistic ADJ cana-4954 50 7 fuzzy fuzzy NOUN cana-4954 50 8 weighted weight VERB cana-4954 50 9 a a DET cana-4954 50 10 averaging averaging NOUN cana-4954 50 11 ( ( PUNCT cana-4954 50 12 difwa difwa NOUN cana-4954 50 13 ) ) PUNCT cana-4954 50 14 operator operator NOUN cana-4954 50 15 . . PUNCT cana-4954 51 1 π·πΌπΉπ‘Šπ΄πœ†(𝑑 π·πΌπΉπ‘Šπ΄πœ†(𝑑 PROPN cana-4954 51 2 ) ) PUNCT cana-4954 51 3 ( ( PUNCT cana-4954 51 4 𝛼(𝑑1 𝛼(𝑑1 ADV cana-4954 51 5 ) ) PUNCT cana-4954 51 6 , , PUNCT cana-4954 51 7 𝛼(𝑑1 𝛼(𝑑1 NUM cana-4954 51 8 ) ) PUNCT cana-4954 51 9 , , PUNCT cana-4954 51 10 … … PUNCT cana-4954 51 11 . . PUNCT cana-4954 51 12 . . PUNCT cana-4954 52 1 , , PUNCT cana-4954 52 2 𝛼(𝑑𝑝 𝛼(𝑑𝑝 NOUN cana-4954 52 3 ) ) PUNCT cana-4954 52 4 ) ) PUNCT cana-4954 53 1 = = PUNCT cana-4954 53 2 ( ( PUNCT cana-4954 53 3 1 1 NUM cana-4954 53 4 βˆ’ βˆ’ PROPN cana-4954 53 5 ∏(1 ∏(1 ADJ cana-4954 53 6 βˆ’ βˆ’ PROPN cana-4954 53 7 πœ‡πœŽ(π‘‘π‘˜ πœ‡πœŽ(π‘‘π‘˜ ADJ cana-4954 53 8 ) ) PUNCT cana-4954 53 9 ) ) PUNCT cana-4954 53 10 𝑝 𝑝 PROPN cana-4954 53 11 π‘˜=1 π‘˜=1 NOUN cana-4954 53 12 πœ†(π‘‘π‘˜ πœ†(π‘‘π‘˜ PROPN cana-4954 53 13 ) ) PUNCT cana-4954 53 14 , , PUNCT cana-4954 53 15 βˆπ›ΎπœŽ(π‘‘π‘˜ βˆπ›ΎπœŽ(π‘‘π‘˜ X cana-4954 53 16 ) ) PUNCT cana-4954 53 17 πœ†(π‘‘π‘˜ πœ†(π‘‘π‘˜ PROPN cana-4954 53 18 ) ) PUNCT cana-4954 53 19 𝑝 𝑝 NOUN cana-4954 53 20 π‘˜=1 π‘˜=1 NOUN cana-4954 53 21 , , PUNCT cana-4954 53 22 ∏(1 ∏(1 ADJ cana-4954 53 23 βˆ’ βˆ’ PROPN cana-4954 53 24 πœ‡πœŽ(π‘‘π‘˜ πœ‡πœŽ(π‘‘π‘˜ ADJ cana-4954 53 25 ) ) PUNCT cana-4954 53 26 ) ) PUNCT cana-4954 54 1 𝑝 𝑝 ADP cana-4954 54 2 π‘˜=1 π‘˜=1 NOUN cana-4954 54 3 πœ†(π‘‘π‘˜ πœ†(π‘‘π‘˜ PROPN cana-4954 54 4 ) ) PUNCT cana-4954 54 5 βˆ’ βˆ’ PROPN cana-4954 54 6 ∏ ∏ PROPN cana-4954 54 7 π›ΎπœŽ(π‘‘π‘˜ π›ΎπœŽ(π‘‘π‘˜ X cana-4954 54 8 ) ) PUNCT cana-4954 54 9 πœ†(π‘‘π‘˜ πœ†(π‘‘π‘˜ PROPN cana-4954 54 10 ) ) PUNCT cana-4954 54 11 𝑝 𝑝 NOUN cana-4954 54 12 π‘˜=1 π‘˜=1 NOUN cana-4954 54 13 ) ) PUNCT cana-4954 54 14 where where SCONJ cana-4954 54 15 πœ†(π‘‘π‘˜ πœ†(π‘‘π‘˜ NOUN cana-4954 54 16 ) ) PUNCT cana-4954 54 17 β‰₯ β‰₯ NOUN cana-4954 54 18 0 0 NUM cana-4954 54 19 , , PUNCT cana-4954 54 20 π‘˜ π‘˜ X cana-4954 54 21 = = SYM cana-4954 54 22 1,2 1,2 NUM cana-4954 54 23 , , PUNCT cana-4954 54 24 . . PUNCT cana-4954 54 25 . . PUNCT cana-4954 54 26 . . PUNCT cana-4954 54 27 . . PUNCT cana-4954 55 1 . . PUNCT cana-4954 56 1 , , PUNCT cana-4954 56 2 𝑝 𝑝 NOUN cana-4954 56 3 , , PUNCT cana-4954 56 4 βˆ‘ βˆ‘ ADV cana-4954 56 5 πœ†(π‘‘π‘˜ πœ†(π‘‘π‘˜ PROPN cana-4954 56 6 ) ) PUNCT cana-4954 56 7 𝑝 𝑝 NOUN cana-4954 56 8 π‘˜=1 π‘˜=1 NOUN cana-4954 56 9 = = SYM cana-4954 56 10 1 1 NUM cana-4954 56 11 communications communication NOUN cana-4954 56 12 on on ADP cana-4954 56 13 applied apply VERB cana-4954 56 14 nonlinear nonlinear ADJ cana-4954 56 15 analysis analysis NOUN cana-4954 56 16 issn issn NOUN cana-4954 56 17 : : PUNCT cana-4954 56 18 1074 1074 NUM cana-4954 56 19 - - PUNCT cana-4954 56 20 133x 133x NUM cana-4954 56 21 vol vol VERB cana-4954 56 22 32 32 NUM cana-4954 56 23 no no NOUN cana-4954 56 24 . . PUNCT cana-4954 57 1 10s 10 NOUN cana-4954 57 2 ( ( PUNCT cana-4954 57 3 2025 2025 NUM cana-4954 57 4 ) ) PUNCT cana-4954 57 5 1033 1033 NUM cana-4954 57 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 57 7 a a DET cana-4954 57 8 method method NOUN cana-4954 57 9 of of ADP cana-4954 57 10 using use VERB cana-4954 57 11 intuitionistic intuitionistic ADJ cana-4954 57 12 fuzzy fuzzy ADJ cana-4954 57 13 information information NOUN cana-4954 57 14 in in ADP cana-4954 57 15 group group NOUN cana-4954 57 16 decision decision NOUN cana-4954 57 17 making making NOUN cana-4954 57 18 : : PUNCT cana-4954 57 19 step step NOUN cana-4954 57 20 1 1 NUM cana-4954 57 21 : : PUNCT cana-4954 57 22 to to PART cana-4954 57 23 create create VERB cana-4954 57 24 a a DET cana-4954 57 25 collective collective ADJ cana-4954 57 26 intuitionistic intuitionistic ADJ cana-4954 57 27 fuzzy fuzzy ADJ cana-4954 57 28 decision decision NOUN cana-4954 57 29 matrix matrix NOUN cana-4954 57 30 =( =( NOUN cana-4954 57 31 rij)mxn rij)mxn NOUN cana-4954 57 32 . . PUNCT cana-4954 58 1 , , PUNCT cana-4954 58 2 combine combine VERB cana-4954 58 3 all all PRON cana-4954 58 4 of of ADP cana-4954 58 5 the the DET cana-4954 58 6 individual individual ADJ cana-4954 58 7 intuitionistic intuitionistic ADJ cana-4954 58 8 fuzzy fuzzy ADJ cana-4954 58 9 decision decision NOUN cana-4954 58 10 matrices matrix NOUN cana-4954 58 11 using use VERB cana-4954 58 12 the the DET cana-4954 58 13 difwa difwa NOUN cana-4954 58 14 operator operator NOUN cana-4954 58 15 . . PUNCT cana-4954 59 1 step step NOUN cana-4954 59 2 2 2 NUM cana-4954 59 3 : : PUNCT cana-4954 59 4 define define VERB cana-4954 59 5 𝒂+ 𝒂+ ADP cana-4954 59 6 = = SYM cana-4954 59 7 ( ( PUNCT cana-4954 59 8 π’‚πŸ π’‚πŸ ADV cana-4954 59 9 + + ADJ cana-4954 59 10 , , PUNCT cana-4954 59 11 π’‚πŸ π’‚πŸ NOUN cana-4954 59 12 + + NOUN cana-4954 59 13 , , PUNCT cana-4954 59 14 . . PUNCT cana-4954 59 15 . . PUNCT cana-4954 59 16 . . PUNCT cana-4954 60 1 . . PUNCT cana-4954 61 1 . . PUNCT cana-4954 62 1 , , PUNCT cana-4954 62 2 π’‚π’Ž π’‚π’Ž PROPN cana-4954 62 3 + + NUM cana-4954 62 4 ) ) PUNCT cana-4954 62 5 𝑻 𝑻 PROPN cana-4954 62 6 and and CCONJ cana-4954 62 7 π’‚βˆ’ π’‚βˆ’ NOUN cana-4954 62 8 = = SYM cana-4954 62 9 ( ( PUNCT cana-4954 62 10 π’‚πŸ π’‚πŸ ADV cana-4954 62 11 βˆ’ βˆ’ NOUN cana-4954 62 12 , , PUNCT cana-4954 62 13 π’‚πŸ π’‚πŸ NOUN cana-4954 62 14 βˆ’ βˆ’ NOUN cana-4954 62 15 , , PUNCT cana-4954 62 16 . . PUNCT cana-4954 62 17 . . PUNCT cana-4954 62 18 . . PUNCT cana-4954 62 19 . . PUNCT cana-4954 63 1 . . PUNCT cana-4954 64 1 , , PUNCT cana-4954 64 2 π’‚π’Ž π’‚π’Ž ADP cana-4954 64 3 βˆ’ βˆ’ NOUN cana-4954 64 4 ) ) PUNCT cana-4954 64 5 𝑻 𝑻 PROPN cana-4954 64 6 as as ADP cana-4954 64 7 the the DET cana-4954 64 8 intuitionistic intuitionistic ADJ cana-4954 64 9 fuzzy fuzzy ADJ cana-4954 64 10 negative negative ADJ cana-4954 64 11 ideal ideal ADJ cana-4954 64 12 solution solution NOUN cana-4954 64 13 ( ( PUNCT cana-4954 64 14 ifnis ifnis NOUN cana-4954 64 15 ) ) PUNCT cana-4954 64 16 and and CCONJ cana-4954 64 17 the the DET cana-4954 64 18 intuitionistic intuitionistic ADJ cana-4954 64 19 fuzzy fuzzy ADJ cana-4954 64 20 ideal ideal ADJ cana-4954 64 21 solution solution NOUN cana-4954 64 22 ( ( PUNCT cana-4954 64 23 ifis ifis PROPN cana-4954 64 24 ) ) PUNCT cana-4954 64 25 , , PUNCT cana-4954 64 26 respectively respectively ADV cana-4954 64 27 , , PUNCT cana-4954 64 28 where where SCONJ cana-4954 64 29 π‘Žπ‘– π‘Žπ‘– ADP cana-4954 64 30 + + NOUN cana-4954 64 31 = = SYM cana-4954 64 32 ( ( PUNCT cana-4954 64 33 1,0,0)(𝑖 1,0,0)(𝑖 NUM cana-4954 64 34 = = SYM cana-4954 64 35 1,2 1,2 NUM cana-4954 64 36 , , PUNCT cana-4954 64 37 . . PUNCT cana-4954 64 38 . . PUNCT cana-4954 65 1 . . PUNCT cana-4954 66 1 , , PUNCT cana-4954 66 2 π‘š π‘š X cana-4954 66 3 ) ) PUNCT cana-4954 66 4 are be AUX cana-4954 66 5 the the DET cana-4954 66 6 m m NOUN cana-4954 66 7 smallest small ADJ cana-4954 66 8 and and CCONJ cana-4954 66 9 π‘Žπ‘– π‘Žπ‘– ADP cana-4954 66 10 βˆ’ βˆ’ PROPN cana-4954 66 11 = = SYM cana-4954 67 1 ( ( PUNCT cana-4954 67 2 0,1,0)(𝑖 0,1,0)(𝑖 NUM cana-4954 67 3 = = SYM cana-4954 67 4 1,2 1,2 NUM cana-4954 67 5 , , PUNCT cana-4954 67 6 . . PUNCT cana-4954 67 7 . . PUNCT cana-4954 68 1 . . PUNCT cana-4954 69 1 , , PUNCT cana-4954 69 2 π‘š π‘š X cana-4954 69 3 ) ) PUNCT cana-4954 69 4 m m VERB cana-4954 69 5 biggest big ADJ cana-4954 69 6 ifns ifns NOUN cana-4954 69 7 . . PUNCT cana-4954 70 1 additionally additionally ADV cana-4954 70 2 , , PUNCT cana-4954 70 3 for for ADP cana-4954 70 4 ease ease NOUN cana-4954 70 5 of of ADP cana-4954 70 6 illustration illustration NOUN cana-4954 70 7 , , PUNCT cana-4954 70 8 we we PRON cana-4954 70 9 indicate indicate VERB cana-4954 70 10 the the DET cana-4954 70 11 options option NOUN cana-4954 70 12 π‘₯𝑖(𝑖 π‘₯𝑖(𝑖 NOUN cana-4954 70 13 = = SYM cana-4954 70 14 1,2 1,2 NUM cana-4954 70 15 , , PUNCT cana-4954 70 16 . . PUNCT cana-4954 70 17 . . PUNCT cana-4954 71 1 . . PUNCT cana-4954 72 1 , , PUNCT cana-4954 72 2 𝑛)𝑏𝑦π‘₯𝑖 𝑛)𝑏𝑦π‘₯𝑖 NOUN cana-4954 72 3 = = SYM cana-4954 72 4 ( ( PUNCT cana-4954 72 5 π‘Ÿπ‘–1 π‘Ÿπ‘–1 NOUN cana-4954 72 6 , , PUNCT cana-4954 72 7 π‘Ÿπ‘–2 π‘Ÿπ‘–2 X cana-4954 72 8 , , PUNCT cana-4954 72 9 . . PUNCT cana-4954 72 10 . . PUNCT cana-4954 73 1 . . PUNCT cana-4954 74 1 , , PUNCT cana-4954 74 2 π‘Ÿπ‘–π‘š)𝑇 π‘Ÿπ‘–π‘š)𝑇 PROPN cana-4954 74 3 , , PUNCT cana-4954 74 4 𝑖 𝑖 X cana-4954 74 5 = = SYM cana-4954 74 6 1,2 1,2 NUM cana-4954 74 7 , , PUNCT cana-4954 74 8 . . PUNCT cana-4954 74 9 . . PUNCT cana-4954 74 10 . . PUNCT cana-4954 74 11 . . PUNCT cana-4954 75 1 . . PUNCT cana-4954 76 1 , , PUNCT cana-4954 76 2 𝑛. 𝑛. NOUN cana-4954 76 3 step step NOUN cana-4954 76 4 3 3 NUM cana-4954 76 5 : : PUNCT cana-4954 76 6 determine determine VERB cana-4954 76 7 the the DET cana-4954 76 8 proximity proximity NOUN cana-4954 76 9 coefficient coefficient NOUN cana-4954 76 10 , , PUNCT cana-4954 76 11 where where SCONJ cana-4954 76 12 , , PUNCT cana-4954 76 13 οΏ½ οΏ½ PROPN cana-4954 76 14 Μƒ Μƒ NOUN cana-4954 76 15 οΏ½ οΏ½ NOUN cana-4954 76 16 𝑖 𝑖 SYM cana-4954 76 17 = = PUNCT cana-4954 76 18 ( ( PUNCT cana-4954 76 19 1,0)between 1,0)between NUM cana-4954 76 20 the the DET cana-4954 76 21 positive positive ADJ cana-4954 76 22 ideal ideal ADJ cana-4954 76 23 value value NOUN cana-4954 76 24 οΏ½ οΏ½ PROPN cana-4954 76 25 Μƒ Μƒ PROPN cana-4954 76 26 οΏ½ οΏ½ NOUN cana-4954 76 27 𝑖 𝑖 PROPN cana-4954 76 28 and and CCONJ cana-4954 76 29 the the DET cana-4954 76 30 collective collective ADJ cana-4954 76 31 overall overall ADJ cana-4954 76 32 preference preference NOUN cana-4954 76 33 values value NOUN cana-4954 76 34 . . PUNCT cana-4954 77 1 step step NOUN cana-4954 77 2 4 4 NUM cana-4954 77 3 : : PUNCT cana-4954 77 4 sort sort VERB cana-4954 77 5 each each DET cana-4954 77 6 option option NOUN cana-4954 77 7 based base VERB cana-4954 77 8 on on ADP cana-4954 77 9 the the DET cana-4954 77 10 proximity proximity NOUN cana-4954 77 11 coefficient coefficient NOUN cana-4954 77 12 𝐢(π‘₯𝑖)(𝑖 𝐢(π‘₯𝑖)(𝑖 NOUN cana-4954 77 13 = = NOUN cana-4954 77 14 1,2 1,2 NUM cana-4954 77 15 , , PUNCT cana-4954 77 16 . . PUNCT cana-4954 77 17 . . PUNCT cana-4954 77 18 . . PUNCT cana-4954 78 1 . . PUNCT cana-4954 79 1 , , PUNCT cana-4954 79 2 𝑛 𝑛 PROPN cana-4954 79 3 ) ) PUNCT cana-4954 79 4 , , PUNCT cana-4954 79 5 ; ; PUNCT cana-4954 79 6 the the DET cana-4954 79 7 better well ADJ cana-4954 79 8 option option NOUN cana-4954 79 9 is be AUX cana-4954 79 10 indicated indicate VERB cana-4954 79 11 by by ADP cana-4954 79 12 a a DET cana-4954 79 13 higher high ADJ cana-4954 79 14 number number NOUN cana-4954 79 15 π‘₯𝑖 π‘₯𝑖 NUM cana-4954 79 16 . . PUNCT cana-4954 80 1 singular singular PROPN cana-4954 80 2 perturbation perturbation NOUN cana-4954 80 3 problems problem NOUN cana-4954 80 4 : : PUNCT cana-4954 80 5 to to PART cana-4954 80 6 differentiate differentiate VERB cana-4954 80 7 between between ADP cana-4954 80 8 regular regular ADJ cana-4954 80 9 and and CCONJ cana-4954 80 10 singular singular ADJ cana-4954 80 11 perturbation perturbation NOUN cana-4954 80 12 problems problem NOUN cana-4954 80 13 , , PUNCT cana-4954 80 14 first first ADV cana-4954 80 15 take take VERB cana-4954 80 16 a a DET cana-4954 80 17 look look NOUN cana-4954 80 18 at at ADP cana-4954 80 19 a a DET cana-4954 80 20 family family NOUN cana-4954 80 21 of of ADP cana-4954 80 22 boundary boundary ADJ cana-4954 80 23 value value NOUN cana-4954 80 24 problems problem NOUN cana-4954 80 25 π‘βˆˆ π‘βˆˆ NOUN cana-4954 80 26 that that SCONJ cana-4954 80 27 , , PUNCT cana-4954 80 28 depending depend VERB cana-4954 80 29 on on ADP cana-4954 80 30 a a DET cana-4954 80 31 small small ADJ cana-4954 80 32 parameter parameter NOUN cana-4954 80 33 πœ€. πœ€. NOUN cana-4954 80 34 can can AUX cana-4954 80 35 have have VERB cana-4954 80 36 a a DET cana-4954 80 37 solution solution NOUN cana-4954 80 38 π‘¦πœ€(π‘₯)π‘œπ‘“π‘ƒπœ€constructed π‘¦πœ€(π‘₯)π‘œπ‘“π‘ƒπœ€constructe VERB cana-4954 80 39 by by ADP cana-4954 80 40 a a DET cana-4954 80 41 well well ADV cana-4954 80 42 - - PUNCT cana-4954 80 43 known know VERB cana-4954 80 44 " " PUNCT cana-4954 80 45 method method NOUN cana-4954 80 46 of of ADP cana-4954 80 47 perturbation perturbation NOUN cana-4954 80 48 " " PUNCT cana-4954 80 49 ; ; PUNCT cana-4954 80 50 that that PRON cana-4954 80 51 is is ADV cana-4954 80 52 , , PUNCT cana-4954 80 53 as as ADP cana-4954 80 54 a a DET cana-4954 80 55 power power NOUN cana-4954 80 56 series series NOUN cana-4954 80 57 πœ€ πœ€ PROPN cana-4954 80 58 in in ADP cana-4954 80 59 which which PRON cana-4954 80 60 the the DET cana-4954 80 61 problem problem NOUN cana-4954 80 62 's 's PART cana-4954 80 63 solution solution NOUN cana-4954 80 64 𝑝0 𝑝0 NOUN cana-4954 80 65 ( ( PUNCT cana-4954 80 66 obtained obtain VERB cana-4954 80 67 by by ADP cana-4954 80 68 putting put VERB cana-4954 80 69 ∈= ∈= PUNCT cana-4954 80 70 0 0 NUM cana-4954 80 71 in in ADP cana-4954 80 72 π‘βˆˆ π‘βˆˆ NOUN cana-4954 80 73 ) ) PUNCT cana-4954 80 74 is be AUX cana-4954 80 75 the the DET cana-4954 80 76 first first ADJ cana-4954 80 77 term term NOUN cana-4954 80 78 𝑦0 𝑦0 NOUN cana-4954 80 79 . . PUNCT cana-4954 81 1 a a DET cana-4954 81 2 power power NOUN cana-4954 81 3 series series NOUN cana-4954 81 4 expansion expansion NOUN cana-4954 81 5 as as ADP cana-4954 81 6 βˆˆβ†’ βˆˆβ†’ NOUN cana-4954 81 7 0 0 NUM cana-4954 81 8 is be AUX cana-4954 81 9 said say VERB cana-4954 81 10 to to PART cana-4954 81 11 be be AUX cana-4954 81 12 a a DET cana-4954 81 13 regular regular ADJ cana-4954 81 14 perturbation perturbation NOUN cana-4954 81 15 issue issue NOUN cana-4954 81 16 when when SCONJ cana-4954 81 17 it it PRON cana-4954 81 18 converges converge VERB cana-4954 81 19 evenly evenly ADV cana-4954 81 20 in in ADP cana-4954 81 21 x. x. PROPN cana-4954 81 22 is be AUX cana-4954 81 23 referred refer VERB cana-4954 81 24 to to ADP cana-4954 81 25 as as ADP cana-4954 81 26 a a DET cana-4954 81 27 single single ADJ cana-4954 81 28 perturbation perturbation NOUN cana-4954 81 29 problem problem NOUN cana-4954 81 30 when when SCONJ cana-4954 81 31 π‘¦βˆˆ(π‘₯ π‘¦βˆˆ(π‘₯ NOUN cana-4954 81 32 ) ) PUNCT cana-4954 82 1 it it PRON cana-4954 82 2 lacks lack VERB cana-4954 82 3 a a DET cana-4954 82 4 uniform uniform ADJ cana-4954 82 5 limit limit NOUN cana-4954 82 6 in in ADP cana-4954 82 7 x x PUNCT cana-4954 82 8 as as ADP cana-4954 82 9 βˆˆβ†’ βˆˆβ†’ NOUN cana-4954 82 10 0 0 NUM cana-4954 82 11 , , PUNCT cana-4954 82 12 as as SCONJ cana-4954 82 13 this this DET cana-4954 82 14 regular regular ADJ cana-4954 82 15 perturbation perturbation NOUN cana-4954 82 16 procedure procedure NOUN cana-4954 82 17 fails fail VERB cana-4954 82 18 . . PUNCT cana-4954 83 1 a a DET cana-4954 83 2 singly singly ADV cana-4954 83 3 perturbed perturb VERB cana-4954 83 4 delay delay NOUN cana-4954 83 5 differential differential ADJ cana-4954 83 6 equation equation NOUN cana-4954 83 7 is be AUX cana-4954 83 8 an an DET cana-4954 83 9 ordinary ordinary ADJ cana-4954 83 10 differential differential ADJ cana-4954 83 11 equation equation NOUN cana-4954 83 12 that that PRON cana-4954 83 13 includes include VERB cana-4954 83 14 at at ADV cana-4954 83 15 least least ADV cana-4954 83 16 one one NUM cana-4954 83 17 delay delay NOUN cana-4954 83 18 term term NOUN cana-4954 83 19 and and CCONJ cana-4954 83 20 has have VERB cana-4954 83 21 its its PRON cana-4954 83 22 highest high ADJ cana-4954 83 23 derivative derivative NOUN cana-4954 83 24 multiplied multiply VERB cana-4954 83 25 by by ADP cana-4954 83 26 a a DET cana-4954 83 27 small small ADJ cana-4954 83 28 parameter parameter NOUN cana-4954 83 29 . . PUNCT cana-4954 84 1 these these DET cana-4954 84 2 equations equation NOUN cana-4954 84 3 frequently frequently ADV cana-4954 84 4 arise arise VERB cana-4954 84 5 in in ADP cana-4954 84 6 various various ADJ cana-4954 84 7 applications application NOUN cana-4954 84 8 , , PUNCT cana-4954 84 9 such such ADJ cana-4954 84 10 as as ADP cana-4954 84 11 control control NOUN cana-4954 84 12 theory theory NOUN cana-4954 84 13 variation variation NOUN cana-4954 84 14 problems problem NOUN cana-4954 84 15 , , PUNCT cana-4954 84 16 depolarization depolarization NOUN cana-4954 84 17 in in ADP cana-4954 84 18 stein stein PROPN cana-4954 84 19 's 's PART cana-4954 84 20 model model NOUN cana-4954 84 21 , , PUNCT cana-4954 84 22 human human ADJ cana-4954 84 23 pupil pupil ADJ cana-4954 84 24 - - PUNCT cana-4954 84 25 light light NOUN cana-4954 84 26 reflex reflex NOUN cana-4954 84 27 modeling modeling NOUN cana-4954 84 28 , , PUNCT cana-4954 84 29 and and CCONJ cana-4954 84 30 the the DET cana-4954 84 31 first first ADJ cana-4954 84 32 exit exit NOUN cana-4954 84 33 time time NOUN cana-4954 84 34 problem problem NOUN cana-4954 84 35 in in ADP cana-4954 84 36 neuronal neuronal ADJ cana-4954 84 37 variability variability NOUN cana-4954 84 38 activation activation NOUN cana-4954 84 39 . . PUNCT cana-4954 85 1 this this DET cana-4954 85 2 study study NOUN cana-4954 85 3 focuses focus VERB cana-4954 85 4 on on ADP cana-4954 85 5 boundary boundary ADJ cana-4954 85 6 value value NOUN cana-4954 85 7 problems problem NOUN cana-4954 85 8 for for ADP cana-4954 85 9 singularly singularly ADV cana-4954 85 10 perturbed perturb VERB cana-4954 85 11 linear linear ADJ cana-4954 85 12 second second ADJ cana-4954 85 13 - - PUNCT cana-4954 85 14 order order NOUN cana-4954 85 15 differential differential ADJ cana-4954 85 16 - - PUNCT cana-4954 85 17 difference difference NOUN cana-4954 85 18 equations equation NOUN cana-4954 85 19 , , PUNCT cana-4954 85 20 where where SCONJ cana-4954 85 21 a a DET cana-4954 85 22 small small ADJ cana-4954 85 23 parameter parameter NOUN cana-4954 85 24 multiplies multiply VERB cana-4954 85 25 the the DET cana-4954 85 26 highest high ADJ cana-4954 85 27 - - PUNCT cana-4954 85 28 order order NOUN cana-4954 85 29 derivative derivative NOUN cana-4954 85 30 . . PUNCT cana-4954 86 1 the the DET cana-4954 86 2 delay delay NOUN cana-4954 86 3 term term NOUN cana-4954 86 4 u(xβˆ’1 u(xβˆ’1 PROPN cana-4954 86 5 ) ) PUNCT cana-4954 86 6 is be AUX cana-4954 86 7 expressed express VERB cana-4954 86 8 using use VERB cana-4954 86 9 a a DET cana-4954 86 10 taylor taylor PROPN cana-4954 86 11 series series NOUN cana-4954 86 12 expansion expansion NOUN cana-4954 86 13 at at ADP cana-4954 86 14 x=1 x=1 PROPN cana-4954 86 15 . . PUNCT cana-4954 87 1 to to PART cana-4954 87 2 address address VERB cana-4954 87 3 the the DET cana-4954 87 4 numerical numerical ADJ cana-4954 87 5 challenges challenge NOUN cana-4954 87 6 posed pose VERB cana-4954 87 7 by by ADP cana-4954 87 8 these these DET cana-4954 87 9 equations equation NOUN cana-4954 87 10 , , PUNCT cana-4954 87 11 a a DET cana-4954 87 12 numerical numerical ADJ cana-4954 87 13 method method NOUN cana-4954 87 14 based base VERB cana-4954 87 15 on on ADP cana-4954 87 16 a a DET cana-4954 87 17 piecewise piecewise NOUN cana-4954 87 18 uniform uniform NOUN cana-4954 87 19 shishkintype shishkintype NOUN cana-4954 87 20 mesh mesh NOUN cana-4954 87 21 is be AUX cana-4954 87 22 implemented implement VERB cana-4954 87 23 within within ADP cana-4954 87 24 a a DET cana-4954 87 25 classical classical ADJ cana-4954 87 26 finite finite ADJ cana-4954 87 27 difference difference NOUN cana-4954 87 28 scheme scheme NOUN cana-4954 87 29 . . PUNCT cana-4954 88 1 a a DET cana-4954 88 2 carefully carefully ADV cana-4954 88 3 constructed construct VERB cana-4954 88 4 piecewise piecewise NOUN cana-4954 88 5 uniform uniform NOUN cana-4954 88 6 shishkin shishkin PROPN cana-4954 88 7 mesh mesh NOUN cana-4954 88 8 is be AUX cana-4954 88 9 derived derive VERB cana-4954 88 10 to to PART cana-4954 88 11 ensure ensure VERB cana-4954 88 12 numerical numerical ADJ cana-4954 88 13 stability stability NOUN cana-4954 88 14 and and CCONJ cana-4954 88 15 accuracy accuracy NOUN cana-4954 88 16 . . PUNCT cana-4954 89 1 it it PRON cana-4954 89 2 is be AUX cana-4954 89 3 proven prove VERB cana-4954 89 4 that that SCONJ cana-4954 89 5 the the DET cana-4954 89 6 proposed propose VERB cana-4954 89 7 approach approach NOUN cana-4954 89 8 achieves achieve VERB cana-4954 89 9 first first ADJ cana-4954 89 10 - - PUNCT cana-4954 89 11 order order NOUN cana-4954 89 12 convergence convergence NOUN cana-4954 89 13 in in ADP cana-4954 89 14 the the DET cana-4954 89 15 communications communication NOUN cana-4954 89 16 on on ADP cana-4954 89 17 applied apply VERB cana-4954 89 18 nonlinear nonlinear ADJ cana-4954 89 19 analysis analysis NOUN cana-4954 89 20 issn issn NOUN cana-4954 89 21 : : PUNCT cana-4954 89 22 1074 1074 NUM cana-4954 89 23 - - PUNCT cana-4954 89 24 133x 133x NUM cana-4954 89 25 vol vol VERB cana-4954 89 26 32 32 NUM cana-4954 89 27 no no NOUN cana-4954 89 28 . . PUNCT cana-4954 89 29 10s 10 NOUN cana-4954 89 30 ( ( PUNCT cana-4954 89 31 2025 2025 NUM cana-4954 89 32 ) ) PUNCT cana-4954 89 33 1034 1034 NUM cana-4954 89 34 https://internationalpubls.com https://internationalpubls.com X cana-4954 89 35 maximum maximum PROPN cana-4954 89 36 norm norm NOUN cana-4954 89 37 , , PUNCT cana-4954 89 38 regardless regardless ADV cana-4954 89 39 of of ADP cana-4954 89 40 the the DET cana-4954 89 41 small small ADJ cana-4954 89 42 parameter parameter NOUN cana-4954 89 43 . . PUNCT cana-4954 90 1 the the DET cana-4954 90 2 taylor taylor PROPN cana-4954 90 3 series series PROPN cana-4954 90 4 expansion expansion NOUN cana-4954 90 5 at at ADP cana-4954 90 6 x x PROPN cana-4954 90 7 is be AUX cana-4954 90 8 employed employ VERB cana-4954 90 9 to to PART cana-4954 90 10 effectively effectively ADV cana-4954 90 11 represent represent VERB cana-4954 90 12 the the DET cana-4954 90 13 delay delay NOUN cana-4954 90 14 term term NOUN cana-4954 90 15 u(xβˆ’1 u(xβˆ’1 PROPN cana-4954 90 16 ) ) PUNCT cana-4954 90 17 , , PUNCT cana-4954 90 18 ensuring ensure VERB cana-4954 90 19 an an DET cana-4954 90 20 accurate accurate ADJ cana-4954 90 21 numerical numerical ADJ cana-4954 90 22 solution solution NOUN cana-4954 90 23 . . PUNCT cana-4954 91 1 𝑳𝒖(𝒙 𝑳𝒖(𝒙 PROPN cana-4954 91 2 ) ) PUNCT cana-4954 91 3 = = SYM cana-4954 92 1 βˆ’πœΊπ’–β€² βˆ’πœΊπ’–β€² PROPN cana-4954 92 2 + + CCONJ cana-4954 92 3 𝒂(𝒙)𝒖(𝒙 𝒂(𝒙)𝒖(𝒙 NOUN cana-4954 92 4 ) ) PUNCT cana-4954 93 1 + + NUM cana-4954 93 2 𝒃(𝒙)𝒖(𝒙 𝒃(𝒙)𝒖(𝒙 NUM cana-4954 93 3 βˆ’ βˆ’ NUM cana-4954 93 4 𝟏 𝟏 NUM cana-4954 93 5 ) ) PUNCT cana-4954 93 6 = = PUNCT cana-4954 93 7 𝒇(𝒙)𝒐𝒏[𝟎,𝟐 𝒇(𝒙)𝒐𝒏[𝟎,𝟐 PROPN cana-4954 93 8 ] ] PUNCT cana-4954 93 9 , , PUNCT cana-4954 93 10 with𝒖 with𝒖 NOUN cana-4954 93 11 = = SYM cana-4954 93 12 𝝓𝒐𝒏[βˆ’πŸ,𝟎]𝒂𝒏𝒅𝒖(𝟐 𝝓𝒐𝒏[βˆ’πŸ,𝟎]𝒂𝒏𝒅𝒖(𝟐 NOUN cana-4954 93 13 ) ) PUNCT cana-4954 93 14 = = VERB cana-4954 93 15 𝒍. 𝒍. NOUN cana-4954 93 16 where where SCONJ cana-4954 93 17 πœ™ πœ™ NOUN cana-4954 93 18 is be AUX cana-4954 93 19 sufficiently sufficiently ADV cana-4954 93 20 smooth smooth ADJ cana-4954 93 21 on on ADP cana-4954 93 22 [ [ X cana-4954 93 23 -1 -1 X cana-4954 93 24 , , PUNCT cana-4954 93 25 0 0 NUM cana-4954 93 26 ] ] PUNCT cana-4954 93 27 . . PUNCT cana-4954 94 1 for for ADP cana-4954 94 2 all all PRON cana-4954 94 3 π‘₯ π‘₯ DET cana-4954 94 4 ∈ ∈ NOUN cana-4954 94 5 [ [ X cana-4954 94 6 0,2 0,2 NUM cana-4954 94 7 ] ] PUNCT cana-4954 94 8 , , PUNCT cana-4954 94 9 it it PRON cana-4954 94 10 is be AUX cana-4954 94 11 assumed assume VERB cana-4954 94 12 that that SCONJ cana-4954 94 13 a(x a(x NOUN cana-4954 94 14 ) ) PUNCT cana-4954 94 15 and and CCONJ cana-4954 94 16 b(x b(x NOUN cana-4954 94 17 ) ) PUNCT cana-4954 94 18 satisfy satisfy NOUN cana-4954 94 19 , , PUNCT cana-4954 94 20 𝒂(𝒙 𝒂(𝒙 NUM cana-4954 94 21 ) ) PUNCT cana-4954 95 1 + + CCONJ cana-4954 95 2 𝒃(𝒙 𝒃(𝒙 NOUN cana-4954 95 3 ) ) PUNCT cana-4954 95 4 > > X cana-4954 95 5 𝜢 𝜢 SYM cana-4954 95 6 , , PUNCT cana-4954 95 7 and𝒃(𝒙 and𝒃(𝒙 PROPN cana-4954 95 8 ) ) PUNCT cana-4954 95 9 < < X cana-4954 95 10 𝟎 𝟎 PROPN cana-4954 95 11 , , PUNCT cana-4954 95 12 π’‡π’π’“π’”π’π’Žπ’†π’“π’†π’‚π’π’π’–π’Žπ’ƒπ’†π’“πœΆ π’‡π’π’“π’”π’π’Žπ’†π’“π’†π’‚π’π’π’–π’Žπ’ƒπ’†π’“πœΆ ADV cana-4954 95 13 > > SYM cana-4954 95 14 𝟎 𝟎 NUM cana-4954 95 15 shishkin shishkin NOUN cana-4954 95 16 mesh mesh NOUN cana-4954 95 17 : : PUNCT cana-4954 95 18 to to PART cana-4954 95 19 construct construct VERB cana-4954 95 20 an an DET cana-4954 95 21 effective effective ADJ cana-4954 95 22 piecewise piecewise NOUN cana-4954 95 23 uniform uniform NOUN cana-4954 95 24 mesh mesh NOUN cana-4954 95 25 within within ADP cana-4954 95 26 the the DET cana-4954 95 27 domain domain NOUN cana-4954 95 28 of of ADP cana-4954 95 29 definition definition NOUN cana-4954 95 30 , , PUNCT cana-4954 95 31 it it PRON cana-4954 95 32 is be AUX cana-4954 95 33 essential essential ADJ cana-4954 95 34 to to PART cana-4954 95 35 account account VERB cana-4954 95 36 for for ADP cana-4954 95 37 the the DET cana-4954 95 38 boundary boundary ADJ cana-4954 95 39 layer layer NOUN cana-4954 95 40 behavior behavior NOUN cana-4954 95 41 near near ADP cana-4954 95 42 x=0 x=0 PROPN cana-4954 95 43 . . PUNCT cana-4954 96 1 the the DET cana-4954 96 2 mesh mesh NOUN cana-4954 96 3 should should AUX cana-4954 96 4 be be AUX cana-4954 96 5 refined refine VERB cana-4954 96 6 in in ADP cana-4954 96 7 this this DET cana-4954 96 8 region region NOUN cana-4954 96 9 while while SCONJ cana-4954 96 10 remaining remain VERB cana-4954 96 11 coarser coarse ADJ cana-4954 96 12 elsewhere elsewhere ADV cana-4954 96 13 . . PUNCT cana-4954 97 1 if if SCONJ cana-4954 97 2 the the DET cana-4954 97 3 total total ADJ cana-4954 97 4 number number NOUN cana-4954 97 5 of of ADP cana-4954 97 6 mesh mesh NOUN cana-4954 97 7 points point NOUN cana-4954 97 8 is be AUX cana-4954 97 9 n n PRON cana-4954 97 10 , , PUNCT cana-4954 97 11 they they PRON cana-4954 97 12 are be AUX cana-4954 97 13 distributed distribute VERB cana-4954 97 14 such such ADJ cana-4954 97 15 that that SCONJ cana-4954 97 16 n/2 n/2 ADJ cana-4954 97 17 points point NOUN cana-4954 97 18 are be AUX cana-4954 97 19 allocated allocate VERB cana-4954 97 20 to to ADP cana-4954 97 21 the the DET cana-4954 97 22 inner inner ADJ cana-4954 97 23 region region NOUN cana-4954 97 24 , , PUNCT cana-4954 97 25 where where SCONJ cana-4954 97 26 the the DET cana-4954 97 27 solution solution NOUN cana-4954 97 28 exhibits exhibit VERB cana-4954 97 29 rapid rapid ADJ cana-4954 97 30 variation variation NOUN cana-4954 97 31 , , PUNCT cana-4954 97 32 and and CCONJ cana-4954 97 33 the the DET cana-4954 97 34 remaining remain VERB cana-4954 97 35 n/2 n/2 NOUN cana-4954 97 36 points point NOUN cana-4954 97 37 are be AUX cana-4954 97 38 placed place VERB cana-4954 97 39 in in ADP cana-4954 97 40 the the DET cana-4954 97 41 outer outer ADJ cana-4954 97 42 region region NOUN cana-4954 97 43 , , PUNCT cana-4954 97 44 where where SCONJ cana-4954 97 45 the the DET cana-4954 97 46 solution solution NOUN cana-4954 97 47 changes change VERB cana-4954 97 48 more more ADV cana-4954 97 49 gradually gradually ADV cana-4954 97 50 . . PUNCT cana-4954 98 1 the the DET cana-4954 98 2 resulting result VERB cana-4954 98 3 mesh mesh NOUN cana-4954 98 4 structure structure NOUN cana-4954 98 5 is be AUX cana-4954 98 6 outlined outline VERB cana-4954 98 7 as as SCONJ cana-4954 98 8 follows follow VERB cana-4954 98 9 . . PUNCT cana-4954 99 1 where where SCONJ cana-4954 99 2 the the DET cana-4954 99 3 parameter parameter NOUN cana-4954 99 4 𝜏 𝜏 NOUN cana-4954 99 5 is be AUX cana-4954 99 6 defined define VERB cana-4954 99 7 as as ADP cana-4954 99 8 𝜏 𝜏 PROPN cana-4954 99 9 = = SYM cana-4954 99 10 π‘šπ‘–π‘› π‘šπ‘–π‘› NOUN cana-4954 99 11 { { PUNCT cana-4954 99 12 1 1 NUM cana-4954 99 13 2 2 NUM cana-4954 99 14 , , PUNCT cana-4954 99 15 πœ€ πœ€ VERB cana-4954 99 16 𝛼 𝛼 ADP cana-4954 99 17 𝑙𝑛 𝑙𝑛 PRON cana-4954 99 18 𝑁 𝑁 PROPN cana-4954 99 19 } } PUNCT cana-4954 99 20 discrete discrete ADJ cana-4954 99 21 problem problem NOUN cana-4954 99 22 : : PUNCT cana-4954 99 23 the the DET cana-4954 99 24 finite finite ADJ cana-4954 99 25 difference difference NOUN cana-4954 99 26 method method NOUN cana-4954 99 27 is be AUX cana-4954 99 28 now now ADV cana-4954 99 29 applied apply VERB cana-4954 99 30 to to PART cana-4954 99 31 formulate formulate VERB cana-4954 99 32 the the DET cana-4954 99 33 discrete discrete ADJ cana-4954 99 34 two two NUM cana-4954 99 35 - - PUNCT cana-4954 99 36 point point NOUN cana-4954 99 37 boundary boundary ADJ cana-4954 99 38 value value NOUN cana-4954 99 39 problem problem NOUN cana-4954 99 40 on on ADP cana-4954 99 41 an an DET cana-4954 99 42 arbitrary arbitrary ADJ cana-4954 99 43 grid grid NOUN cana-4954 99 44 . . PUNCT cana-4954 100 1 πΏπ‘π‘ˆ(π‘₯𝑗 πΏπ‘π‘ˆ(π‘₯𝑗 ADJ cana-4954 100 2 ) ) PUNCT cana-4954 100 3 = = SYM cana-4954 100 4 πœ€π·βˆ’π‘ˆ(π‘₯𝑗 πœ€π·βˆ’π‘ˆ(π‘₯𝑗 NOUN cana-4954 100 5 ) ) PUNCT cana-4954 100 6 + + SYM cana-4954 100 7 π‘Ž(π‘₯𝑗)π‘ˆ(π‘₯𝑗 π‘Ž(π‘₯𝑗)π‘ˆ(π‘₯𝑗 NOUN cana-4954 100 8 ) ) PUNCT cana-4954 100 9 + + CCONJ cana-4954 100 10 𝑏(π‘₯𝑗)π‘ˆ(π‘₯𝑗 𝑏(π‘₯𝑗)π‘ˆ(π‘₯𝑗 PROPN cana-4954 100 11 βˆ’ βˆ’ NOUN cana-4954 100 12 1 1 NUM cana-4954 100 13 ) ) PUNCT cana-4954 100 14 = = NOUN cana-4954 100 15 𝑓(π‘₯𝑗)π‘“π‘œπ‘Ÿπ‘Žπ‘™π‘™(π‘₯𝑗 𝑓(π‘₯𝑗)π‘“π‘œπ‘Ÿπ‘Žπ‘™π‘™(π‘₯𝑗 NOUN cana-4954 100 16 ) ) PUNCT cana-4954 100 17 , , PUNCT cana-4954 100 18 𝑗 𝑗 NOUN cana-4954 100 19 = = SYM cana-4954 100 20 1,𝑁 1,𝑁 NUM cana-4954 100 21 πΏπ‘π‘ˆ πΏπ‘π‘ˆ NOUN cana-4954 100 22 = = SYM cana-4954 100 23 𝑓 𝑓 PROPN cana-4954 100 24 , , PUNCT cana-4954 100 25 π‘ˆ(0 π‘ˆ(0 NUM cana-4954 100 26 ) ) PUNCT cana-4954 100 27 = = SYM cana-4954 100 28 𝑒(0 𝑒(0 PROPN cana-4954 100 29 ) ) PUNCT cana-4954 100 30 , , PUNCT cana-4954 100 31 π‘ˆ(1 π‘ˆ(1 X cana-4954 100 32 ) ) PUNCT cana-4954 100 33 = = PUNCT cana-4954 100 34 𝑒(1 𝑒(1 PROPN cana-4954 100 35 ) ) PUNCT cana-4954 100 36 . . PUNCT cana-4954 101 1 where where SCONJ cana-4954 101 2 π‘ˆ(π‘₯𝑗 π‘ˆ(π‘₯𝑗 NOUN cana-4954 101 3 βˆ’ βˆ’ PROPN cana-4954 101 4 1 1 NUM cana-4954 101 5 ) ) PUNCT cana-4954 101 6 = = NOUN cana-4954 101 7 π‘ˆ(π‘₯𝑗 π‘ˆ(π‘₯𝑗 NOUN cana-4954 101 8 ) ) PUNCT cana-4954 101 9 βˆ’ βˆ’ PROPN cana-4954 101 10 π·βˆ’π‘ˆ(π‘₯𝑗 π·βˆ’π‘ˆ(π‘₯𝑗 NOUN cana-4954 101 11 ) ) PUNCT cana-4954 101 12 π·βˆ’π‘ˆ(π‘₯𝑗 π·βˆ’π‘ˆ(π‘₯𝑗 NOUN cana-4954 101 13 ) ) PUNCT cana-4954 101 14 = = SYM cana-4954 101 15 π‘ˆ(π‘₯𝑗 π‘ˆ(π‘₯𝑗 NOUN cana-4954 101 16 ) ) PUNCT cana-4954 101 17 βˆ’ βˆ’ PROPN cana-4954 101 18 π‘ˆ(π‘₯π‘—βˆ’1 π‘ˆ(π‘₯π‘—βˆ’1 NOUN cana-4954 101 19 ) ) PUNCT cana-4954 101 20 β„Žπ‘— β„Žπ‘— PROPN cana-4954 101 21 communications communication NOUN cana-4954 101 22 on on ADP cana-4954 101 23 applied apply VERB cana-4954 101 24 nonlinear nonlinear ADJ cana-4954 101 25 analysis analysis NOUN cana-4954 101 26 issn issn NOUN cana-4954 101 27 : : PUNCT cana-4954 101 28 1074 1074 NUM cana-4954 101 29 - - PUNCT cana-4954 101 30 133x 133x NUM cana-4954 101 31 vol vol VERB cana-4954 101 32 32 32 NUM cana-4954 101 33 no no NOUN cana-4954 101 34 . . PUNCT cana-4954 102 1 10s 10 NOUN cana-4954 102 2 ( ( PUNCT cana-4954 102 3 2025 2025 NUM cana-4954 102 4 ) ) PUNCT cana-4954 102 5 1035 1035 NUM cana-4954 102 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 102 7 magdm magdm NOUN cana-4954 102 8 problem problem VERB cana-4954 102 9 determination determination NOUN cana-4954 102 10 experts expert NOUN cana-4954 102 11 weights weight VERB cana-4954 102 12 using use VERB cana-4954 102 13 a a DET cana-4954 102 14 singularly singularly ADV cana-4954 102 15 perturbed perturb VERB cana-4954 102 16 initial initial ADJ cana-4954 102 17 value value NOUN cana-4954 102 18 problem problem NOUN cana-4954 102 19 : : PUNCT cana-4954 102 20 problem problem NOUN cana-4954 102 21 proposed propose VERB cana-4954 102 22 by by ADP cana-4954 102 23 decision decision NOUN cana-4954 102 24 maker maker NOUN cana-4954 102 25 . . PUNCT cana-4954 103 1 the the DET cana-4954 103 2 unknown unknown ADJ cana-4954 103 3 decision decision NOUN cana-4954 103 4 - - PUNCT cana-4954 103 5 maker maker NOUN cana-4954 103 6 weights weight NOUN cana-4954 103 7 are be AUX cana-4954 103 8 determined determine VERB cana-4954 103 9 by by ADP cana-4954 103 10 solving solve VERB cana-4954 103 11 a a DET cana-4954 103 12 singularly singularly ADV cana-4954 103 13 perturbed perturb VERB cana-4954 103 14 initial initial ADJ cana-4954 103 15 value value NOUN cana-4954 103 16 problem problem NOUN cana-4954 103 17 . . PUNCT cana-4954 104 1 βˆ’πœ€π‘’β€² βˆ’πœ€π‘’β€² ADJ cana-4954 104 2 + + CCONJ cana-4954 104 3 1.5𝑒 1.5𝑒 NUM cana-4954 104 4 βˆ’ βˆ’ NOUN cana-4954 104 5 0.1𝑒(π‘₯ 0.1𝑒(π‘₯ NOUN cana-4954 104 6 βˆ’ βˆ’ NOUN cana-4954 104 7 1 1 NUM cana-4954 104 8 ) ) PUNCT cana-4954 104 9 = = PUNCT cana-4954 105 1 1π‘“π‘œπ‘Ÿπ‘₯ 1π‘“π‘œπ‘Ÿπ‘₯ NUM cana-4954 105 2 ∈ ∈ PROPN cana-4954 105 3 ( ( PUNCT cana-4954 105 4 0,1 0,1 NUM cana-4954 105 5 ) ) PUNCT cana-4954 105 6 βˆͺ βˆͺ NOUN cana-4954 105 7 ( ( PUNCT cana-4954 105 8 1,2 1,2 NUM cana-4954 105 9 ) ) PUNCT cana-4954 105 10 𝑒(0 𝑒(0 PROPN cana-4954 105 11 ) ) PUNCT cana-4954 105 12 = = PUNCT cana-4954 106 1 1π‘“π‘œπ‘Ÿπ‘₯ 1π‘“π‘œπ‘Ÿπ‘₯ NUM cana-4954 106 2 ∈ ∈ PROPN cana-4954 106 3 [ [ X cana-4954 106 4 βˆ’1,0 βˆ’1,0 X cana-4954 106 5 ] ] X cana-4954 106 6 the the DET cana-4954 106 7 numerical numerical ADJ cana-4954 106 8 solution solution NOUN cana-4954 106 9 presented present VERB cana-4954 106 10 above above ADV cana-4954 106 11 can can AUX cana-4954 106 12 be be AUX cana-4954 106 13 obtained obtain VERB cana-4954 106 14 using use VERB cana-4954 106 15 the the DET cana-4954 106 16 classical classical ADJ cana-4954 106 17 finite finite ADJ cana-4954 106 18 difference difference NOUN cana-4954 106 19 scheme scheme NOUN cana-4954 106 20 . . PUNCT cana-4954 107 1 the the DET cana-4954 107 2 normalization normalization NOUN cana-4954 107 3 of of ADP cana-4954 107 4 weighting weight VERB cana-4954 107 5 vectors vector NOUN cana-4954 107 6 is be AUX cana-4954 107 7 shown show VERB cana-4954 107 8 in in ADP cana-4954 107 9 tables table NOUN cana-4954 107 10 1 1 NUM cana-4954 107 11 and and CCONJ cana-4954 107 12 2 2 NUM cana-4954 107 13 , , PUNCT cana-4954 107 14 and and CCONJ cana-4954 107 15 the the DET cana-4954 107 16 weighting weight VERB cana-4954 107 17 vectors vector NOUN cana-4954 107 18 can can AUX cana-4954 107 19 be be AUX cana-4954 107 20 calculated calculate VERB cana-4954 107 21 for for ADP cana-4954 107 22 different different ADJ cana-4954 107 23 values value NOUN cana-4954 107 24 of of ADP cana-4954 107 25 Ο„ Ο„ PROPN cana-4954 107 26 . . PUNCT cana-4954 107 27 table table NOUN cana-4954 107 28 1 1 NUM cana-4954 107 29 : : PUNCT cana-4954 107 30 numerical numerical ADJ cana-4954 107 31 solution solution NOUN cana-4954 107 32 of of ADP cana-4954 107 33 βˆ’πœΊπ’–β€² βˆ’πœΊπ’–β€² PROPN cana-4954 107 34 + + CCONJ cana-4954 107 35 𝒂(𝒙)𝒖(𝒙 𝒂(𝒙)𝒖(𝒙 NOUN cana-4954 107 36 ) ) PUNCT cana-4954 108 1 + + NUM cana-4954 108 2 𝒃(𝒙)𝒖(𝒙 𝒃(𝒙)𝒖(𝒙 NUM cana-4954 108 3 βˆ’ βˆ’ NUM cana-4954 108 4 𝟏 𝟏 NUM cana-4954 108 5 ) ) PUNCT cana-4954 108 6 x x SYM cana-4954 108 7 𝑒(π‘₯ 𝑒(π‘₯ PROPN cana-4954 108 8 ) ) PUNCT cana-4954 108 9 normalize normalize VERB cana-4954 108 10 0.1406080 0.1406080 NUM cana-4954 108 11 0.9994382 0.9994382 NUM cana-4954 108 12 0.33333 0.33333 NUM cana-4954 108 13 0.1407457 0.1407457 NUM cana-4954 108 14 0.9994377 0.9994377 NUM cana-4954 108 15 0.33333 0.33333 NUM cana-4954 108 16 0.1408834 0.1408834 NUM cana-4954 108 17 0.9994371 0.9994371 NUM cana-4954 108 18 0.33333 0.33333 NUM cana-4954 108 19 table table NOUN cana-4954 108 20 2 2 NUM cana-4954 108 21 : : PUNCT cana-4954 108 22 numerical numerical ADJ cana-4954 108 23 solution solution NOUN cana-4954 108 24 of of ADP cana-4954 108 25 βˆ’πœΊπ’–β€² βˆ’πœΊπ’–β€² PROPN cana-4954 108 26 + + CCONJ cana-4954 108 27 𝒂(𝒙)𝒖(𝒙 𝒂(𝒙)𝒖(𝒙 NOUN cana-4954 108 28 ) ) PUNCT cana-4954 108 29 + + NUM cana-4954 108 30 𝒃(𝒙)𝒖(𝒙 𝒃(𝒙)𝒖(𝒙 NUM cana-4954 108 31 βˆ’ βˆ’ NUM cana-4954 108 32 𝟏 𝟏 NUM cana-4954 108 33 ) ) PUNCT cana-4954 108 34 x x SYM cana-4954 108 35 𝑒(π‘₯ 𝑒(π‘₯ PROPN cana-4954 108 36 ) ) PUNCT cana-4954 108 37 normalize normalize VERB cana-4954 108 38 0.1410212 0.1410212 NUM cana-4954 108 39 0.9994366 0.9994366 NUM cana-4954 108 40 0.20152 0.20152 NUM cana-4954 108 41 0.1117446 0.1117446 NUM cana-4954 108 42 0.9955917 0.9955917 NUM cana-4954 108 43 0.20075 0.20075 NUM cana-4954 108 44 0.2093871 0.2093871 NUM cana-4954 108 45 0.9917987 0.9917987 NUM cana-4954 108 46 0.19998 0.19998 NUM cana-4954 108 47 0.3070296 0.3070296 NUM cana-4954 108 48 0.9880568 0.9880568 NUM cana-4954 108 49 0.19923 0.19923 NUM cana-4954 108 50 0.4046720 0.4046720 NUM cana-4954 108 51 0.9843654 0.9843654 NUM cana-4954 108 52 0.19849 0.19849 NUM cana-4954 108 53 hence hence ADV cana-4954 108 54 , , PUNCT cana-4954 108 55 the the DET cana-4954 108 56 weighting weight VERB cana-4954 108 57 vectors vector NOUN cana-4954 108 58 given give VERB cana-4954 108 59 by by ADP cana-4954 108 60 the the DET cana-4954 108 61 decision decision NOUN cana-4954 108 62 maker maker NOUN cana-4954 108 63 is be AUX cana-4954 108 64 calculated calculate VERB cana-4954 108 65 as as ADP cana-4954 108 66 πœ” πœ” X cana-4954 108 67 = = NUM cana-4954 108 68 ( ( PUNCT cana-4954 108 69 0.33333,0.33333,0.33333)𝑇 0.33333,0.33333,0.33333)𝑇 NOUN cana-4954 108 70 , , PUNCT cana-4954 108 71 𝑀 𝑀 X cana-4954 108 72 = = PUNCT cana-4954 108 73 ( ( PUNCT cana-4954 108 74 0.20152,0.20075,0.19998,0.19923,0.19849)𝑇 0.20152,0.20075,0.19998,0.19923,0.19849)𝑇 VERB cana-4954 108 75 the the DET cana-4954 108 76 two two NUM cana-4954 108 77 mesh mesh NOUN cana-4954 108 78 algorithm algorithm NOUN cana-4954 108 79 is be AUX cana-4954 108 80 used use VERB cana-4954 108 81 to to PART cana-4954 108 82 calculate calculate VERB cana-4954 108 83 the the DET cana-4954 108 84 order order NOUN cana-4954 108 85 of of ADP cana-4954 108 86 convergence convergence NOUN cana-4954 108 87 and and CCONJ cana-4954 108 88 the the DET cana-4954 108 89 maximum maximum ADJ cana-4954 108 90 pointwise pointwise PROPN cana-4954 108 91 error error NOUN cana-4954 108 92 . . PUNCT cana-4954 109 1 table table NOUN cana-4954 109 2 1 1 NUM cana-4954 109 3 : : PUNCT cana-4954 109 4 values value NOUN cana-4954 109 5 of of ADP cana-4954 109 6 π‘«πœΊ π‘«πœΊ PROPN cana-4954 109 7 𝑡 𝑡 PROPN cana-4954 109 8 , , PUNCT cana-4954 109 9 𝑫𝑡 𝑫𝑡 PROPN cana-4954 109 10 , , PUNCT cana-4954 109 11 𝑷𝑡 𝑷𝑡 PROPN cana-4954 109 12 , , PUNCT cana-4954 109 13 π‘·βˆ—π’‚π’π’…π‘ͺ𝑷 π‘·βˆ—π’‚π’π’…π‘ͺ𝑷 NUM cana-4954 109 14 π‘΅π’‡π’π’“πœΊπŸ π‘΅π’‡π’π’“πœΊπŸ PROPN cana-4954 110 1 = = PUNCT cana-4954 110 2 𝜼 𝜼 PROPN cana-4954 110 3 πŸ– πŸ– NUM cana-4954 110 4 π’‚π’π’…πœΆ π’‚π’π’…πœΆ NOUN cana-4954 110 5 = = NOUN cana-4954 110 6 𝟎. 𝟎. X cana-4954 110 7 πŸ— πŸ— NUM cana-4954 110 8 𝜼 𝜼 PROPN cana-4954 110 9 128 128 NUM cana-4954 110 10 256 256 NUM cana-4954 110 11 512 512 NUM cana-4954 110 12 1024 1024 NUM cana-4954 110 13 2048 2048 NUM cana-4954 110 14 πŸβˆ’πŸ‘ πŸβˆ’πŸ‘ ADP cana-4954 110 15 0.625e-01 0.625e-01 NUM cana-4954 110 16 0.147e-02 0.147e-02 NUM cana-4954 111 1 0.862e-03 0.862e-03 NUM cana-4954 111 2 0.491e-03 0.491e-03 NUM cana-4954 111 3 0.275e-03 0.275e-03 NUM cana-4954 111 4 communications communication NOUN cana-4954 111 5 on on ADP cana-4954 111 6 applied apply VERB cana-4954 111 7 nonlinear nonlinear ADJ cana-4954 111 8 analysis analysis NOUN cana-4954 111 9 issn issn NOUN cana-4954 111 10 : : PUNCT cana-4954 111 11 1074 1074 NUM cana-4954 111 12 - - PUNCT cana-4954 111 13 133x 133x NUM cana-4954 111 14 vol vol VERB cana-4954 111 15 32 32 NUM cana-4954 111 16 no no NOUN cana-4954 111 17 . . PUNCT cana-4954 112 1 10s 10 NOUN cana-4954 112 2 ( ( PUNCT cana-4954 112 3 2025 2025 NUM cana-4954 112 4 ) ) PUNCT cana-4954 112 5 1036 1036 NUM cana-4954 112 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 113 1 πŸβˆ’πŸ’ πŸβˆ’πŸ’ PUNCT cana-4954 113 2 0.391e-02 0.391e-02 NUM cana-4954 113 3 0.147e-02 0.147e-02 X cana-4954 114 1 0.862e-03 0.862e-03 NUM cana-4954 114 2 0.491e-03 0.491e-03 NUM cana-4954 114 3 0.275e-03 0.275e-03 NUM cana-4954 115 1 πŸβˆ’πŸ“ πŸβˆ’πŸ“ NOUN cana-4954 115 2 0.244e-03 0.244e-03 NUM cana-4954 115 3 0.147e-02 0.147e-02 NUM cana-4954 115 4 0.862e-03 0.862e-03 NUM cana-4954 115 5 0.491e-03 0.491e-03 NUM cana-4954 115 6 0.275e-03 0.275e-03 NUM cana-4954 115 7 πŸβˆ’πŸ” πŸβˆ’πŸ” PROPN cana-4954 115 8 0.153e-04 0.153e-04 NUM cana-4954 115 9 0`147e-02 0`147e-02 NOUN cana-4954 115 10 0.862e-03 0.862e-03 NUM cana-4954 115 11 0.491e-03 0.491e-03 NUM cana-4954 115 12 0.275e-03 0.275e-03 NUM cana-4954 116 1 πŸβˆ’πŸ• πŸβˆ’πŸ• NOUN cana-4954 116 2 0.954e-06 0.954e-06 NOUN cana-4954 116 3 0.147e-02 0.147e-02 NUM cana-4954 116 4 0.862e-03 0.862e-03 NUM cana-4954 116 5 0.491e-03 0.491e-03 NUM cana-4954 116 6 0.275e-03 0.275e-03 NUM cana-4954 117 1 𝑫𝑡 𝑫𝑡 NOUN cana-4954 117 2 0.147e-02 0.147e-02 NUM cana-4954 117 3 0.862e-03 0.862e-03 NUM cana-4954 117 4 0.491e-03 0.491e-03 NUM cana-4954 117 5 0.275e-03 0.275e-03 NUM cana-4954 118 1 𝑷𝑡 𝑷𝑡 NOUN cana-4954 118 2 0.771e+00 0.771e+00 NOUN cana-4954 118 3 0.813e+00 0.813e+00 NOUN cana-4954 118 4 0.838e+00 0.838e+00 NUM cana-4954 118 5 π‘ͺ𝑷 π‘ͺ𝑷 PROPN cana-4954 118 6 𝑡 𝑡 PROPN cana-4954 118 7 0.256e+00 0.256e+00 NUM cana-4954 118 8 0.256e+00 0.256e+00 NUM cana-4954 118 9 0.249e+00 0.249e+00 NUM cana-4954 118 10 0.237e+00 0.237e+00 NOUN cana-4954 119 1 the the DET cana-4954 119 2 order order NOUN cana-4954 119 3 of of ADP cana-4954 119 4 convergence=0.7713155e+00 convergence=0.7713155e+00 PROPN cana-4954 119 5 the the DET cana-4954 119 6 error error NOUN cana-4954 119 7 constant=0.2559836e+00 constant=0.2559836e+00 NOUN cana-4954 119 8 figure figure VERB cana-4954 119 9 1 1 NUM cana-4954 119 10 : : PUNCT cana-4954 119 11 numerical numerical ADJ cana-4954 119 12 solution solution NOUN cana-4954 119 13 ofβˆ’πœΊπ’–β€² ofβˆ’πœΊπ’–β€² PROPN cana-4954 119 14 + + NUM cana-4954 119 15 𝒂(𝒙)𝒖(𝒙 𝒂(𝒙)𝒖(𝒙 NOUN cana-4954 119 16 ) ) PUNCT cana-4954 119 17 + + NUM cana-4954 119 18 𝒃(𝒙)𝒖(𝒙 𝒃(𝒙)𝒖(𝒙 NUM cana-4954 119 19 βˆ’ βˆ’ NUM cana-4954 119 20 𝟏 𝟏 NUM cana-4954 119 21 ) ) PUNCT cana-4954 119 22 = = SYM cana-4954 119 23 𝒇(𝒙 𝒇(𝒙 NUM cana-4954 119 24 ) ) PUNCT cana-4954 119 25 numerical numerical ADJ cana-4954 119 26 illustration illustration NOUN cana-4954 119 27 : : PUNCT cana-4954 119 28 a a DET cana-4954 119 29 company company NOUN cana-4954 119 30 is be AUX cana-4954 119 31 looking look VERB cana-4954 119 32 to to PART cana-4954 119 33 invest invest VERB cana-4954 119 34 in in ADP cana-4954 119 35 a a DET cana-4954 119 36 renewable renewable ADJ cana-4954 119 37 energy energy NOUN cana-4954 119 38 source source NOUN cana-4954 119 39 and and CCONJ cana-4954 119 40 has have AUX cana-4954 119 41 identified identify VERB cana-4954 119 42 four four NUM cana-4954 119 43 potential potential ADJ cana-4954 119 44 alternatives alternative NOUN cana-4954 119 45 : : PUNCT cana-4954 119 46 geothermal geothermal ADJ cana-4954 119 47 , , PUNCT cana-4954 119 48 solar solar ADJ cana-4954 119 49 , , PUNCT cana-4954 119 50 wind wind NOUN cana-4954 119 51 , , PUNCT cana-4954 119 52 and and CCONJ cana-4954 119 53 biomass biomass NOUN cana-4954 119 54 . . PUNCT cana-4954 120 1 to to PART cana-4954 120 2 evaluate evaluate VERB cana-4954 120 3 these these DET cana-4954 120 4 options option NOUN cana-4954 120 5 , , PUNCT cana-4954 120 6 the the DET cana-4954 120 7 company company NOUN cana-4954 120 8 has have AUX cana-4954 120 9 established establish VERB cana-4954 120 10 five five NUM cana-4954 120 11 key key ADJ cana-4954 120 12 criteria criterion NOUN cana-4954 120 13 : : PUNCT cana-4954 120 14 risk risk NOUN cana-4954 120 15 factor factor NOUN cana-4954 120 16 , , PUNCT cana-4954 120 17 industry industry NOUN cana-4954 120 18 growth growth NOUN cana-4954 120 19 rate rate NOUN cana-4954 120 20 , , PUNCT cana-4954 120 21 payback payback NOUN cana-4954 120 22 reliability reliability NOUN cana-4954 120 23 , , PUNCT cana-4954 120 24 social social ADJ cana-4954 120 25 benefits benefit NOUN cana-4954 120 26 , , PUNCT cana-4954 120 27 and and CCONJ cana-4954 120 28 demand demand NOUN cana-4954 120 29 change change NOUN cana-4954 120 30 . . PUNCT cana-4954 121 1 given give VERB cana-4954 121 2 the the DET cana-4954 121 3 increasing increase VERB cana-4954 121 4 energy energy NOUN cana-4954 121 5 demand demand NOUN cana-4954 121 6 , , PUNCT cana-4954 121 7 growing grow VERB cana-4954 121 8 environmental environmental ADJ cana-4954 121 9 awareness awareness NOUN cana-4954 121 10 , , PUNCT cana-4954 121 11 and and CCONJ cana-4954 121 12 strong strong ADJ cana-4954 121 13 government government NOUN cana-4954 121 14 support support NOUN cana-4954 121 15 for for ADP cana-4954 121 16 renewable renewable ADJ cana-4954 121 17 energy energy NOUN cana-4954 121 18 projects project NOUN cana-4954 121 19 in in ADP cana-4954 121 20 recent recent ADJ cana-4954 121 21 years year NOUN cana-4954 121 22 , , PUNCT cana-4954 121 23 the the DET cana-4954 121 24 company company NOUN cana-4954 121 25 recognizes recognize VERB cana-4954 121 26 the the DET cana-4954 121 27 need need NOUN cana-4954 121 28 for for SCONJ cana-4954 121 29 a a DET cana-4954 121 30 communications communication NOUN cana-4954 121 31 on on ADP cana-4954 121 32 applied apply VERB cana-4954 121 33 nonlinear nonlinear ADJ cana-4954 121 34 analysis analysis NOUN cana-4954 121 35 issn issn NOUN cana-4954 121 36 : : PUNCT cana-4954 121 37 1074 1074 NUM cana-4954 121 38 - - PUNCT cana-4954 121 39 133x 133x NUM cana-4954 121 40 vol vol VERB cana-4954 121 41 32 32 NUM cana-4954 121 42 no no NOUN cana-4954 121 43 . . PUNCT cana-4954 122 1 10s 10 NOUN cana-4954 122 2 ( ( PUNCT cana-4954 122 3 2025 2025 NUM cana-4954 122 4 ) ) PUNCT cana-4954 122 5 1037 1037 NUM cana-4954 122 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 122 7 dynamic dynamic ADJ cana-4954 122 8 assessment assessment NOUN cana-4954 122 9 approach approach NOUN cana-4954 122 10 . . PUNCT cana-4954 123 1 as as ADP cana-4954 123 2 a a DET cana-4954 123 3 result result NOUN cana-4954 123 4 , , PUNCT cana-4954 123 5 renewable renewable ADJ cana-4954 123 6 energy energy NOUN cana-4954 123 7 sources source NOUN cana-4954 123 8 have have AUX cana-4954 123 9 been be AUX cana-4954 123 10 evaluated evaluate VERB cana-4954 123 11 over over ADP cana-4954 123 12 the the DET cana-4954 123 13 past past ADJ cana-4954 123 14 six six NUM cana-4954 123 15 years year NOUN cana-4954 123 16 in in ADP cana-4954 123 17 two two NUM cana-4954 123 18 - - PUNCT cana-4954 123 19 year year NOUN cana-4954 123 20 intervals interval NOUN cana-4954 123 21 to to PART cana-4954 123 22 account account VERB cana-4954 123 23 for for ADP cana-4954 123 24 changing change VERB cana-4954 123 25 conditions condition NOUN cana-4954 123 26 . . PUNCT cana-4954 124 1 to to PART cana-4954 124 2 ensure ensure VERB cana-4954 124 3 a a DET cana-4954 124 4 well well ADV cana-4954 124 5 - - PUNCT cana-4954 124 6 informed inform VERB cana-4954 124 7 decision decision NOUN cana-4954 124 8 , , PUNCT cana-4954 124 9 a a DET cana-4954 124 10 three three NUM cana-4954 124 11 - - PUNCT cana-4954 124 12 member member NOUN cana-4954 124 13 decision decision NOUN cana-4954 124 14 - - PUNCT cana-4954 124 15 making make VERB cana-4954 124 16 group group NOUN cana-4954 124 17 has have AUX cana-4954 124 18 been be AUX cana-4954 124 19 assembled assemble VERB cana-4954 124 20 to to PART cana-4954 124 21 analyze analyze VERB cana-4954 124 22 the the DET cana-4954 124 23 data datum NOUN cana-4954 124 24 and and CCONJ cana-4954 124 25 determine determine VERB cana-4954 124 26 the the DET cana-4954 124 27 most most ADV cana-4954 124 28 suitable suitable ADJ cana-4954 124 29 investment investment NOUN cana-4954 124 30 option option NOUN cana-4954 124 31 . . PUNCT cana-4954 125 1 𝑅1 𝑅1 PROPN cana-4954 125 2 = = PRON cana-4954 126 1 ( ( PUNCT cana-4954 126 2 ( ( PUNCT cana-4954 126 3 0.6,0.3,0.1 0.6,0.3,0.1 NOUN cana-4954 126 4 ) ) PUNCT cana-4954 126 5 ( ( PUNCT cana-4954 126 6 0.7,0.2,0.1 0.7,0.2,0.1 NOUN cana-4954 126 7 ) ) PUNCT cana-4954 126 8 ( ( PUNCT cana-4954 126 9 0.3,0.6,0.1 0.3,0.6,0.1 NUM cana-4954 126 10 ) ) PUNCT cana-4954 126 11 ( ( PUNCT cana-4954 126 12 0.6,0.2,0.2 0.6,0.2,0.2 NOUN cana-4954 126 13 ) ) PUNCT cana-4954 126 14 ( ( PUNCT cana-4954 126 15 0.4,0.5,0.1 0.4,0.5,0.1 NUM cana-4954 126 16 ) ) PUNCT cana-4954 126 17 ( ( PUNCT cana-4954 126 18 0.9,0.1,0.0 0.9,0.1,0.0 NUM cana-4954 126 19 ) ) PUNCT cana-4954 126 20 ( ( PUNCT cana-4954 126 21 0.1,0.8,0.1 0.1,0.8,0.1 NUM cana-4954 126 22 ) ) PUNCT cana-4954 126 23 ( ( PUNCT cana-4954 126 24 0.4,0.5,0.1 0.4,0.5,0.1 NUM cana-4954 126 25 ) ) PUNCT cana-4954 126 26 ( ( PUNCT cana-4954 126 27 0.7,0.1,0.2 0.7,0.1,0.2 NUM cana-4954 126 28 ) ) PUNCT cana-4954 126 29 ( ( PUNCT cana-4954 126 30 0.4,0.5,0.1 0.4,0.5,0.1 NUM cana-4954 126 31 ) ) PUNCT cana-4954 126 32 ( ( PUNCT cana-4954 126 33 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 126 34 ) ) PUNCT cana-4954 126 35 ( ( PUNCT cana-4954 126 36 0.8,0.2,0.0 0.8,0.2,0.0 NUM cana-4954 126 37 ) ) PUNCT cana-4954 126 38 ( ( PUNCT cana-4954 126 39 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 126 40 ) ) PUNCT cana-4954 126 41 ( ( PUNCT cana-4954 126 42 0.5,0.3,0.2 0.5,0.3,0.2 NUM cana-4954 126 43 ) ) PUNCT cana-4954 126 44 ( ( PUNCT cana-4954 126 45 0.5,0.2,0.3 0.5,0.2,0.3 NUM cana-4954 126 46 ) ) PUNCT cana-4954 126 47 ( ( PUNCT cana-4954 126 48 0.4,0.6,0.0 0.4,0.6,0.0 NUM cana-4954 126 49 ) ) PUNCT cana-4954 126 50 ( ( PUNCT cana-4954 126 51 0.2,0.6,0.1 0.2,0.6,0.1 NUM cana-4954 126 52 ) ) PUNCT cana-4954 126 53 ( ( PUNCT cana-4954 126 54 0.6,0.3,0.1 0.6,0.3,0.1 NUM cana-4954 126 55 ) ) PUNCT cana-4954 126 56 ( ( PUNCT cana-4954 126 57 0.6,0.2,0.1 0.6,0.2,0.1 NUM cana-4954 126 58 ) ) PUNCT cana-4954 126 59 ( ( PUNCT cana-4954 126 60 0.8,0.1,0.1 0.8,0.1,0.1 NOUN cana-4954 126 61 ) ) PUNCT cana-4954 126 62 ) ) PUNCT cana-4954 127 1 𝑅2 𝑅2 NOUN cana-4954 127 2 = = PUNCT cana-4954 127 3 ( ( PUNCT cana-4954 127 4 ( ( PUNCT cana-4954 127 5 0.9,0.1,0.0 0.9,0.1,0.0 NUM cana-4954 127 6 ) ) PUNCT cana-4954 127 7 ( ( PUNCT cana-4954 127 8 0.7,0.2,0.1 0.7,0.2,0.1 NOUN cana-4954 127 9 ) ) PUNCT cana-4954 128 1 ( ( PUNCT cana-4954 128 2 0.8,0.2,0.0 0.8,0.2,0.0 NUM cana-4954 128 3 ) ) PUNCT cana-4954 128 4 ( ( PUNCT cana-4954 128 5 0.7,0.2,0.1 0.7,0.2,0.1 NOUN cana-4954 128 6 ) ) PUNCT cana-4954 128 7 ( ( PUNCT cana-4954 128 8 0.2,0.6,0.2 0.2,0.6,0.2 NUM cana-4954 128 9 ) ) PUNCT cana-4954 128 10 ( ( PUNCT cana-4954 128 11 0.8,0.1,0.1 0.8,0.1,0.1 NOUN cana-4954 128 12 ) ) PUNCT cana-4954 128 13 ( ( PUNCT cana-4954 128 14 0.1,0.8,0.1 0.1,0.8,0.1 NUM cana-4954 128 15 ) ) PUNCT cana-4954 128 16 ( ( PUNCT cana-4954 128 17 0.3,0.5,0.2 0.3,0.5,0.2 NUM cana-4954 128 18 ) ) PUNCT cana-4954 128 19 ( ( PUNCT cana-4954 128 20 0.7,0.3,0.0 0.7,0.3,0.0 NUM cana-4954 128 21 ) ) PUNCT cana-4954 128 22 ( ( PUNCT cana-4954 128 23 0.3,0.4,0.3 0.3,0.4,0.3 NUM cana-4954 128 24 ) ) PUNCT cana-4954 128 25 ( ( PUNCT cana-4954 128 26 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 128 27 ) ) PUNCT cana-4954 128 28 ( ( PUNCT cana-4954 128 29 0.9,0.1,0.0 0.9,0.1,0.0 NUM cana-4954 128 30 ) ) PUNCT cana-4954 128 31 ( ( PUNCT cana-4954 128 32 0.6,0.3,0.1 0.6,0.3,0.1 NUM cana-4954 128 33 ) ) PUNCT cana-4954 128 34 ( ( PUNCT cana-4954 128 35 0.3,0.5,0.2 0.3,0.5,0.2 NUM cana-4954 128 36 ) ) PUNCT cana-4954 128 37 ( ( PUNCT cana-4954 128 38 0.5,0.3,0.2 0.5,0.3,0.2 NUM cana-4954 128 39 ) ) PUNCT cana-4954 128 40 ( ( PUNCT cana-4954 128 41 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 128 42 ) ) PUNCT cana-4954 128 43 ( ( PUNCT cana-4954 128 44 0.3,0.7,0.0 0.3,0.7,0.0 NOUN cana-4954 128 45 ) ) PUNCT cana-4954 128 46 ( ( PUNCT cana-4954 128 47 0.9,0.1,0.0 0.9,0.1,0.0 NUM cana-4954 128 48 ) ) PUNCT cana-4954 128 49 ( ( PUNCT cana-4954 128 50 0.7,0.1,0.2 0.7,0.1,0.2 NUM cana-4954 128 51 ) ) PUNCT cana-4954 128 52 ( ( PUNCT cana-4954 128 53 0.4,0.6,0.0 0.4,0.6,0.0 NUM cana-4954 128 54 ) ) PUNCT cana-4954 128 55 ) ) PUNCT cana-4954 128 56 𝑅3 𝑅3 PROPN cana-4954 129 1 = = PUNCT cana-4954 129 2 ( ( PUNCT cana-4954 129 3 ( ( PUNCT cana-4954 129 4 0.5,0.5,0.0 0.5,0.5,0.0 NUM cana-4954 129 5 ) ) PUNCT cana-4954 129 6 ( ( PUNCT cana-4954 129 7 0.6,0.2,0.2 0.6,0.2,0.2 NOUN cana-4954 129 8 ) ) PUNCT cana-4954 129 9 ( ( PUNCT cana-4954 129 10 0.7,0.3,0.0 0.7,0.3,0.0 NUM cana-4954 129 11 ) ) PUNCT cana-4954 129 12 ( ( PUNCT cana-4954 129 13 0.6,0.3,0.1 0.6,0.3,0.1 NUM cana-4954 129 14 ) ) PUNCT cana-4954 129 15 ( ( PUNCT cana-4954 129 16 0.6,0.3,0.1 0.6,0.3,0.1 NUM cana-4954 129 17 ) ) PUNCT cana-4954 129 18 ( ( PUNCT cana-4954 129 19 0.8,0.1,0.1 0.8,0.1,0.1 NOUN cana-4954 129 20 ) ) PUNCT cana-4954 129 21 ( ( PUNCT cana-4954 129 22 0.8,0.2,0.0 0.8,0.2,0.0 NUM cana-4954 129 23 ) ) PUNCT cana-4954 129 24 ( ( PUNCT cana-4954 129 25 0.4,0.5,0.1 0.4,0.5,0.1 NUM cana-4954 129 26 ) ) PUNCT cana-4954 129 27 ( ( PUNCT cana-4954 129 28 0.3,0.4,0.3 0.3,0.4,0.3 NUM cana-4954 129 29 ) ) PUNCT cana-4954 129 30 ( ( PUNCT cana-4954 129 31 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 129 32 ) ) PUNCT cana-4954 129 33 ( ( PUNCT cana-4954 129 34 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 129 35 ) ) PUNCT cana-4954 129 36 ( ( PUNCT cana-4954 129 37 0.7,0.2,0.1 0.7,0.2,0.1 NOUN cana-4954 129 38 ) ) PUNCT cana-4954 129 39 ( ( PUNCT cana-4954 129 40 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 129 41 ) ) PUNCT cana-4954 129 42 ( ( PUNCT cana-4954 129 43 0.5,0.2,0.3 0.5,0.2,0.3 NUM cana-4954 129 44 ) ) PUNCT cana-4954 129 45 ( ( PUNCT cana-4954 129 46 0.6,0.2,0.2 0.6,0.2,0.2 NOUN cana-4954 129 47 ) ) PUNCT cana-4954 129 48 ( ( PUNCT cana-4954 129 49 0.4,0.6,0.0 0.4,0.6,0.0 NUM cana-4954 129 50 ) ) PUNCT cana-4954 129 51 ( ( PUNCT cana-4954 129 52 0.3,0.7,0.0 0.3,0.7,0.0 NOUN cana-4954 129 53 ) ) PUNCT cana-4954 129 54 ( ( PUNCT cana-4954 129 55 0.6,0.3,0.1 0.6,0.3,0.1 NUM cana-4954 129 56 ) ) PUNCT cana-4954 129 57 ( ( PUNCT cana-4954 129 58 0.6,0.2,0.2 0.6,0.2,0.2 NOUN cana-4954 129 59 ) ) PUNCT cana-4954 129 60 ( ( PUNCT cana-4954 129 61 0.5,0.4,0.1 0.5,0.4,0.1 NOUN cana-4954 129 62 ) ) PUNCT cana-4954 129 63 ) ) PUNCT cana-4954 129 64 step step NOUN cana-4954 129 65 : : PUNCT cana-4954 129 66 1use 1use NUM cana-4954 129 67 the the DET cana-4954 129 68 difwa difwa NOUN cana-4954 129 69 operator operator NOUN cana-4954 129 70 to to PART cana-4954 129 71 aggregate aggregate VERB cana-4954 129 72 all all DET cana-4954 129 73 individual individual ADJ cana-4954 129 74 intuitionistic intuitionistic ADJ cana-4954 129 75 fuzzy fuzzy ADJ cana-4954 129 76 decision decision NOUN cana-4954 129 77 matrices matrix NOUN cana-4954 129 78 into into ADP cana-4954 129 79 a a DET cana-4954 129 80 collective collective ADJ cana-4954 129 81 intuitionistic intuitionistic ADJ cana-4954 129 82 fuzzy fuzzy ADJ cana-4954 129 83 decision decision NOUN cana-4954 129 84 matrix matrix NOUN cana-4954 129 85 r=(rij)mxn r=(rij)mxn NOUN cana-4954 129 86 . . PUNCT cana-4954 130 1 𝑅 𝑅 NOUN cana-4954 130 2 = = SYM cana-4954 130 3 [ [ PUNCT cana-4954 130 4 [ [ X cana-4954 130 5 ( ( PUNCT cana-4954 130 6 0.72855,0.24662,0.02482 0.72855,0.24662,0.02482 NUM cana-4954 130 7 ) ) PUNCT cana-4954 130 8 ] ] PUNCT cana-4954 130 9 , , PUNCT cana-4954 130 10 [ [ X cana-4954 130 11 ( ( PUNCT cana-4954 130 12 0.66980,0.20000,0.13019 0.66980,0.20000,0.13019 NOUN cana-4954 130 13 ) ) PUNCT cana-4954 130 14 ] ] PUNCT cana-4954 130 15 , , PUNCT cana-4954 130 16 [ [ X cana-4954 130 17 ( ( PUNCT cana-4954 130 18 0.65239,0.33019,0.01741 0.65239,0.33019,0.01741 NUM cana-4954 130 19 ) ) PUNCT cana-4954 130 20 ] ] PUNCT cana-4954 130 21 , , PUNCT cana-4954 130 22 [ [ X cana-4954 130 23 ( ( PUNCT cana-4954 130 24 0.63657,0.22895,0.13448 0.63657,0.22895,0.13448 NUM cana-4954 130 25 ) ) PUNCT cana-4954 130 26 ] ] PUNCT cana-4954 130 27 , , PUNCT cana-4954 130 28 [ [ X cana-4954 130 29 ( ( PUNCT cana-4954 130 30 0.26813,0.66494,0.06692 0.26813,0.66494,0.06692 NUM cana-4954 130 31 ) ) PUNCT cana-4954 130 32 ] ] PUNCT cana-4954 131 1 [ [ X cana-4954 131 2 ( ( PUNCT cana-4954 131 3 0.42310,0.44814,0.12876 0.42310,0.44814,0.12876 NUM cana-4954 131 4 ) ) PUNCT cana-4954 131 5 ] ] PUNCT cana-4954 131 6 , , PUNCT cana-4954 131 7 [ [ X cana-4954 131 8 ( ( PUNCT cana-4954 131 9 0.84125,0.10000,0.05874 0.84125,0.10000,0.05874 NUM cana-4954 131 10 ) ) PUNCT cana-4954 131 11 ] ] PUNCT cana-4954 131 12 , , PUNCT cana-4954 131 13 [ [ X cana-4954 131 14 ( ( PUNCT cana-4954 131 15 0.45486,0.50397,0.04116 0.45486,0.50397,0.04116 NUM cana-4954 131 16 ) ) PUNCT cana-4954 131 17 ] ] PUNCT cana-4954 131 18 , , PUNCT cana-4954 131 19 [ [ X cana-4954 131 20 ( ( PUNCT cana-4954 131 21 0.36836,0.46416,0.20075 0.36836,0.46416,0.20075 NUM cana-4954 131 22 ) ) PUNCT cana-4954 131 23 ] ] PUNCT cana-4954 131 24 , , PUNCT cana-4954 131 25 [ [ X cana-4954 131 26 ( ( PUNCT cana-4954 131 27 0.74801,0.20801,0.04397 0.74801,0.20801,0.04397 NOUN cana-4954 131 28 ) ) PUNCT cana-4954 131 29 ] ] PUNCT cana-4954 132 1 [ [ X cana-4954 132 2 ( ( PUNCT cana-4954 132 3 0.60209,0.22895,0.16896 0.60209,0.22895,0.16896 NUM cana-4954 132 4 ) ) PUNCT cana-4954 132 5 ] ] PUNCT cana-4954 132 6 , , PUNCT cana-4954 132 7 [ [ X cana-4954 132 8 ( ( PUNCT cana-4954 132 9 0.40560,0.43089,0.16350 0.40560,0.43089,0.16350 NUM cana-4954 132 10 ) ) PUNCT cana-4954 132 11 ] ] PUNCT cana-4954 132 12 , , PUNCT cana-4954 132 13 [ [ X cana-4954 132 14 ( ( PUNCT cana-4954 132 15 0.49999,0.40000,0.10000 0.49999,0.40000,0.10000 NUM cana-4954 132 16 ) ) PUNCT cana-4954 132 17 ] ] PUNCT cana-4954 132 18 , , PUNCT cana-4954 132 19 [ [ X cana-4954 132 20 ( ( PUNCT cana-4954 132 21 0.81828,0.15874,0.02297 0.81828,0.15874,0.02297 NUM cana-4954 132 22 ) ) PUNCT cana-4954 132 23 ] ] PUNCT cana-4954 132 24 , , PUNCT cana-4954 132 25 [ [ X cana-4954 132 26 ( ( PUNCT cana-4954 132 27 0.63657,0.15874,0.02297 0.63657,0.15874,0.02297 NOUN cana-4954 132 28 ) ) PUNCT cana-4954 132 29 ] ] PUNCT cana-4954 133 1 [ [ X cana-4954 133 2 ( ( PUNCT cana-4954 133 3 0.53584,0.36343,0.10073 0.53584,0.36343,0.10073 NOUN cana-4954 133 4 ) ) PUNCT cana-4954 133 5 ] ] PUNCT cana-4954 133 6 , , PUNCT cana-4954 133 7 [ [ X cana-4954 133 8 ( ( PUNCT cana-4954 133 9 0.44065,0.31073,0.24862 0.44065,0.31073,0.24862 NOUN cana-4954 133 10 ) ) PUNCT cana-4954 133 11 ] ] PUNCT cana-4954 133 12 , , PUNCT cana-4954 133 13 [ [ X cana-4954 133 14 ( ( PUNCT cana-4954 133 15 0.53584,0.22895,0.23522 0.53584,0.22895,0.23522 PROPN cana-4954 133 16 ) ) PUNCT cana-4954 133 17 ] ] PUNCT cana-4954 133 18 , , PUNCT cana-4954 133 19 [ [ X cana-4954 133 20 ( ( PUNCT cana-4954 133 21 0.43537,0.52415,0.04047 0.43537,0.52415,0.04047 NUM cana-4954 133 22 ) ) PUNCT cana-4954 133 23 ] ] PUNCT cana-4954 133 24 , , PUNCT cana-4954 133 25 [ [ X cana-4954 133 26 ( ( PUNCT cana-4954 133 27 0.60851,0.28845,0.10304 0.60851,0.28845,0.10304 NOUN cana-4954 133 28 ) ) PUNCT cana-4954 133 29 ] ] PUNCT cana-4954 133 30 ] ] PUNCT cana-4954 133 31 using use VERB cana-4954 133 32 step2 step2 PROPN cana-4954 133 33 , , PUNCT cana-4954 133 34 we we PRON cana-4954 133 35 obtain obtain VERB cana-4954 133 36 π‘Ÿ1 π‘Ÿ1 NOUN cana-4954 133 37 = = PUNCT cana-4954 133 38 [ [ PUNCT cana-4954 133 39 ( ( PUNCT cana-4954 133 40 0.72855,0.24662,0.02482 0.72855,0.24662,0.02482 NUM cana-4954 133 41 ) ) PUNCT cana-4954 133 42 , , PUNCT cana-4954 133 43 ( ( PUNCT cana-4954 133 44 0.66980,0.20000,0.13019 0.66980,0.20000,0.13019 NOUN cana-4954 133 45 ) ) PUNCT cana-4954 133 46 , , PUNCT cana-4954 133 47 ( ( PUNCT cana-4954 133 48 0.65239,0.33019,0.01741 0.65239,0.33019,0.01741 NUM cana-4954 133 49 ) ) PUNCT cana-4954 133 50 , , PUNCT cana-4954 133 51 ( ( PUNCT cana-4954 133 52 0.63657,0.22895,0.13448 0.63657,0.22895,0.13448 NUM cana-4954 133 53 ) ) PUNCT cana-4954 133 54 , , PUNCT cana-4954 133 55 ( ( PUNCT cana-4954 133 56 0.26813,0.66494,0.06692 0.26813,0.66494,0.06692 NUM cana-4954 133 57 ) ) PUNCT cana-4954 133 58 ] ] PUNCT cana-4954 134 1 𝑇 𝑇 NOUN cana-4954 134 2 π‘Ÿ2 π‘Ÿ2 NOUN cana-4954 134 3 = = PUNCT cana-4954 134 4 [ [ PUNCT cana-4954 134 5 ( ( PUNCT cana-4954 134 6 0.42310,0.44814,0.12876 0.42310,0.44814,0.12876 NUM cana-4954 134 7 ) ) PUNCT cana-4954 134 8 , , PUNCT cana-4954 134 9 ( ( PUNCT cana-4954 134 10 0.84125,0.10000,0.05874 0.84125,0.10000,0.05874 NUM cana-4954 134 11 ) ) PUNCT cana-4954 134 12 , , PUNCT cana-4954 134 13 ( ( PUNCT cana-4954 134 14 0.45486,0.50397,0.04116 0.45486,0.50397,0.04116 NUM cana-4954 134 15 ) ) PUNCT cana-4954 134 16 , , PUNCT cana-4954 134 17 ( ( PUNCT cana-4954 134 18 0.36836,0.46416,0.20075 0.36836,0.46416,0.20075 NUM cana-4954 134 19 ) ) PUNCT cana-4954 134 20 , , PUNCT cana-4954 134 21 ( ( PUNCT cana-4954 134 22 0.74801,0.20801,0.04397 0.74801,0.20801,0.04397 NUM cana-4954 134 23 ) ) PUNCT cana-4954 134 24 ] ] PUNCT cana-4954 134 25 𝑇 𝑇 NOUN cana-4954 134 26 π‘Ÿ3 π‘Ÿ3 NOUN cana-4954 134 27 = = PUNCT cana-4954 134 28 [ [ PUNCT cana-4954 134 29 ( ( PUNCT cana-4954 134 30 0.60209,0.22895,0.16896 0.60209,0.22895,0.16896 NUM cana-4954 134 31 ) ) PUNCT cana-4954 134 32 , , PUNCT cana-4954 134 33 ( ( PUNCT cana-4954 134 34 0.40560,0.43089,0.16350 0.40560,0.43089,0.16350 NUM cana-4954 134 35 ) ) PUNCT cana-4954 134 36 , , PUNCT cana-4954 134 37 ( ( PUNCT cana-4954 134 38 0.49999,0.40000,0.10000 0.49999,0.40000,0.10000 NUM cana-4954 134 39 ) ) PUNCT cana-4954 134 40 , , PUNCT cana-4954 134 41 ( ( PUNCT cana-4954 134 42 0.81828,0.15874,0.02297 0.81828,0.15874,0.02297 NOUN cana-4954 134 43 ) ) PUNCT cana-4954 134 44 , , PUNCT cana-4954 134 45 ( ( PUNCT cana-4954 134 46 0.63657,0.15874,0.02297 0.63657,0.15874,0.02297 NOUN cana-4954 134 47 ) ) PUNCT cana-4954 134 48 ] ] PUNCT cana-4954 135 1 𝑇 𝑇 PROPN cana-4954 135 2 π‘Ÿ4 π‘Ÿ4 PROPN cana-4954 135 3 = = SYM cana-4954 135 4 [ [ PUNCT cana-4954 135 5 ( ( PUNCT cana-4954 135 6 0.53584,0.36343,0.10073 0.53584,0.36343,0.10073 NOUN cana-4954 135 7 ) ) PUNCT cana-4954 135 8 , , PUNCT cana-4954 135 9 ( ( PUNCT cana-4954 135 10 0.44065,0.31073,0.24862 0.44065,0.31073,0.24862 NOUN cana-4954 135 11 ) ) PUNCT cana-4954 135 12 , , PUNCT cana-4954 135 13 ( ( PUNCT cana-4954 135 14 0.53584,0.22895,0.23522 0.53584,0.22895,0.23522 NUM cana-4954 135 15 ) ) PUNCT cana-4954 135 16 , , PUNCT cana-4954 135 17 ( ( PUNCT cana-4954 135 18 0.43537,0.52415,0.04047 0.43537,0.52415,0.04047 NUM cana-4954 135 19 ) ) PUNCT cana-4954 135 20 , , PUNCT cana-4954 135 21 ( ( PUNCT cana-4954 135 22 0.60851,0.28845,0.10304 0.60851,0.28845,0.10304 NOUN cana-4954 135 23 ) ) PUNCT cana-4954 135 24 ] ] PUNCT cana-4954 135 25 𝑇 𝑇 PROPN cana-4954 135 26 step step NOUN cana-4954 135 27 : : PUNCT cana-4954 135 28 3 3 NUM cana-4954 135 29 calculate calculate VERB cana-4954 135 30 the the DET cana-4954 135 31 closeness closeness NOUN cana-4954 135 32 coefficient coefficient NOUN cana-4954 135 33 of of ADP cana-4954 135 34 each each DET cana-4954 135 35 alternatives alternative NOUN cana-4954 135 36 communications communication NOUN cana-4954 135 37 on on ADP cana-4954 135 38 applied apply VERB cana-4954 135 39 nonlinear nonlinear ADJ cana-4954 135 40 analysis analysis NOUN cana-4954 135 41 issn issn NOUN cana-4954 135 42 : : PUNCT cana-4954 135 43 1074 1074 NUM cana-4954 135 44 - - PUNCT cana-4954 135 45 133x 133x NUM cana-4954 135 46 vol vol VERB cana-4954 135 47 32 32 NUM cana-4954 135 48 no no NOUN cana-4954 135 49 . . PUNCT cana-4954 135 50 10s 10 NOUN cana-4954 135 51 ( ( PUNCT cana-4954 135 52 2025 2025 NUM cana-4954 135 53 ) ) PUNCT cana-4954 135 54 1038 1038 NUM cana-4954 135 55 https://internationalpubls.com https://internationalpubls.com X cana-4954 135 56 𝑐(π‘₯𝑖 𝑐(π‘₯𝑖 PROPN cana-4954 135 57 ) ) PUNCT cana-4954 135 58 = = PUNCT cana-4954 136 1 βˆ‘ βˆ‘ PUNCT cana-4954 136 2 πœ”π‘—(1 πœ”π‘—(1 PRON cana-4954 136 3 βˆ’ βˆ’ PROPN cana-4954 136 4 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-4954 136 5 ) ) PUNCT cana-4954 136 6 𝑛 𝑛 PRON cana-4954 136 7 𝑗=1 𝑗=1 PROPN cana-4954 136 8 βˆ‘ βˆ‘ PUNCT cana-4954 137 1 πœ”π‘—(1 πœ”π‘—(1 X cana-4954 137 2 + + NUM cana-4954 137 3 πœ‹π‘–π‘— πœ‹π‘–π‘— NOUN cana-4954 137 4 ) ) PUNCT cana-4954 137 5 𝑛 𝑛 PRON cana-4954 137 6 𝑗=1 𝑗=1 PROPN cana-4954 137 7 𝐢( 𝐢( X cana-4954 137 8 οΏ½ οΏ½ PROPN cana-4954 137 9 Μƒ Μƒ PROPN cana-4954 137 10 οΏ½ οΏ½ NOUN cana-4954 137 11 1 1 NUM cana-4954 137 12 , , PUNCT cana-4954 137 13 οΏ½ οΏ½ PROPN cana-4954 137 14 Μƒ Μƒ NOUN cana-4954 137 15 οΏ½ οΏ½ NOUN cana-4954 137 16 + + NOUN cana-4954 137 17 ) ) PUNCT cana-4954 137 18 = = SYM cana-4954 137 19 0.62019 0.62019 NUM cana-4954 137 20 𝐢( 𝐢( NOUN cana-4954 137 21 οΏ½ οΏ½ PROPN cana-4954 137 22 Μƒ Μƒ NOUN cana-4954 137 23 οΏ½ οΏ½ NOUN cana-4954 137 24 2 2 NUM cana-4954 137 25 , , PUNCT cana-4954 137 26 οΏ½ οΏ½ PROPN cana-4954 137 27 Μƒ Μƒ PROPN cana-4954 137 28 οΏ½ οΏ½ NOUN cana-4954 137 29 + + NOUN cana-4954 137 30 ) ) PUNCT cana-4954 137 31 = = NOUN cana-4954 137 32 0.59839 0.59839 NUM cana-4954 137 33 𝐢( 𝐢( NOUN cana-4954 137 34 οΏ½ οΏ½ PROPN cana-4954 137 35 Μƒ Μƒ PROPN cana-4954 137 36 οΏ½ οΏ½ NOUN cana-4954 137 37 3 3 NUM cana-4954 137 38 , , PUNCT cana-4954 137 39 οΏ½ οΏ½ PROPN cana-4954 137 40 Μƒ Μƒ NOUN cana-4954 137 41 οΏ½ οΏ½ NOUN cana-4954 137 42 + + NOUN cana-4954 137 43 ) ) PUNCT cana-4954 137 44 = = SYM cana-4954 137 45 0.66079 0.66079 NUM cana-4954 137 46 𝐢( 𝐢( NOUN cana-4954 137 47 οΏ½ οΏ½ PROPN cana-4954 137 48 Μƒ Μƒ PROPN cana-4954 137 49 οΏ½ οΏ½ NOUN cana-4954 137 50 4 4 NUM cana-4954 137 51 , , PUNCT cana-4954 137 52 οΏ½ οΏ½ PROPN cana-4954 137 53 Μƒ Μƒ PROPN cana-4954 137 54 οΏ½ οΏ½ NOUN cana-4954 137 55 + + NOUN cana-4954 137 56 ) ) PUNCT cana-4954 137 57 = = SYM cana-4954 137 58 0.57333 0.57333 NUM cana-4954 137 59 rank rank VERB cana-4954 137 60 all all DET cana-4954 137 61 the the DET cana-4954 137 62 alternatives alternative NOUN cana-4954 137 63 π‘₯𝑖(𝑖 π‘₯𝑖(𝑖 PRON cana-4954 137 64 = = NOUN cana-4954 137 65 1,2,3,4 1,2,3,4 NUM cana-4954 137 66 ) ) PUNCT cana-4954 137 67 according accord VERB cana-4954 137 68 to to ADP cana-4954 137 69 the the DET cana-4954 137 70 closeness closeness NOUN cana-4954 137 71 coefficient coefficient NOUN cana-4954 137 72 of of ADP cana-4954 137 73 𝑐(π‘₯𝑖)(𝑖 𝑐(π‘₯𝑖)(𝑖 PROPN cana-4954 137 74 = = NOUN cana-4954 137 75 1,2,3,4 1,2,3,4 NUM cana-4954 137 76 ) ) PUNCT cana-4954 137 77 . . PUNCT cana-4954 138 1 π‘₯3 π‘₯3 NOUN cana-4954 138 2 > > X cana-4954 138 3 π‘₯1 π‘₯1 PROPN cana-4954 138 4 > > X cana-4954 138 5 π‘₯2 π‘₯2 PROPN cana-4954 138 6 > > X cana-4954 138 7 π‘₯4 π‘₯4 PROPN cana-4954 138 8 . . PUNCT cana-4954 139 1 conclusion conclusion NOUN cana-4954 139 2 : : PUNCT cana-4954 139 3 in in ADP cana-4954 139 4 this this DET cana-4954 139 5 study study NOUN cana-4954 139 6 , , PUNCT cana-4954 139 7 the the DET cana-4954 139 8 numerical numerical ADJ cana-4954 139 9 solution solution NOUN cana-4954 139 10 of of ADP cana-4954 139 11 the the DET cana-4954 139 12 singularly singularly ADV cana-4954 139 13 perturbed perturb VERB cana-4954 139 14 initial initial ADJ cana-4954 139 15 value value NOUN cana-4954 139 16 problem problem NOUN cana-4954 139 17 for for ADP cana-4954 139 18 the the DET cana-4954 139 19 decisionmaking decisionmake VERB cana-4954 139 20 process process NOUN cana-4954 139 21 is be AUX cana-4954 139 22 determined determine VERB cana-4954 139 23 using use VERB cana-4954 139 24 the the DET cana-4954 139 25 unknown unknown ADJ cana-4954 139 26 weights weight NOUN cana-4954 139 27 of of ADP cana-4954 139 28 the the DET cana-4954 139 29 decision decision NOUN cana-4954 139 30 - - PUNCT cana-4954 139 31 makers maker NOUN cana-4954 139 32 . . PUNCT cana-4954 140 1 to to PART cana-4954 140 2 select select VERB cana-4954 140 3 the the DET cana-4954 140 4 optimal optimal ADJ cana-4954 140 5 alternative alternative NOUN cana-4954 140 6 , , PUNCT cana-4954 140 7 the the DET cana-4954 140 8 dynamic dynamic ADJ cana-4954 140 9 intuitionistic intuitionistic ADJ cana-4954 140 10 multi multi ADJ cana-4954 140 11 - - ADJ cana-4954 140 12 attribute attribute NOUN cana-4954 140 13 decision decision NOUN cana-4954 140 14 - - PUNCT cana-4954 140 15 making make VERB cana-4954 140 16 approach approach NOUN cana-4954 140 17 is be AUX cana-4954 140 18 applied apply VERB cana-4954 140 19 , , PUNCT cana-4954 140 20 computing compute VERB cana-4954 140 21 the the DET cana-4954 140 22 proximity proximity NOUN cana-4954 140 23 coefficient coefficient NOUN cana-4954 140 24 for for ADP cana-4954 140 25 each each DET cana-4954 140 26 option option NOUN cana-4954 140 27 . . PUNCT cana-4954 141 1 this this DET cana-4954 141 2 method method NOUN cana-4954 141 3 ensures ensure VERB cana-4954 141 4 a a DET cana-4954 141 5 systematic systematic ADJ cana-4954 141 6 and and CCONJ cana-4954 141 7 dynamic dynamic ADJ cana-4954 141 8 evaluation evaluation NOUN cana-4954 141 9 of of ADP cana-4954 141 10 alternatives alternative NOUN cana-4954 141 11 , , PUNCT cana-4954 141 12 leading lead VERB cana-4954 141 13 to to ADP cana-4954 141 14 a a DET cana-4954 141 15 well well ADV cana-4954 141 16 - - PUNCT cana-4954 141 17 informed inform VERB cana-4954 141 18 investment investment NOUN cana-4954 141 19 decision decision NOUN cana-4954 141 20 . . PUNCT cana-4954 142 1 reference reference NOUN cana-4954 142 2 : : PUNCT cana-4954 143 1 [ [ X cana-4954 143 2 1 1 NUM cana-4954 143 3 ] ] X cana-4954 143 4 k.atanassov k.atanassov ADJ cana-4954 143 5 , , PUNCT cana-4954 143 6 intuitionistic intuitionistic ADJ cana-4954 143 7 fuzzy fuzzy ADJ cana-4954 143 8 sets set NOUN cana-4954 143 9 , , PUNCT cana-4954 143 10 fuzzy fuzzy ADJ cana-4954 143 11 sets set NOUN cana-4954 143 12 and and CCONJ cana-4954 143 13 systems system NOUN cana-4954 143 14 , , PUNCT cana-4954 143 15 20 20 NUM cana-4954 143 16 ( ( PUNCT cana-4954 143 17 1986 1986 NUM cana-4954 143 18 ) ) PUNCT cana-4954 143 19 , , PUNCT cana-4954 143 20 87 87 NUM cana-4954 143 21 - - SYM cana-4954 143 22 96 96 NUM cana-4954 143 23 , , PUNCT cana-4954 143 24 http://dx.doi.org/10.1016/s0165-0114(86)80034-3 http://dx.doi.org/10.1016/s0165-0114(86)80034-3 PROPN cana-4954 143 25 . . PUNCT cana-4954 144 1 [ [ X cana-4954 144 2 2 2 NUM cana-4954 144 3 ] ] SYM cana-4954 144 4 k.atanassov k.atanassov ADJ cana-4954 144 5 , , PUNCT cana-4954 144 6 intuitionistic intuitionistic ADJ cana-4954 144 7 fuzzy fuzzy ADJ cana-4954 144 8 sets set NOUN cana-4954 144 9 , , PUNCT cana-4954 144 10 theory theory NOUN cana-4954 144 11 and and CCONJ cana-4954 144 12 applications application NOUN cana-4954 144 13 , , PUNCT cana-4954 144 14 physica physica NOUN cana-4954 144 15 - - PUNCT cana-4954 144 16 verlag verlag PROPN cana-4954 144 17 , , PUNCT cana-4954 144 18 heidelberg heidelberg PROPN cana-4954 144 19 ( ( PUNCT cana-4954 144 20 1999 1999 NUM cana-4954 144 21 ) ) PUNCT cana-4954 144 22 , , PUNCT cana-4954 144 23 https://doi.org/10.1007/978-3-7908-1870-3_1 https://doi.org/10.1007/978-3-7908-1870-3_1 PROPN cana-4954 145 1 [ [ X cana-4954 145 2 3 3 NUM cana-4954 145 3 ] ] X cana-4954 145 4 k.atanassov k.atanassov NOUN cana-4954 145 5 , , PUNCT cana-4954 145 6 g.pasi g.pasi NOUN cana-4954 145 7 , , PUNCT cana-4954 145 8 and and CCONJ cana-4954 145 9 r.r r.r PROPN cana-4954 145 10 yager yager NOUN cana-4954 145 11 , , PUNCT cana-4954 145 12 intuitionistic intuitionistic ADJ cana-4954 145 13 fuzzy fuzzy ADJ cana-4954 145 14 interpretations interpretation NOUN cana-4954 145 15 of of ADP cana-4954 145 16 multi multi ADJ cana-4954 145 17 - - ADJ cana-4954 145 18 criteria criteria ADJ cana-4954 145 19 multiperson multiperson NOUN cana-4954 145 20 and and CCONJ cana-4954 145 21 multi multi ADJ cana-4954 145 22 - - ADJ cana-4954 145 23 measurement measurement ADJ cana-4954 145 24 tool tool NOUN cana-4954 145 25 decision decision NOUN cana-4954 145 26 making making NOUN cana-4954 145 27 , , PUNCT cana-4954 145 28 international international ADJ cana-4954 145 29 journal journal NOUN cana-4954 145 30 of of ADP cana-4954 145 31 systems system NOUN cana-4954 145 32 science science NOUN cana-4954 145 33 36 36 NUM cana-4954 145 34 ( ( PUNCT cana-4954 145 35 2005 2005 NUM cana-4954 145 36 ) ) PUNCT cana-4954 145 37 , , PUNCT cana-4954 145 38 859–868 859–868 NUM cana-4954 145 39 , , PUNCT cana-4954 145 40 doi:10.1080/00207720500382365 doi:10.1080/00207720500382365 VERB cana-4954 145 41 [ [ X cana-4954 145 42 4 4 NUM cana-4954 145 43 ] ] SYM cana-4954 145 44 h.bustine h.bustine NOUN cana-4954 145 45 , , PUNCT cana-4954 145 46 and and CCONJ cana-4954 145 47 p.burillo p.burillo ADV cana-4954 145 48 , , PUNCT cana-4954 145 49 vague vague ADJ cana-4954 145 50 sets set NOUN cana-4954 145 51 are be AUX cana-4954 145 52 intuitionistic intuitionistic ADJ cana-4954 145 53 fuzzy fuzzy ADJ cana-4954 145 54 sets set NOUN cana-4954 145 55 , , PUNCT cana-4954 145 56 fuzzy fuzzy ADJ cana-4954 145 57 sets set NOUN cana-4954 145 58 and and CCONJ cana-4954 145 59 systems system NOUN cana-4954 145 60 79(1996 79(1996 NOUN cana-4954 145 61 ) ) PUNCT cana-4954 146 1 403–405 403–405 NUM cana-4954 146 2 , , PUNCT cana-4954 146 3 https://doi.org/10.1016/j.ijar.2007.08.008 https://doi.org/10.1016/j.ijar.2007.08.008 NOUN cana-4954 146 4 [ [ X cana-4954 146 5 5 5 NUM cana-4954 146 6 ] ] SYM cana-4954 146 7 s.kde s.kde NUM cana-4954 146 8 , , PUNCT cana-4954 146 9 r.biswas r.biswa VERB cana-4954 146 10 , , PUNCT cana-4954 146 11 and and CCONJ cana-4954 146 12 a.r a.r PROPN cana-4954 146 13 roy roy PROPN cana-4954 146 14 , , PUNCT cana-4954 146 15 some some DET cana-4954 146 16 operations operation NOUN cana-4954 146 17 on on ADP cana-4954 146 18 intuitionistic intuitionistic ADJ cana-4954 146 19 fuzzy fuzzy ADJ cana-4954 146 20 sets set NOUN cana-4954 146 21 , , PUNCT cana-4954 146 22 fuzzy fuzzy ADJ cana-4954 146 23 sets set NOUN cana-4954 146 24 and and CCONJ cana-4954 146 25 systems system NOUN cana-4954 146 26 114 114 NUM cana-4954 146 27 ( ( PUNCT cana-4954 146 28 2000 2000 NUM cana-4954 146 29 ) ) PUNCT cana-4954 146 30 , , PUNCT cana-4954 146 31 477–484 477–484 NUM cana-4954 146 32 , , PUNCT cana-4954 146 33 doi:10.1016 doi:10.1016 PROPN cana-4954 146 34 / / SYM cana-4954 146 35 s0165 s0165 PROPN cana-4954 146 36 - - PUNCT cana-4954 146 37 0114(98)00191 0114(98)00191 NOUN cana-4954 146 38 - - PUNCT cana-4954 146 39 2 2 NUM cana-4954 146 40 [ [ X cana-4954 146 41 6 6 NUM cana-4954 146 42 ] ] SYM cana-4954 146 43 e.pdoolan e.pdoolan ADJ cana-4954 146 44 , , PUNCT cana-4954 146 45 j.j.h j.j.h ADJ cana-4954 146 46 miller miller NOUN cana-4954 146 47 and and CCONJ cana-4954 146 48 w.h.aschilders w.h.aschilder NOUN cana-4954 146 49 , , PUNCT cana-4954 146 50 uniform uniform ADJ cana-4954 146 51 numerical numerical ADJ cana-4954 146 52 methods method NOUN cana-4954 146 53 for for ADP cana-4954 146 54 problems problem NOUN cana-4954 146 55 with with ADP cana-4954 146 56 initial initial ADJ cana-4954 146 57 and and CCONJ cana-4954 146 58 boundary boundary ADJ cana-4954 146 59 layers layer NOUN cana-4954 146 60 . . PUNCT cana-4954 147 1 boole boole PROPN cana-4954 147 2 prees prees PROPN cana-4954 147 3 , , PUNCT cana-4954 147 4 dublin dublin PROPN cana-4954 147 5 , , PUNCT cana-4954 147 6 ireland,(1980 ireland,(1980 PROPN cana-4954 147 7 ) ) PUNCT cana-4954 147 8 , , PUNCT cana-4954 147 9 doi doi NOUN cana-4954 147 10 : : PUNCT cana-4954 147 11 10.4236 10.4236 NUM cana-4954 147 12 / / SYM cana-4954 147 13 ajcm.2018.82012 ajcm.2018.82012 NOUN cana-4954 148 1 [ [ X cana-4954 148 2 7 7 X cana-4954 148 3 ] ] PUNCT cana-4954 148 4 m.kkadalbajoo m.kkadalbajoo ADV cana-4954 148 5 , , PUNCT cana-4954 148 6 and and CCONJ cana-4954 148 7 y.nreddy y.nreddy NOUN cana-4954 148 8 , , PUNCT cana-4954 148 9 initial initial ADJ cana-4954 148 10 values value NOUN cana-4954 148 11 technique technique NOUN cana-4954 148 12 for for ADP cana-4954 148 13 a a DET cana-4954 148 14 class class NOUN cana-4954 148 15 of of ADP cana-4954 148 16 nonlinear nonlinear ADJ cana-4954 148 17 singular singular ADJ cana-4954 148 18 perturbation perturbation NOUN cana-4954 148 19 problems problem NOUN cana-4954 148 20 . . PUNCT cana-4954 149 1 journal journal NOUN cana-4954 149 2 of of ADP cana-4954 149 3 optimization optimization NOUN cana-4954 149 4 theory theory NOUN cana-4954 149 5 and and CCONJ cana-4954 149 6 applications application NOUN cana-4954 149 7 53(3),(1987 53(3),(1987 NUM cana-4954 149 8 ) ) PUNCT cana-4954 149 9 , , PUNCT cana-4954 149 10 395 395 NUM cana-4954 149 11 - - SYM cana-4954 149 12 406 406 NUM cana-4954 149 13 , , PUNCT cana-4954 149 14 doi doi NOUN cana-4954 149 15 : : PUNCT cana-4954 149 16 10.12691 10.12691 NUM cana-4954 149 17 / / SYM cana-4954 149 18 ajna-2 ajna-2 NUM cana-4954 149 19 - - PUNCT cana-4954 149 20 2 2 NUM cana-4954 149 21 - - SYM cana-4954 149 22 3 3 NUM cana-4954 149 23 [ [ NOUN cana-4954 149 24 8 8 NUM cana-4954 149 25 ] ] SYM cana-4954 149 26 h.wliu h.wliu NUM cana-4954 149 27 , , PUNCT cana-4954 149 28 and and CCONJ cana-4954 149 29 g.jwang g.jwang NOUN cana-4954 149 30 , , PUNCT cana-4954 149 31 multi multi ADJ cana-4954 149 32 - - ADJ cana-4954 149 33 criteria criterion NOUN cana-4954 149 34 decision decision NOUN cana-4954 149 35 - - PUNCT cana-4954 149 36 making make VERB cana-4954 149 37 methods method NOUN cana-4954 149 38 based base VERB cana-4954 149 39 on on ADP cana-4954 149 40 intuitionistic intuitionistic ADJ cana-4954 149 41 fuzzy fuzzy ADJ cana-4954 149 42 sets set NOUN cana-4954 149 43 , , PUNCT cana-4954 149 44 european european ADJ cana-4954 149 45 journal journal PROPN cana-4954 149 46 of of ADP cana-4954 149 47 operational operational ADJ cana-4954 149 48 research research NOUN cana-4954 149 49 179 179 NUM cana-4954 149 50 ( ( PUNCT cana-4954 149 51 2007 2007 NUM cana-4954 149 52 ) ) PUNCT cana-4954 149 53 , , PUNCT cana-4954 149 54 220 220 NUM cana-4954 149 55 – – SYM cana-4954 149 56 233 233 NUM cana-4954 149 57 , , PUNCT cana-4954 149 58 doi:10.1016 doi:10.1016 PROPN cana-4954 149 59 / / SYM cana-4954 149 60 j.ejor.2006.04.009 j.ejor.2006.04.009 PROPN cana-4954 149 61 http://dx.doi.org/10.1080/00207720500382365 http://dx.doi.org/10.1080/00207720500382365 PROPN cana-4954 149 62 https://doi.org/10.1016/j.ijar.2007.08.008 https://doi.org/10.1016/j.ijar.2007.08.008 NOUN cana-4954 149 63 http://dx.doi.org/10.1016/s0165-0114(98)00191-2 http://dx.doi.org/10.1016/s0165-0114(98)00191-2 ADP cana-4954 149 64 https://doi.org/10.4236/ajcm.2018.82012 https://doi.org/10.4236/ajcm.2018.82012 PROPN cana-4954 149 65 http://dx.doi.org/10.1016/j.ejor.2006.04.009 http://dx.doi.org/10.1016/j.ejor.2006.04.009 NOUN cana-4954 149 66 communications communication NOUN cana-4954 149 67 on on ADP cana-4954 149 68 applied apply VERB cana-4954 149 69 nonlinear nonlinear ADJ cana-4954 149 70 analysis analysis NOUN cana-4954 149 71 issn issn NOUN cana-4954 149 72 : : PUNCT cana-4954 149 73 1074 1074 NUM cana-4954 149 74 - - PUNCT cana-4954 149 75 133x 133x NUM cana-4954 149 76 vol vol VERB cana-4954 149 77 32 32 NUM cana-4954 149 78 no no NOUN cana-4954 149 79 . . PUNCT cana-4954 150 1 10s 10 NOUN cana-4954 150 2 ( ( PUNCT cana-4954 150 3 2025 2025 NUM cana-4954 150 4 ) ) PUNCT cana-4954 150 5 1039 1039 NUM cana-4954 150 6 https://internationalpubls.com https://internationalpubls.com X cana-4954 151 1 [ [ X cana-4954 151 2 9 9 NUM cana-4954 151 3 ] ] SYM cana-4954 151 4 j.j.hmiller j.j.hmiller NOUN cana-4954 151 5 , , PUNCT cana-4954 151 6 e.oriordan e.oriordan ADJ cana-4954 151 7 , , PUNCT cana-4954 151 8 and and CCONJ cana-4954 151 9 g.ishishkin g.ishishkin PROPN cana-4954 151 10 , , PUNCT cana-4954 151 11 fitted fit VERB cana-4954 151 12 numerical numerical ADJ cana-4954 151 13 methods method NOUN cana-4954 151 14 for for ADP cana-4954 151 15 singular singular ADJ cana-4954 151 16 perturbation perturbation NOUN cana-4954 151 17 problems.error problems.error NOUN cana-4954 151 18 estimates estimate NOUN cana-4954 151 19 in in ADP cana-4954 151 20 the the DET cana-4954 151 21 maximum maximum ADJ cana-4954 151 22 norm norm NOUN cana-4954 151 23 for for ADP cana-4954 151 24 linear linear ADJ cana-4954 151 25 problems problem NOUN cana-4954 151 26 in in ADP cana-4954 151 27 one one NUM cana-4954 151 28 and and CCONJ cana-4954 151 29 two two NUM cana-4954 151 30 dimensions dimension NOUN cana-4954 151 31 . . PUNCT cana-4954 152 1 world world NOUN cana-4954 152 2 scientific scientific ADJ cana-4954 152 3 publishing publishing PROPN cana-4954 152 4 co co NOUN cana-4954 152 5 , , PUNCT cana-4954 152 6 pvt.ltd pvt.ltd PROPN cana-4954 152 7 . . PUNCT cana-4954 152 8 ,singapore,(1996 ,singapore,(1996 PUNCT cana-4954 152 9 ) ) PUNCT cana-4954 152 10 . . PUNCT cana-4954 153 1 https://doi.org/10.1142/8410v https://doi.org/10.1142/8410v X cana-4954 153 2 . . PUNCT cana-4954 154 1 : : PUNCT cana-4954 154 2 ; ; PUNCT cana-4954 154 3 [ [ X cana-4954 154 4 10 10 NUM cana-4954 154 5 ] ] SYM cana-4954 154 6 e.szmidt e.szmidt NOUN cana-4954 154 7 , , PUNCT cana-4954 154 8 and and CCONJ cana-4954 154 9 j.kacprzyk j.kacprzyk PROPN cana-4954 154 10 , , PUNCT cana-4954 154 11 distances distance NOUN cana-4954 154 12 between between ADP cana-4954 154 13 intuitionistic intuitionistic ADJ cana-4954 154 14 fuzzy fuzzy ADJ cana-4954 154 15 sets set NOUN cana-4954 154 16 , , PUNCT cana-4954 154 17 fuzzy fuzzy ADJ cana-4954 154 18 sets set NOUN cana-4954 154 19 and and CCONJ cana-4954 154 20 systems system NOUN cana-4954 154 21 114 114 NUM cana-4954 154 22 ( ( PUNCT cana-4954 154 23 2000 2000 NUM cana-4954 154 24 ) ) PUNCT cana-4954 154 25 , , PUNCT cana-4954 154 26 505–518 505–518 NUM cana-4954 154 27 , , PUNCT cana-4954 154 28 https://doi.org/10.1016/s0165-0114(98)00244-9 https://doi.org/10.1016/s0165-0114(98)00244-9 ADJ cana-4954 154 29 [ [ X cana-4954 154 30 11 11 NUM cana-4954 154 31 ] ] SYM cana-4954 154 32 e.szmidt e.szmidt NOUN cana-4954 154 33 , , PUNCT cana-4954 154 34 and and CCONJ cana-4954 154 35 j.kacprzyk j.kacprzyk PROPN cana-4954 154 36 , , PUNCT cana-4954 154 37 using use VERB cana-4954 154 38 intuitionistic intuitionistic ADJ cana-4954 154 39 fuzzy fuzzy ADJ cana-4954 154 40 sets set NOUN cana-4954 154 41 in in ADP cana-4954 154 42 group group NOUN cana-4954 154 43 decision decision NOUN cana-4954 154 44 making making NOUN cana-4954 154 45 , , PUNCT cana-4954 154 46 control control NOUN cana-4954 154 47 and and CCONJ cana-4954 154 48 cybernetics cybernetic NOUN cana-4954 154 49 31(2002 31(2002 NUM cana-4954 154 50 ) ) PUNCT cana-4954 154 51 , , PUNCT cana-4954 154 52 1037–1053 1037–1053 NUM cana-4954 154 53 , , PUNCT cana-4954 154 54 doi doi NOUN cana-4954 154 55 : : PUNCT cana-4954 154 56 10.1002 10.1002 NUM cana-4954 154 57 / / SYM cana-4954 154 58 mp.17313isbn mp.17313isbn NOUN cana-4954 154 59 : : PUNCT cana-4954 154 60 2473 2473 NUM cana-4954 154 61 - - SYM cana-4954 154 62 4209 4209 NUM cana-4954 155 1 [ [ X cana-4954 155 2 12]z.sxu 12]z.sxu NUM cana-4954 155 3 , , PUNCT cana-4954 155 4 an an DET cana-4954 155 5 overview overview NOUN cana-4954 155 6 of of ADP cana-4954 155 7 methods method NOUN cana-4954 155 8 for for ADP cana-4954 155 9 determining determine VERB cana-4954 155 10 owa owa PROPN cana-4954 155 11 weights weight NOUN cana-4954 155 12 , , PUNCT cana-4954 155 13 international international ADJ cana-4954 155 14 journal journal NOUN cana-4954 155 15 of of ADP cana-4954 155 16 intelligent intelligent ADJ cana-4954 155 17 systems system NOUN cana-4954 155 18 20 20 NUM cana-4954 155 19 ( ( PUNCT cana-4954 155 20 2005 2005 NUM cana-4954 155 21 ) ) PUNCT cana-4954 155 22 , , PUNCT cana-4954 155 23 843–865 843–865 NUM cana-4954 155 24 , , PUNCT cana-4954 155 25 doi:10.1002 doi:10.1002 NOUN cana-4954 155 26 / / SYM cana-4954 155 27 int.20097 int.20097 PRON cana-4954 156 1 [ [ X cana-4954 156 2 13]z.sxu 13]z.sxu ADJ cana-4954 156 3 , , PUNCT cana-4954 156 4 intuitionistic intuitionistic ADJ cana-4954 156 5 preference preference NOUN cana-4954 156 6 relations relation NOUN cana-4954 156 7 and and CCONJ cana-4954 156 8 their their PRON cana-4954 156 9 application application NOUN cana-4954 156 10 in in ADP cana-4954 156 11 group group NOUN cana-4954 156 12 decision decision NOUN cana-4954 156 13 making making NOUN cana-4954 156 14 , , PUNCT cana-4954 156 15 information information NOUN cana-4954 156 16 sciences science NOUN cana-4954 156 17 177 177 NUM cana-4954 156 18 ( ( PUNCT cana-4954 156 19 2007 2007 NUM cana-4954 156 20 ) ) PUNCT cana-4954 156 21 , , PUNCT cana-4954 156 22 2363–2379 2363–2379 NUM cana-4954 156 23 , , PUNCT cana-4954 156 24 doi:10.1016 doi:10.1016 PROPN cana-4954 156 25 / / SYM cana-4954 156 26 j.ins.2006.12.019 j.ins.2006.12.019 PRON cana-4954 157 1 [ [ X cana-4954 157 2 14]z.sxu 14]z.sxu NUM cana-4954 157 3 , , PUNCT cana-4954 157 4 and and CCONJ cana-4954 157 5 r.ryager r.ryager NOUN cana-4954 157 6 , , PUNCT cana-4954 157 7 dynamic dynamic ADJ cana-4954 157 8 intuitionistic intuitionistic ADJ cana-4954 157 9 fuzzy fuzzy ADJ cana-4954 157 10 multi multi ADJ cana-4954 157 11 - - ADJ cana-4954 157 12 attribute attribute NOUN cana-4954 157 13 decision decision NOUN cana-4954 157 14 making making NOUN cana-4954 157 15 , , PUNCT cana-4954 157 16 international international ADJ cana-4954 157 17 journal journal NOUN cana-4954 157 18 of of ADP cana-4954 157 19 approximate approximate ADJ cana-4954 157 20 reasoning,48(2008),246–262 reasoning,48(2008),246–262 PROPN cana-4954 157 21 , , PUNCT cana-4954 157 22 doi:10.1016 doi:10.1016 PROPN cana-4954 157 23 / / SYM cana-4954 157 24 j.ijar.2007.08.008 j.ijar.2007.08.008 PROPN cana-4954 158 1 [ [ X cana-4954 158 2 15 15 NUM cana-4954 158 3 ] ] SYM cana-4954 158 4 r.ryager r.ryager NOUN cana-4954 158 5 , , PUNCT cana-4954 158 6 owa owa ADJ cana-4954 158 7 aggregation aggregation NOUN cana-4954 158 8 over over ADP cana-4954 158 9 a a DET cana-4954 158 10 continuous continuous ADJ cana-4954 158 11 interval interval NOUN cana-4954 158 12 argument argument NOUN cana-4954 158 13 with with ADP cana-4954 158 14 applications application NOUN cana-4954 158 15 to to PART cana-4954 158 16 decision decision VERB cana-4954 158 17 making making NOUN cana-4954 158 18 , , PUNCT cana-4954 158 19 ieee ieee NOUN cana-4954 158 20 transactions transaction NOUN cana-4954 158 21 on on ADP cana-4954 158 22 systems system NOUN cana-4954 158 23 , , PUNCT cana-4954 158 24 man man NOUN cana-4954 158 25 , , PUNCT cana-4954 158 26 and and CCONJ cana-4954 158 27 cybernetics cybernetic NOUN cana-4954 158 28 – – PUNCT cana-4954 158 29 part part NOUN cana-4954 158 30 34 34 NUM cana-4954 158 31 ( ( PUNCT cana-4954 158 32 2004 2004 NUM cana-4954 158 33 ) ) PUNCT cana-4954 158 34 , , PUNCT cana-4954 158 35 1952–1963 1952–1963 NUM cana-4954 158 36 , , PUNCT cana-4954 158 37 doi doi NOUN cana-4954 158 38 : : PUNCT cana-4954 158 39 10.1109 10.1109 NUM cana-4954 158 40 / / SYM cana-4954 158 41 tsmcb.2004.831154 tsmcb.2004.831154 NOUN cana-4954 159 1 [ [ X cana-4954 159 2 16]l.azadeh 16]l.azadeh NUM cana-4954 159 3 , , PUNCT cana-4954 159 4 fuzzy fuzzy ADJ cana-4954 159 5 sets set NOUN cana-4954 159 6 , , PUNCT cana-4954 159 7 information information NOUN cana-4954 159 8 and and CCONJ cana-4954 159 9 control control NOUN cana-4954 159 10 8 8 NUM cana-4954 159 11 ( ( PUNCT cana-4954 159 12 1965 1965 NUM cana-4954 159 13 ) ) PUNCT cana-4954 159 14 , , PUNCT cana-4954 159 15 338–353 338–353 NUM cana-4954 159 16 , , PUNCT cana-4954 159 17 doi doi NOUN cana-4954 159 18 : : PUNCT cana-4954 159 19 https://doi.org/10.2307/2272014 https://doi.org/10.2307/2272014 PROPN cana-4954 159 20 https://doi.org/10.1142/8410v https://doi.org/10.1142/8410v X cana-4954 159 21 https://doi.org/10.1016/s0165-0114(98)00244-9 https://doi.org/10.1016/s0165-0114(98)00244-9 VERB cana-4954 159 22 http://dx.doi.org/10.1002/int.20097 http://dx.doi.org/10.1002/int.20097 PRON cana-4954 159 23 http://dx.doi.org/10.1016/j.ins.2006.12.019 http://dx.doi.org/10.1016/j.ins.2006.12.019 VERB cana-4954 159 24 https://doi.org/10.1109/tsmcb.2004.831154 https://doi.org/10.1109/tsmcb.2004.831154 PROPN cana-4954 159 25 https://doi.org/10.2307/2272014 https://doi.org/10.2307/2272014 X