id sid tid token lemma pos cana-733 1 1 communications communication NOUN cana-733 1 2 on on ADP cana-733 1 3 applied apply VERB cana-733 1 4 nonlinear nonlinear ADJ cana-733 1 5 analysis analysis NOUN cana-733 1 6 issn issn NOUN cana-733 1 7 : : PUNCT cana-733 1 8 1074 1074 NUM cana-733 1 9 - - PUNCT cana-733 1 10 133x 133x NUM cana-733 1 11 vol vol NOUN cana-733 1 12 31 31 NUM cana-733 1 13 no no NOUN cana-733 1 14 . . PUNCT cana-733 2 1 3s 3s NUM cana-733 2 2 ( ( PUNCT cana-733 2 3 2024 2024 NUM cana-733 2 4 ) ) PUNCT cana-733 2 5 82 82 NUM cana-733 2 6 https://internationalpubls.com https://internationalpubls.com X cana-733 2 7 fuzzy fuzzy ADJ cana-733 2 8 soft soft ADJ cana-733 2 9 set set NOUN cana-733 2 10 applications application NOUN cana-733 2 11 explored explore VERB cana-733 2 12 in in ADP cana-733 2 13 w w NOUN cana-733 2 14 - - PUNCT cana-733 2 15 algebras algebras ADJ cana-733 2 16 m. m. NOUN cana-733 2 17 indhumathi indhumathi PROPN cana-733 2 18 1 1 NUM cana-733 2 19 , , PUNCT cana-733 2 20 k. k. PROPN cana-733 2 21 jeya jeya PROPN cana-733 2 22 lekshmi2 lekshmi2 PROPN cana-733 2 23 , , PUNCT cana-733 2 24 a. a. PROPN cana-733 2 25 ibrahim3 ibrahim3 PROPN cana-733 2 26 1 1 NUM cana-733 2 27 department department NOUN cana-733 2 28 of of ADP cana-733 2 29 mathematics mathematic NOUN cana-733 2 30 , , PUNCT cana-733 2 31 rvs rvs ADJ cana-733 2 32 college college NOUN cana-733 2 33 of of ADP cana-733 2 34 arts art NOUN cana-733 2 35 and and CCONJ cana-733 2 36 science science NOUN cana-733 2 37 , , PUNCT cana-733 2 38 sulur sulur PROPN cana-733 2 39 , , PUNCT cana-733 2 40 affiliated affiliate VERB cana-733 2 41 to to ADP cana-733 2 42 bharathiar bharathiar PROPN cana-733 3 1 university university PROPN cana-733 3 2 , , PUNCT cana-733 3 3 coimbatore coimbatore PROPN cana-733 3 4 , , PUNCT cana-733 3 5 tamil tamil PROPN cana-733 3 6 nadu nadu PROPN cana-733 3 7 , , PUNCT cana-733 3 8 india india PROPN cana-733 3 9 . . PUNCT cana-733 3 10 email email NOUN cana-733 3 11 : : PUNCT cana-733 3 12 indumathi@rvsgroup.com indumathi@rvsgroup.com X cana-733 3 13 2 2 NUM cana-733 3 14 department department NOUN cana-733 3 15 of of ADP cana-733 3 16 mathematics mathematics PROPN cana-733 3 17 rvs rvs PROPN cana-733 3 18 college college PROPN cana-733 3 19 of of ADP cana-733 3 20 arts art NOUN cana-733 3 21 and and CCONJ cana-733 3 22 science science NOUN cana-733 3 23 , , PUNCT cana-733 3 24 sulur sulur PROPN cana-733 3 25 , , PUNCT cana-733 3 26 affiliated affiliate VERB cana-733 3 27 to to ADP cana-733 3 28 bharathiar bharathiar PROPN cana-733 3 29 university university PROPN cana-733 3 30 , , PUNCT cana-733 3 31 coimbatore coimbatore PROPN cana-733 3 32 , , PUNCT cana-733 3 33 tamil tamil PROPN cana-733 3 34 nadu nadu PROPN cana-733 3 35 , , PUNCT cana-733 3 36 india india PROPN cana-733 3 37 . . PUNCT cana-733 3 38 email email NOUN cana-733 3 39 : : PUNCT cana-733 4 1 jeyalekshmi@rvsgroup.com jeyalekshmi@rvsgroup.com X cana-733 4 2 3 3 NUM cana-733 5 1 p.g p.g PROPN cana-733 5 2 . . PROPN cana-733 5 3 and and CCONJ cana-733 5 4 research research PROPN cana-733 5 5 department department PROPN cana-733 5 6 of of ADP cana-733 5 7 mathematics mathematics PROPN cana-733 5 8 , , PUNCT cana-733 5 9 h. h. PROPN cana-733 5 10 h. h. PROPN cana-733 6 1 the the DET cana-733 6 2 rajah rajah NOUN cana-733 6 3 โ€™s โ€™s PART cana-733 6 4 college college NOUN cana-733 6 5 , , PUNCT cana-733 6 6 pudukkottai pudukkottai NOUN cana-733 6 7 , , PUNCT cana-733 6 8 affiliated affiliate VERB cana-733 6 9 to to PART cana-733 6 10 bharathidasan bharathidasan VERB cana-733 6 11 university university PROPN cana-733 6 12 , , PUNCT cana-733 6 13 tiruchirappalli tiruchirappalli PROPN cana-733 6 14 , , PUNCT cana-733 6 15 tamil tamil PROPN cana-733 6 16 nadu nadu PROPN cana-733 6 17 , , PUNCT cana-733 6 18 india india PROPN cana-733 6 19 . . PUNCT cana-733 6 20 email email NOUN cana-733 6 21 : : PUNCT cana-733 7 1 ibrahimaadhil@yahoo.com ibrahimaadhil@yahoo.com X cana-733 7 2 , , PUNCT cana-733 7 3 dribrahimaadhil@gmail.com dribrahimaadhil@gmail.com PROPN cana-733 7 4 article article NOUN cana-733 7 5 history history NOUN cana-733 7 6 : : PUNCT cana-733 7 7 received receive VERB cana-733 7 8 : : PUNCT cana-733 7 9 12 12 NUM cana-733 7 10 - - PUNCT cana-733 7 11 04 04 NUM cana-733 7 12 - - PUNCT cana-733 7 13 2024 2024 NUM cana-733 7 14 revised revise VERB cana-733 7 15 : : PUNCT cana-733 7 16 24 24 NUM cana-733 7 17 - - PUNCT cana-733 7 18 05 05 NUM cana-733 7 19 - - PUNCT cana-733 7 20 2024 2024 NUM cana-733 7 21 accepted accept VERB cana-733 7 22 : : PUNCT cana-733 7 23 06 06 NUM cana-733 7 24 - - SYM cana-733 7 25 06 06 NUM cana-733 7 26 - - PUNCT cana-733 7 27 2024 2024 NUM cana-733 7 28 abstract abstract ADJ cana-733 7 29 fuzzy fuzzy ADJ cana-733 7 30 soft soft ADJ cana-733 7 31 set set NOUN cana-733 7 32 theory theory NOUN cana-733 7 33 in in ADP cana-733 7 34 wajsberg wajsberg PROPN cana-733 7 35 algebras algebras PROPN cana-733 7 36 ( ( PUNCT cana-733 7 37 w w NOUN cana-733 7 38 - - PUNCT cana-733 7 39 algebras algebras X cana-733 7 40 ) ) PUNCT cana-733 7 41 is be AUX cana-733 7 42 presented present VERB cana-733 7 43 in in ADP cana-733 7 44 this this DET cana-733 7 45 paper paper NOUN cana-733 7 46 and and CCONJ cana-733 7 47 its its PRON cana-733 7 48 application application NOUN cana-733 7 49 to to ADP cana-733 7 50 a a DET cana-733 7 51 problem problem NOUN cana-733 7 52 of of ADP cana-733 7 53 decision decision NOUN cana-733 7 54 making make VERB cana-733 7 55 is be AUX cana-733 7 56 illustrated illustrate VERB cana-733 7 57 . . PUNCT cana-733 8 1 we we PRON cana-733 8 2 first first ADV cana-733 8 3 introduce introduce VERB cana-733 8 4 the the DET cana-733 8 5 notion notion NOUN cana-733 8 6 of of ADP cana-733 8 7 fuzzy fuzzy ADJ cana-733 8 8 soft soft ADJ cana-733 8 9 ideals ideal NOUN cana-733 8 10 ( ( PUNCT cana-733 8 11 fs f NOUN cana-733 8 12 - - PUNCT cana-733 8 13 ideals ideal NOUN cana-733 8 14 ) ) PUNCT cana-733 8 15 and and CCONJ cana-733 8 16 then then ADV cana-733 8 17 analyse analyse VERB cana-733 8 18 some some PRON cana-733 8 19 of of ADP cana-733 8 20 the the DET cana-733 8 21 associated associated ADJ cana-733 8 22 characteristics characteristic NOUN cana-733 8 23 . . PUNCT cana-733 9 1 keywords keyword NOUN cana-733 9 2 : : PUNCT cana-733 9 3 walgebras walgebras ADJ cana-733 9 4 , , PUNCT cana-733 9 5 soft soft ADJ cana-733 9 6 set set NOUN cana-733 9 7 , , PUNCT cana-733 9 8 fs fs NOUN cana-733 9 9 - - PUNCT cana-733 9 10 set set ADJ cana-733 9 11 , , PUNCT cana-733 9 12 fs f NOUN cana-733 9 13 - - PUNCT cana-733 9 14 ideals ideal NOUN cana-733 9 15 , , PUNCT cana-733 9 16 soft soft ADJ cana-733 9 17 engine engine NOUN cana-733 9 18 . . PUNCT cana-733 10 1 2010 2010 NUM cana-733 10 2 msc msc NOUN cana-733 10 3 : : PUNCT cana-733 10 4 03b20 03b20 NUM cana-733 10 5 , , PUNCT cana-733 10 6 03b52 03b52 NUM cana-733 10 7 , , PUNCT cana-733 10 8 18b20 18b20 NUM cana-733 10 9 1 1 NUM cana-733 10 10 . . PUNCT cana-733 10 11 introduction introduction NOUN cana-733 10 12 research research NOUN cana-733 10 13 on on ADP cana-733 10 14 the the DET cana-733 10 15 soft soft ADJ cana-733 10 16 set set NOUN cana-733 10 17 theory theory NOUN cana-733 10 18 is be AUX cana-733 10 19 now now ADV cana-733 10 20 progressing progress VERB cana-733 10 21 at at ADP cana-733 10 22 a a DET cana-733 10 23 rapid rapid ADJ cana-733 10 24 pace pace NOUN cana-733 10 25 . . PUNCT cana-733 11 1 the the DET cana-733 11 2 application application NOUN cana-733 11 3 of of ADP cana-733 11 4 soft soft ADJ cana-733 11 5 set set NOUN cana-733 11 6 theory theory NOUN cana-733 11 7 to to ADP cana-733 11 8 a a DET cana-733 11 9 decision decision NOUN cana-733 11 10 - - PUNCT cana-733 11 11 making make VERB cana-733 11 12 issue issue NOUN cana-733 11 13 was be AUX cana-733 11 14 covered cover VERB cana-733 11 15 by by ADP cana-733 11 16 maji maji PROPN cana-733 11 17 et et PROPN cana-733 11 18 al al PROPN cana-733 11 19 . . PUNCT cana-733 12 1 [ [ X cana-733 12 2 12 12 NUM cana-733 12 3 ] ] PUNCT cana-733 12 4 . . PUNCT cana-733 13 1 maji maji PROPN cana-733 13 2 and and CCONJ cana-733 13 3 [ [ X cana-733 13 4 13 13 NUM cana-733 13 5 ] ] PUNCT cana-733 13 6 additionally additionally ADV cana-733 13 7 investigated investigate VERB cana-733 13 8 some some DET cana-733 13 9 techniques technique NOUN cana-733 13 10 related relate VERB cana-733 13 11 to to ADP cana-733 13 12 soft soft ADJ cana-733 13 13 set set NOUN cana-733 13 14 theory theory NOUN cana-733 13 15 . . PUNCT cana-733 14 1 a a DET cana-733 14 2 new new ADJ cana-733 14 3 definition definition NOUN cana-733 14 4 of of ADP cana-733 14 5 soft soft ADJ cana-733 14 6 set set NOUN cana-733 14 7 parametrization parametrization NOUN cana-733 14 8 reduction reduction NOUN cana-733 14 9 was be AUX cana-733 14 10 developed develop VERB cana-733 14 11 out out ADP cana-733 14 12 by by ADP cana-733 14 13 chen chen PROPN cana-733 14 14 et et PROPN cana-733 14 15 al al PROPN cana-733 14 16 . . PUNCT cana-733 15 1 [ [ X cana-733 15 2 4 4 NUM cana-733 15 3 ] ] PUNCT cana-733 15 4 , , PUNCT cana-733 15 5 who who PRON cana-733 15 6 also also ADV cana-733 15 7 compared compare VERB cana-733 15 8 it it PRON cana-733 15 9 to to ADP cana-733 15 10 the the DET cana-733 15 11 same same ADJ cana-733 15 12 attribute attribute NOUN cana-733 15 13 reduction reduction NOUN cana-733 15 14 idea idea NOUN cana-733 15 15 in in ADP cana-733 15 16 rough rough ADJ cana-733 15 17 set set NOUN cana-733 15 18 theory theory NOUN cana-733 15 19 . . PUNCT cana-733 16 1 the the DET cana-733 16 2 algebraic algebraic ADJ cana-733 16 3 structure structure NOUN cana-733 16 4 of of ADP cana-733 16 5 uncertainty uncertainty NOUN cana-733 16 6 - - PUNCT cana-733 16 7 aware aware ADJ cana-733 16 8 set set NOUN cana-733 16 9 theories theory NOUN cana-733 16 10 has have AUX cana-733 16 11 been be AUX cana-733 16 12 studied study VERB cana-733 16 13 by by ADP cana-733 16 14 a a DET cana-733 16 15 few few ADJ cana-733 16 16 authors author NOUN cana-733 16 17 . . PUNCT cana-733 17 1 the the DET cana-733 17 2 best good ADJ cana-733 17 3 theory theory NOUN cana-733 17 4 for for ADP cana-733 17 5 dealing deal VERB cana-733 17 6 with with ADP cana-733 17 7 uncertainty uncertainty NOUN cana-733 17 8 is be AUX cana-733 17 9 zadeh zadeh PROPN cana-733 17 10 's 's PART cana-733 17 11 notion notion NOUN cana-733 17 12 of of ADP cana-733 17 13 fuzzy fuzzy ADJ cana-733 17 14 sets set NOUN cana-733 17 15 . . PUNCT cana-733 18 1 m. m. NOUN cana-733 18 2 wajsberg wajsberg PROPN cana-733 18 3 introduced introduce VERB cana-733 18 4 the the DET cana-733 18 5 ideas idea NOUN cana-733 18 6 of of ADP cana-733 18 7 w w NOUN cana-733 18 8 - - PUNCT cana-733 18 9 algebra algebra NOUN cana-733 18 10 [ [ X cana-733 18 11 15 15 NUM cana-733 18 12 ] ] PUNCT cana-733 18 13 . . PUNCT cana-733 19 1 lpw lpw VERB cana-733 19 2 - - PUNCT cana-733 19 3 algebras algebras PROPN cana-733 19 4 were be AUX cana-733 19 5 first first ADV cana-733 19 6 presented present VERB cana-733 19 7 by by ADP cana-733 19 8 ceterchi ceterchi ADJ cana-733 19 9 rodica rodica PROPN cana-733 20 1 [ [ X cana-733 20 2 2 2 NUM cana-733 20 3 ] ] PUNCT cana-733 20 4 . . PUNCT cana-733 21 1 a a DET cana-733 21 2 generalisation generalisation NOUN cana-733 21 3 of of ADP cana-733 21 4 regular regular ADJ cana-733 21 5 soft soft ADJ cana-733 21 6 sets set NOUN cana-733 21 7 , , PUNCT cana-733 21 8 known know VERB cana-733 21 9 as as ADP cana-733 21 10 fs f NOUN cana-733 21 11 - - PUNCT cana-733 21 12 sets set NOUN cana-733 21 13 , , PUNCT cana-733 21 14 is be AUX cana-733 21 15 presented present VERB cana-733 21 16 in in ADP cana-733 21 17 [ [ X cana-733 21 18 11 11 NUM cana-733 21 19 ] ] PUNCT cana-733 21 20 . . PUNCT cana-733 22 1 the the DET cana-733 22 2 use use NOUN cana-733 22 3 of of ADP cana-733 22 4 fs f NOUN cana-733 22 5 - - PUNCT cana-733 22 6 sets set NOUN cana-733 22 7 to to ADP cana-733 22 8 a a DET cana-733 22 9 decision decision NOUN cana-733 22 10 - - PUNCT cana-733 22 11 making make VERB cana-733 22 12 scenario scenario NOUN cana-733 22 13 is be AUX cana-733 22 14 then then ADV cana-733 22 15 demonstrated demonstrate VERB cana-733 22 16 . . PUNCT cana-733 23 1 in in ADP cana-733 23 2 this this DET cana-733 23 3 work work NOUN cana-733 23 4 , , PUNCT cana-733 23 5 we we PRON cana-733 23 6 use use VERB cana-733 23 7 the the DET cana-733 23 8 notion notion NOUN cana-733 23 9 of of ADP cana-733 23 10 fsideals fsideal NOUN cana-733 23 11 and and CCONJ cana-733 23 12 fs f NOUN cana-733 23 13 - - PUNCT cana-733 23 14 w w NOUN cana-733 23 15 - - PUNCT cana-733 23 16 algebras algebras PROPN cana-733 23 17 and and CCONJ cana-733 23 18 then then ADV cana-733 23 19 derive derive VERB cana-733 23 20 their their PRON cana-733 23 21 basic basic ADJ cana-733 23 22 characteristics characteristic NOUN cana-733 23 23 . . PUNCT cana-733 24 1 in in ADP cana-733 24 2 the the DET cana-733 24 3 future future NOUN cana-733 24 4 , , PUNCT cana-733 24 5 this this DET cana-733 24 6 paper paper NOUN cana-733 24 7 's 's PART cana-733 24 8 approach approach NOUN cana-733 24 9 will will AUX cana-733 24 10 be be AUX cana-733 24 11 expanded expand VERB cana-733 24 12 upon upon SCONJ cana-733 24 13 to to PART cana-733 24 14 analyse analyse VERB cana-733 24 15 many many ADJ cana-733 24 16 kinds kind NOUN cana-733 24 17 of of ADP cana-733 24 18 ideals ideal NOUN cana-733 24 19 in in ADP cana-733 24 20 w w NOUN cana-733 24 21 - - PUNCT cana-733 24 22 algebras algebras ADJ cana-733 24 23 . . PUNCT cana-733 25 1 2 2 X cana-733 25 2 . . NUM cana-733 25 3 basic basic ADJ cana-733 25 4 results result NOUN cana-733 25 5 on on ADP cana-733 25 6 soft soft ADJ cana-733 25 7 sets set NOUN cana-733 25 8 the the DET cana-733 25 9 following follow VERB cana-733 25 10 is be AUX cana-733 25 11 a a DET cana-733 25 12 description description NOUN cana-733 25 13 of of ADP cana-733 25 14 molodtsov molodtsov NOUN cana-733 25 15 's 's PART cana-733 25 16 [ [ NOUN cana-733 25 17 14 14 NUM cana-733 25 18 ] ] PUNCT cana-733 25 19 definition definition NOUN cana-733 25 20 of of ADP cana-733 25 21 the the DET cana-733 25 22 soft soft ADJ cana-733 25 23 set set NOUN cana-733 25 24 . . PUNCT cana-733 26 1 suppose suppose VERB cana-733 26 2 that that SCONJ cana-733 26 3 โ„ณ โ„ณ PROPN cana-733 26 4 is be AUX cana-733 26 5 an an DET cana-733 26 6 initial initial ADJ cana-733 26 7 universe universe NOUN cana-733 26 8 set set VERB cana-733 26 9 and and CCONJ cana-733 26 10 that that SCONJ cana-733 26 11 ๐’ฆ ๐’ฆ PROPN cana-733 26 12 is be AUX cana-733 26 13 a a DET cana-733 26 14 set set NOUN cana-733 26 15 of of ADP cana-733 26 16 parameters parameter NOUN cana-733 26 17 . . PUNCT cana-733 27 1 let let VERB cana-733 27 2 ๐ผโŠ‚ ๐ผโŠ‚ PROPN cana-733 27 3 ๐’ฆ ๐’ฆ PROPN cana-733 27 4 and and CCONJ cana-733 27 5 ๐’ฏ(โ„ณ ๐’ฏ(โ„ณ NUM cana-733 27 6 ) ) PUNCT cana-733 27 7 represent represent VERB cana-733 27 8 the the DET cana-733 27 9 power power NOUN cana-733 27 10 set set NOUN cana-733 27 11 of of ADP cana-733 27 12 โ„ณ โ„ณ PROPN cana-733 27 13 and and CCONJ cana-733 27 14 ๐ผ ๐ผ PROPN cana-733 27 15 โŠ‚ โŠ‚ PROPN cana-733 27 16 ๐’ฆ. ๐’ฆ. PROPN cana-733 27 17 definition definition NOUN cana-733 27 18 2.1 2.1 NUM cana-733 27 19 . . PUNCT cana-733 28 1 [ [ X cana-733 28 2 14 14 NUM cana-733 28 3 ] ] X cana-733 28 4 [ [ X cana-733 28 5 17 17 NUM cana-733 28 6 ] ] PUNCT cana-733 28 7 a a DET cana-733 28 8 pair pair NOUN cana-733 28 9 ( ( PUNCT cana-733 28 10 ๐’ฎ ๐’ฎ PROPN cana-733 28 11 , , PUNCT cana-733 28 12 ๐ผ ๐ผ PROPN cana-733 28 13 ) ) PUNCT cana-733 28 14 is be AUX cana-733 28 15 called call VERB cana-733 28 16 a a DET cana-733 28 17 soft soft ADJ cana-733 28 18 set set NOUN cana-733 28 19 over over ADP cana-733 28 20 โ„ณ โ„ณ PROPN cana-733 28 21 , , PUNCT cana-733 28 22 where where SCONJ cana-733 28 23 ๐’ฎ ๐’ฎ PROPN cana-733 28 24 is be AUX cana-733 28 25 a a DET cana-733 28 26 mapping mapping NOUN cana-733 28 27 given give VERB cana-733 28 28 by by ADP cana-733 28 29 ๐’ฎ ๐’ฎ PROPN cana-733 28 30 : : PUNCT cana-733 28 31 ๐ผ ๐ผ PROPN cana-733 28 32 โŸถ โŸถ ADJ cana-733 28 33 ๐’ฏ(โ„ณ ๐’ฏ(โ„ณ NUM cana-733 28 34 ) ) PUNCT cana-733 28 35 . . PUNCT cana-733 29 1 mailto:ibrahimaadhil@yahoo.com mailto:ibrahimaadhil@yahoo.com X cana-733 30 1 mailto:dribrahimaadhil@gmail.com mailto:dribrahimaadhil@gmail.com X cana-733 30 2 communications communication NOUN cana-733 30 3 on on ADP cana-733 30 4 applied apply VERB cana-733 30 5 nonlinear nonlinear ADJ cana-733 30 6 analysis analysis NOUN cana-733 30 7 issn issn NOUN cana-733 30 8 : : PUNCT cana-733 30 9 1074 1074 NUM cana-733 30 10 - - PUNCT cana-733 30 11 133x 133x NUM cana-733 30 12 vol vol NOUN cana-733 30 13 31 31 NUM cana-733 30 14 no no NOUN cana-733 30 15 . . PUNCT cana-733 31 1 3s 3s NUM cana-733 31 2 ( ( PUNCT cana-733 31 3 2024 2024 NUM cana-733 31 4 ) ) PUNCT cana-733 31 5 83 83 NUM cana-733 31 6 https://internationalpubls.com https://internationalpubls.com X cana-733 31 7 a a DET cana-733 31 8 soft soft ADJ cana-733 31 9 set set NOUN cana-733 31 10 over over ADP cana-733 31 11 โ„ณ โ„ณ PROPN cana-733 31 12 , , PUNCT cana-733 31 13 stated state VERB cana-733 31 14 differently differently ADV cana-733 31 15 , , PUNCT cana-733 31 16 defines define VERB cana-733 31 17 a a DET cana-733 31 18 parameterized parameterized ADJ cana-733 31 19 family family NOUN cana-733 31 20 of of ADP cana-733 31 21 universe universe ADJ cana-733 31 22 โ„ณ โ„ณ NOUN cana-733 31 23 subsets subset NOUN cana-733 31 24 . . PUNCT cana-733 32 1 it it PRON cana-733 32 2 is be AUX cana-733 32 3 possible possible ADJ cana-733 32 4 to to PART cana-733 32 5 consider consider VERB cana-733 32 6 elements element NOUN cana-733 32 7 of of ADP cana-733 32 8 the the DET cana-733 32 9 soft soft ADJ cana-733 32 10 set set NOUN cana-733 32 11 ( ( PUNCT cana-733 32 12 ๐’ฎ ๐’ฎ PROPN cana-733 32 13 , , PUNCT cana-733 32 14 ๐ผ ๐ผ PROPN cana-733 32 15 ) ) PUNCT cana-733 32 16 that that PRON cana-733 32 17 are be AUX cana-733 32 18 ๐›ผ ๐›ผ X cana-733 32 19 โ€“ โ€“ PUNCT cana-733 32 20 approximate approximate ADJ cana-733 32 21 if if SCONJ cana-733 32 22 ๐›ผ ๐›ผ PRON cana-733 32 23 โˆˆ โˆˆ PROPN cana-733 32 24 ๐ผ. ๐ผ. NOUN cana-733 32 25 it it PRON cana-733 32 26 is be AUX cana-733 32 27 evident evident ADJ cana-733 32 28 that that SCONJ cana-733 32 29 a a DET cana-733 32 30 soft soft ADJ cana-733 32 31 set set NOUN cana-733 32 32 is be AUX cana-733 32 33 not not PART cana-733 32 34 a a DET cana-733 32 35 set set NOUN cana-733 32 36 . . PUNCT cana-733 33 1 definition definition NOUN cana-733 33 2 2.2 2.2 NUM cana-733 33 3 . . PUNCT cana-733 34 1 [ [ X cana-733 34 2 11 11 NUM cana-733 34 3 ] ] PUNCT cana-733 34 4 let let VERB cana-733 34 5 ๐’ฆ ๐’ฆ PRON cana-733 34 6 be be AUX cana-733 34 7 a a DET cana-733 34 8 set set NOUN cana-733 34 9 of of ADP cana-733 34 10 parameters parameter NOUN cana-733 34 11 and and CCONJ cana-733 34 12 let let VERB cana-733 34 13 โ„ณ โ„ณ PRON cana-733 34 14 be be AUX cana-733 34 15 the the DET cana-733 34 16 initial initial ADJ cana-733 34 17 universe universe NOUN cana-733 34 18 set set NOUN cana-733 34 19 . . PUNCT cana-733 35 1 ๐’ฏ(โ„ณ ๐’ฏ(โ„ณ NUM cana-733 35 2 ) ) PUNCT cana-733 35 3 denote denote VERB cana-733 35 4 the the DET cana-733 35 5 set set NOUN cana-733 35 6 of of ADP cana-733 35 7 fuzzy fuzzy ADJ cana-733 35 8 sets set NOUN cana-733 35 9 within within ADP cana-733 35 10 โ„ณ. โ„ณ. PROPN cana-733 35 11 where where SCONJ cana-733 35 12 ๐ผ ๐ผ PROPN cana-733 35 13 โŠ† โŠ† NUM cana-733 35 14 ๐’ฆ ๐’ฆ PROPN cana-733 35 15 and and CCONJ cana-733 35 16 ๏ฟฝ ๏ฟฝ PROPN cana-733 35 17 ฬŒ ฬŒ NUM cana-733 35 18 ๏ฟฝ ๏ฟฝ NOUN cana-733 35 19 โˆถ โˆถ NOUN cana-733 35 20 ๐ผ ๐ผ PROPN cana-733 35 21 โŸถ โŸถ ADJ cana-733 35 22 ๐’ฏ(โ„ณ ๐’ฏ(โ„ณ NUM cana-733 35 23 ) ) PUNCT cana-733 35 24 . . PUNCT cana-733 36 1 ๏ฟฝ ๏ฟฝ PROPN cana-733 36 2 ฬŒ ฬŒ NUM cana-733 36 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 37 1 [ [ X cana-733 37 2 a a X cana-733 37 3 ] ] X cana-733 37 4 is be AUX cana-733 37 5 often often ADV cana-733 37 6 referred refer VERB cana-733 37 7 to to ADP cana-733 37 8 as as ADP cana-733 37 9 the the DET cana-733 37 10 fuzzy fuzzy ADJ cana-733 37 11 value value NOUN cana-733 37 12 set set NOUN cana-733 37 13 of of ADP cana-733 37 14 parameter parameter NOUN cana-733 37 15 a. a. NOUN cana-733 37 16 it it PRON cana-733 37 17 is be AUX cana-733 37 18 a a DET cana-733 37 19 fuzzy fuzzy ADJ cana-733 37 20 set set NOUN cana-733 37 21 in in ADP cana-733 37 22 โ„ณ โ„ณ PROPN cana-733 37 23 for for ADP cana-733 37 24 every every DET cana-733 37 25 a a DET cana-733 37 26 โˆˆ โˆˆ PROPN cana-733 37 27 ๐ผ. ๐ผ. PROPN cana-733 37 28 ( ( PUNCT cana-733 37 29 ๏ฟฝ ๏ฟฝ PROPN cana-733 37 30 ฬŒ ฬŒ NUM cana-733 37 31 ๏ฟฝ ๏ฟฝ PROPN cana-733 37 32 , , PUNCT cana-733 37 33 ๐ผ ๐ผ PROPN cana-733 37 34 ) ) PUNCT cana-733 37 35 degenerates degenerate NOUN cana-733 37 36 to to ADP cana-733 37 37 the the DET cana-733 37 38 usual usual ADJ cana-733 37 39 soft soft ADJ cana-733 37 40 set set NOUN cana-733 37 41 . . PUNCT cana-733 38 1 if if SCONJ cana-733 38 2 ๏ฟฝ ๏ฟฝ PROPN cana-733 38 3 ฬŒ ฬŒ NUM cana-733 38 4 ๏ฟฝ ๏ฟฝ NOUN cana-733 38 5 [ [ X cana-733 38 6 a a X cana-733 38 7 ] ] X cana-733 38 8 is be AUX cana-733 38 9 a a DET cana-733 38 10 crisp crisp ADJ cana-733 38 11 subset subset NOUN cana-733 38 12 of of ADP cana-733 38 13 โ„ณ โ„ณ PROPN cana-733 38 14 for for ADP cana-733 38 15 every every DET cana-733 38 16 a a PRON cana-733 38 17 in in ADP cana-733 38 18 ๐ผ ๐ผ PROPN cana-733 38 19 , , PUNCT cana-733 38 20 fs fs ADP cana-733 38 21 sets set NOUN cana-733 38 22 are be AUX cana-733 38 23 therefore therefore ADV cana-733 38 24 a a DET cana-733 38 25 generalization generalization NOUN cana-733 38 26 of of ADP cana-733 38 27 standard standard ADJ cana-733 38 28 soft soft ADJ cana-733 38 29 sets set NOUN cana-733 38 30 due due ADP cana-733 38 31 to to ADP cana-733 38 32 the the DET cana-733 38 33 above above ADJ cana-733 38 34 concept concept NOUN cana-733 38 35 . . PUNCT cana-733 39 1 3 3 X cana-733 39 2 . . X cana-733 39 3 main main ADJ cana-733 39 4 result result NOUN cana-733 39 5 ( ( PUNCT cana-733 39 6 fuzzy fuzzy ADJ cana-733 39 7 soft soft ADJ cana-733 39 8 wajsberg wajsberg NOUN cana-733 39 9 - - PUNCT cana-733 39 10 algebras algebra NOUN cana-733 39 11 ) ) PUNCT cana-733 39 12 unless unless SCONJ cana-733 39 13 otherwise otherwise ADV cana-733 39 14 noted note VERB cana-733 39 15 , , PUNCT cana-733 39 16 let let VERB cana-733 39 17 ๐’ฆ ๐’ฆ PRON cana-733 39 18 be be AUX cana-733 39 19 a a DET cana-733 39 20 collection collection NOUN cana-733 39 21 of of ADP cana-733 39 22 the the DET cana-733 39 23 following follow VERB cana-733 39 24 text text NOUN cana-733 39 25 โ€™s โ€™s PART cana-733 39 26 parameters parameter NOUN cana-733 39 27 . . PUNCT cana-733 40 1 the the DET cana-733 40 2 expression expression NOUN cana-733 40 3 โ€œ " PUNCT cana-733 40 4 soft soft ADJ cana-733 40 5 engine engine NOUN cana-733 40 6 โ€ " PUNCT cana-733 40 7 will will AUX cana-733 40 8 be be AUX cana-733 40 9 used use VERB cana-733 40 10 , , PUNCT cana-733 40 11 referring refer VERB cana-733 40 12 to to ADP cana-733 40 13 the the DET cana-733 40 14 fact fact NOUN cana-733 40 15 that that SCONJ cana-733 40 16 it it PRON cana-733 40 17 generates generate VERB cana-733 40 18 a a DET cana-733 40 19 w w NOUN cana-733 40 20 - - PUNCT cana-733 40 21 algebras algebras NOUN cana-733 40 22 . . PUNCT cana-733 41 1 definition definition NOUN cana-733 41 2 3.1 3.1 NUM cana-733 41 3 . . PUNCT cana-733 42 1 let let AUX cana-733 42 2 ( ( PUNCT cana-733 42 3 ๏ฟฝ ๏ฟฝ NOUN cana-733 42 4 ฬŒ ฬŒ NUM cana-733 42 5 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 6 , , PUNCT cana-733 42 7 ๐ผ ๐ผ PROPN cana-733 42 8 ) ) PUNCT cana-733 42 9 be be VERB cana-733 42 10 a a DET cana-733 42 11 fs fs NOUN cana-733 42 12 - - PUNCT cana-733 42 13 set set NOUN cana-733 42 14 over over ADP cana-733 42 15 a a DET cana-733 42 16 w w NOUN cana-733 42 17 - - PUNCT cana-733 42 18 algebra algebra NOUN cana-733 42 19 ๐’ณ ๐’ณ PROPN cana-733 42 20 , , PUNCT cana-733 42 21 because because SCONJ cana-733 42 22 ๐ผ ๐ผ PROPN cana-733 42 23 is be AUX cana-733 42 24 a a DET cana-733 42 25 subset subset NOUN cana-733 42 26 of of ADP cana-733 42 27 ๐’ฆ. ๐’ฆ. PROPN cana-733 42 28 we we PRON cana-733 42 29 say say VERB cana-733 42 30 that that SCONJ cana-733 42 31 ( ( PUNCT cana-733 42 32 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 33 ฬŒ ฬŒ NUM cana-733 42 34 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 35 , , PUNCT cana-733 42 36 ๐ผ ๐ผ PROPN cana-733 42 37 ) ) PUNCT cana-733 42 38 is be AUX cana-733 42 39 a a DET cana-733 42 40 fs fs ADJ cana-733 42 41 - - PUNCT cana-733 42 42 set set ADJ cana-733 42 43 set set NOUN cana-733 42 44 on on ADP cana-733 42 45 โ„ณ โ„ณ PROPN cana-733 42 46 over over ADP cana-733 42 47 ๐’ณ ๐’ณ PROPN cana-733 42 48 , , PUNCT cana-733 42 49 if if SCONJ cana-733 42 50 there there PRON cana-733 42 51 exist exist VERB cana-733 42 52 ๐“‚ ๐“‚ NOUN cana-733 42 53 โˆˆ โˆˆ PROPN cana-733 42 54 ๐ผ ๐ผ ADP cana-733 42 55 such such ADJ cana-733 42 56 that that PRON cana-733 42 57 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 58 ฬŒ ฬŒ NUM cana-733 42 59 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 60 (๐“‚ (๐“‚ PROPN cana-733 42 61 ) ) PUNCT cana-733 42 62 is be AUX cana-733 42 63 a a DET cana-733 42 64 fuzzy fuzzy ADJ cana-733 42 65 w w NOUN cana-733 42 66 - - NOUN cana-733 42 67 algebra algebra NOUN cana-733 42 68 in in ADP cana-733 42 69 ๐’ณ. ๐’ณ. PROPN cana-733 42 70 it it PRON cana-733 42 71 may may AUX cana-733 42 72 be be AUX cana-733 42 73 stated state VERB cana-733 42 74 that that SCONJ cana-733 42 75 ( ( PUNCT cana-733 42 76 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 77 ฬŒ ฬŒ NUM cana-733 42 78 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 79 , , PUNCT cana-733 42 80 ๐ผ ๐ผ PROPN cana-733 42 81 ) ) PUNCT cana-733 42 82 is be AUX cana-733 42 83 a a DET cana-733 42 84 fs fs PROPN cana-733 42 85 - - PUNCT cana-733 42 86 w w NOUN cana-733 42 87 - - PUNCT cana-733 42 88 algebra algebra NOUN cana-733 42 89 over over ADP cana-733 42 90 ๐’ณ. ๐’ณ. PROPN cana-733 42 91 if if SCONJ cana-733 42 92 ( ( PUNCT cana-733 42 93 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 94 ฬŒ ฬŒ NUM cana-733 42 95 ๏ฟฝ ๏ฟฝ PROPN cana-733 42 96 , , PUNCT cana-733 42 97 ๐ผ ๐ผ PROPN cana-733 42 98 ) ) PUNCT cana-733 42 99 is be AUX cana-733 42 100 based base VERB cana-733 42 101 on on ADP cana-733 42 102 parameter parameter PROPN cana-733 42 103 ๐“‚ ๐“‚ PROPN cana-733 42 104 over over ADP cana-733 42 105 ๐’ณ ๐’ณ PROPN cana-733 42 106 for for ADP cana-733 42 107 all all DET cana-733 42 108 ๐“‚ ๐“‚ PROPN cana-733 42 109 โˆˆ โˆˆ PROPN cana-733 42 110 ๐ผ. ๐ผ. PROPN cana-733 42 111 example example NOUN cana-733 42 112 3.2 3.2 NUM cana-733 42 113 . . PUNCT cana-733 43 1 assuming assume VERB cana-733 43 2 the the DET cana-733 43 3 universe universe ADJ cana-733 43 4 โ„ณ โ„ณ NOUN cana-733 43 5 has have VERB cana-733 43 6 five five NUM cana-733 43 7 colours colour NOUN cana-733 43 8 , , PUNCT cana-733 43 9 that that PRON cana-733 43 10 is be AUX cana-733 43 11 โ„ณ โ„ณ PROPN cana-733 43 12 = = SYM cana-733 43 13 { { PUNCT cana-733 43 14 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 43 15 , , PUNCT cana-733 43 16 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 43 17 , , PUNCT cana-733 43 18 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 43 19 , , PUNCT cana-733 43 20 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 43 21 , , PUNCT cana-733 43 22 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 43 23 } } PUNCT cana-733 43 24 . . PUNCT cana-733 44 1 assume assume VERB cana-733 44 2 the the DET cana-733 44 3 role role NOUN cana-733 44 4 of of ADP cana-733 44 5 โŠ› โŠ› NUM cana-733 44 6 a a DET cana-733 44 7 soft soft ADJ cana-733 44 8 engine engine NOUN cana-733 44 9 that that PRON cana-733 44 10 combines combine VERB cana-733 44 11 two two NUM cana-733 44 12 colours colour NOUN cana-733 44 13 in in ADP cana-733 44 14 the the DET cana-733 44 15 prescribed prescribed ADJ cana-733 44 16 order order NOUN cana-733 44 17 to to PART cana-733 44 18 get get VERB cana-733 44 19 the the DET cana-733 44 20 desired desire VERB cana-733 44 21 results result NOUN cana-733 44 22 . . PUNCT cana-733 45 1 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ NOUN cana-733 45 2 โŠ› โŠ› NUM cana-733 45 3 ๐œš ๐œš NOUN cana-733 45 4 = = SYM cana-733 45 5 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 6 for for SCONJ cana-733 45 7 all all PRON cana-733 45 8 ๐œš ๐œš PRON cana-733 45 9 โˆˆ โˆˆ NOUN cana-733 45 10 โ„ณ โ„ณ NOUN cana-733 45 11 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ VERB cana-733 45 12 โŠ› โŠ› ADV cana-733 45 13 ๐œ ๐œ PART cana-733 45 14 = = SYM cana-733 45 15 { { PUNCT cana-733 45 16 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 17 โˆถ โˆถ NOUN cana-733 45 18 ๐œ ๐œ ADP cana-733 45 19 โˆˆ โˆˆ PROPN cana-733 45 20 { { PUNCT cana-733 45 21 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 45 22 , , PUNCT cana-733 45 23 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 24 , , PUNCT cana-733 45 25 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 45 26 } } PUNCT cana-733 45 27 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ VERB cana-733 45 28 โˆถ โˆถ ADV cana-733 45 29 ๐œ ๐œ ADP cana-733 45 30 โˆˆ โˆˆ PROPN cana-733 45 31 { { PUNCT cana-733 45 32 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ NOUN cana-733 45 33 , , PUNCT cana-733 45 34 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 45 35 } } PUNCT cana-733 45 36 } } PUNCT cana-733 45 37 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 45 38 โŠ› โŠ› NUM cana-733 45 39 ๐‘ง ๐‘ง X cana-733 45 40 = = PRON cana-733 45 41 { { PUNCT cana-733 45 42 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 43 โˆถ โˆถ NOUN cana-733 45 44 ๐‘ง ๐‘ง PRON cana-733 45 45 โˆˆ โˆˆ PROPN cana-733 45 46 { { PUNCT cana-733 45 47 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 45 48 , , PUNCT cana-733 45 49 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 45 50 } } PUNCT cana-733 45 51 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ VERB cana-733 45 52 โˆถ โˆถ PROPN cana-733 45 53 ๐‘ง ๐‘ง PRON cana-733 45 54 โˆˆ โˆˆ PROPN cana-733 45 55 { { PUNCT cana-733 45 56 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 57 , , PUNCT cana-733 45 58 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 45 59 , , PUNCT cana-733 45 60 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 61 } } PUNCT cana-733 45 62 } } PUNCT cana-733 45 63 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 64 โŠ› โŠ› NUM cana-733 45 65 ๐‘ข ๐‘ข X cana-733 45 66 = = SYM cana-733 45 67 { { PUNCT cana-733 45 68 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 69 โˆถ โˆถ PROPN cana-733 45 70 ๐‘ข ๐‘ข X cana-733 45 71 โˆˆ โˆˆ PROPN cana-733 45 72 { { PUNCT cana-733 45 73 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 74 , , PUNCT cana-733 45 75 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 45 76 } } PUNCT cana-733 45 77 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 78 โˆถ โˆถ NOUN cana-733 45 79 ๐‘ข ๐‘ข ADP cana-733 45 80 โˆˆ โˆˆ PROPN cana-733 45 81 { { PUNCT cana-733 45 82 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 83 , , PUNCT cana-733 45 84 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 45 85 , , PUNCT cana-733 45 86 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 45 87 } } PUNCT cana-733 45 88 } } PUNCT cana-733 45 89 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 45 90 โŠ› โŠ› ADJ cana-733 45 91 ๐‘ฃ ๐‘ฃ PART cana-733 45 92 = = SYM cana-733 45 93 { { PUNCT cana-733 45 94 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 45 95 โˆถ โˆถ NOUN cana-733 45 96 ๐‘ฃ ๐‘ฃ ADP cana-733 45 97 = = NOUN cana-733 45 98 ๐‘ก๐‘Ž ๐‘ก๐‘Ž ADP cana-733 45 99 ๐‘› ๐‘› DET cana-733 45 100 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 45 101 โˆถ โˆถ NOUN cana-733 45 102 ๐‘ฃ ๐‘ฃ ADP cana-733 45 103 = = PUNCT cana-733 45 104 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 105 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 45 106 โˆถ โˆถ NOUN cana-733 45 107 ๐‘ฃ ๐‘ฃ ADP cana-733 45 108 = = PUNCT cana-733 45 109 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 45 110 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 46 1 โˆถ โˆถ VERB cana-733 46 2 ๐‘ฃ ๐‘ฃ ADP cana-733 46 3 = = PUNCT cana-733 46 4 { { PUNCT cana-733 46 5 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ ADJ cana-733 46 6 , , PUNCT cana-733 46 7 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 46 8 } } PUNCT cana-733 46 9 } } PUNCT cana-733 46 10 then then ADV cana-733 46 11 ( ( PUNCT cana-733 46 12 โ„ณ,โŠ›,๐‘๐‘–๐‘›๐‘˜ โ„ณ,โŠ›,๐‘๐‘–๐‘›๐‘˜ NOUN cana-733 46 13 ) ) PUNCT cana-733 46 14 is be AUX cana-733 46 15 a a DET cana-733 46 16 w w NOUN cana-733 46 17 - - PUNCT cana-733 46 18 algebra algebra NOUN cana-733 46 19 . . PUNCT cana-733 47 1 communications communication NOUN cana-733 47 2 on on ADP cana-733 47 3 applied apply VERB cana-733 47 4 nonlinear nonlinear ADJ cana-733 47 5 analysis analysis NOUN cana-733 47 6 issn issn NOUN cana-733 47 7 : : PUNCT cana-733 47 8 1074 1074 NUM cana-733 47 9 - - PUNCT cana-733 47 10 133x 133x NUM cana-733 47 11 vol vol NOUN cana-733 47 12 31 31 NUM cana-733 47 13 no no NOUN cana-733 47 14 . . PUNCT cana-733 48 1 3s 3s NUM cana-733 48 2 ( ( PUNCT cana-733 48 3 2024 2024 NUM cana-733 48 4 ) ) PUNCT cana-733 48 5 84 84 NUM cana-733 48 6 https://internationalpubls.com https://internationalpubls.com X cana-733 48 7 ( ( PUNCT cana-733 48 8 i i NOUN cana-733 48 9 ) ) PUNCT cana-733 48 10 let let AUX cana-733 48 11 ( ( PUNCT cana-733 48 12 ๏ฟฝ ๏ฟฝ NOUN cana-733 48 13 ฬŒ ฬŒ NUM cana-733 48 14 ๏ฟฝ ๏ฟฝ NOUN cana-733 48 15 ,๐’ฆ ,๐’ฆ PUNCT cana-733 48 16 ) ) PUNCT cana-733 48 17 be be AUX cana-733 48 18 a a DET cana-733 48 19 fs fs NOUN cana-733 48 20 - - PUNCT cana-733 48 21 set set VERB cana-733 48 22 over over ADP cana-733 48 23 โ„ณ โ„ณ PROPN cana-733 48 24 , , PUNCT cana-733 48 25 then then ADV cana-733 48 26 ๏ฟฝ ๏ฟฝ PROPN cana-733 48 27 ฬŒ ฬŒ NUM cana-733 48 28 ๏ฟฝ ๏ฟฝ PROPN cana-733 48 29 [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  X cana-733 48 30 ] ] X cana-733 48 31 , , PUNCT cana-733 48 32 ๏ฟฝ ๏ฟฝ PROPN cana-733 48 33 ฬŒ ฬŒ NUM cana-733 48 34 ๏ฟฝ ๏ฟฝ NOUN cana-733 48 35 [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก X cana-733 48 36 ] ] PUNCT cana-733 48 37 & & CCONJ cana-733 48 38 ๏ฟฝ ๏ฟฝ PROPN cana-733 48 39 ฬŒ ฬŒ NUM cana-733 48 40 ๏ฟฝ ๏ฟฝ PROPN cana-733 48 41 [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก X cana-733 48 42 ] ] X cana-733 48 43 are be AUX cana-733 48 44 fuzzy fuzzy ADJ cana-733 48 45 sets set NOUN cana-733 48 46 in in ADP cana-733 48 47 โ„ณ. โ„ณ. PROPN cana-733 48 48 here here ADV cana-733 48 49 is be AUX cana-733 48 50 how how SCONJ cana-733 48 51 we we PRON cana-733 48 52 define define VERB cana-733 48 53 them they PRON cana-733 49 1 : : PUNCT cana-733 49 2 ๏ฟฝ ๏ฟฝ PROPN cana-733 49 3 ฬŒ ฬŒ NUM cana-733 49 4 ๏ฟฝ ๏ฟฝ PROPN cana-733 49 5 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 49 6 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 49 7 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ PROPN cana-733 49 8 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ PROPN cana-733 49 9 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 49 10 ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  NOUN cana-733 49 11 0.7 0.7 NUM cana-733 49 12 0.7 0.7 NUM cana-733 49 13 0.7 0.7 NUM cana-733 49 14 0.4 0.4 NUM cana-733 49 15 0.4 0.4 NUM cana-733 49 16 ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก NOUN cana-733 49 17 0.8 0.8 NUM cana-733 49 18 0.7 0.7 NUM cana-733 49 19 0.4 0.4 NUM cana-733 49 20 0.6 0.6 NUM cana-733 49 21 0.4 0.4 NUM cana-733 49 22 ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก NOUN cana-733 49 23 0.6 0.6 NUM cana-733 49 24 0.2 0.2 NUM cana-733 49 25 0.5 0.5 NUM cana-733 49 26 0.2 0.2 NUM cana-733 49 27 0.2 0.2 NUM cana-733 49 28 then then ADV cana-733 49 29 , , PUNCT cana-733 49 30 fs f NOUN cana-733 49 31 - - PUNCT cana-733 49 32 sets set VERB cana-733 49 33 w w NOUN cana-733 49 34 - - PUNCT cana-733 49 35 algebras algebra VERB cana-733 49 36 ๏ฟฝ ๏ฟฝ PROPN cana-733 49 37 ฬŒ ฬŒ NUM cana-733 49 38 ๏ฟฝ ๏ฟฝ NOUN cana-733 49 39 [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  X cana-733 49 40 ] ] X cana-733 49 41 , , PUNCT cana-733 49 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 49 43 ฬŒ ฬŒ NUM cana-733 49 44 ๏ฟฝ ๏ฟฝ NOUN cana-733 49 45 [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก X cana-733 49 46 ] ] PUNCT cana-733 49 47 and and CCONJ cana-733 49 48 ๏ฟฝ ๏ฟฝ PROPN cana-733 49 49 ฬŒ ฬŒ NUM cana-733 49 50 ๏ฟฝ ๏ฟฝ PROPN cana-733 49 51 [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก X cana-733 49 52 ] ] X cana-733 49 53 are be AUX cana-733 49 54 based base VERB cana-733 49 55 on on ADP cana-733 49 56 parameters parameter NOUN cana-733 49 57 โ€œ " PUNCT cana-733 49 58 ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  NOUN cana-733 49 59 โ€ " PUNCT cana-733 49 60 , , PUNCT cana-733 49 61 โ€œ " PUNCT cana-733 49 62 ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก NOUN cana-733 49 63 โ€ " PUNCT cana-733 49 64 and and CCONJ cana-733 49 65 โ€œ " PUNCT cana-733 49 66 ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก NOUN cana-733 49 67 โ€ " PUNCT cana-733 49 68 over over ADP cana-733 49 69 โ„ณ โ„ณ PROPN cana-733 49 70 , , PUNCT cana-733 49 71 respectively respectively ADV cana-733 49 72 . . PUNCT cana-733 50 1 thus thus ADV cana-733 50 2 , , PUNCT cana-733 50 3 ( ( PUNCT cana-733 50 4 ๏ฟฝ ๏ฟฝ PROPN cana-733 50 5 ฬŒ ฬŒ NUM cana-733 50 6 ๏ฟฝ ๏ฟฝ NOUN cana-733 50 7 ,๐’ฆ ,๐’ฆ PUNCT cana-733 50 8 ) ) PUNCT cana-733 50 9 is be AUX cana-733 50 10 a a DET cana-733 50 11 fs fs PROPN cana-733 50 12 - - PUNCT cana-733 50 13 w w NOUN cana-733 50 14 - - PUNCT cana-733 50 15 algebras algebras ADJ cana-733 50 16 over over ADP cana-733 50 17 โ„ณ. โ„ณ. PROPN cana-733 50 18 ( ( PUNCT cana-733 50 19 ii ii NOUN cana-733 50 20 ) ) PUNCT cana-733 50 21 ๏ฟฝ ๏ฟฝ PROPN cana-733 50 22 ฬŒ ฬŒ NUM cana-733 50 23 ๏ฟฝ ๏ฟฝ NOUN cana-733 50 24 [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  X cana-733 50 25 ] ] X cana-733 50 26 , , PUNCT cana-733 50 27 ๏ฟฝ ๏ฟฝ PROPN cana-733 50 28 ฬŒ ฬŒ NUM cana-733 50 29 ๏ฟฝ ๏ฟฝ NOUN cana-733 50 30 [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก X cana-733 50 31 ] ] PUNCT cana-733 50 32 and and CCONJ cana-733 50 33 ๏ฟฝ ๏ฟฝ PROPN cana-733 50 34 ฬŒ ฬŒ NUM cana-733 50 35 ๏ฟฝ ๏ฟฝ PROPN cana-733 50 36 [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก X cana-733 50 37 ] ] X cana-733 50 38 are be AUX cana-733 50 39 fuzzy fuzzy ADJ cana-733 50 40 sets set NOUN cana-733 50 41 in in ADP cana-733 50 42 โ„ณ. โ„ณ. PROPN cana-733 50 43 let let VERB cana-733 50 44 ( ( PUNCT cana-733 50 45 ๏ฟฝ ๏ฟฝ NOUN cana-733 50 46 ฬŒ ฬŒ NUM cana-733 50 47 ๏ฟฝ ๏ฟฝ NOUN cana-733 50 48 ,๐’ฆ ,๐’ฆ PUNCT cana-733 50 49 ) ) PUNCT cana-733 50 50 be be AUX cana-733 50 51 fs fs PROPN cana-733 50 52 - - PUNCT cana-733 50 53 set set VERB cana-733 50 54 over over ADP cana-733 50 55 โ„ณ. โ„ณ. PROPN cana-733 50 56 we we PRON cana-733 50 57 define define VERB cana-733 50 58 them they PRON cana-733 50 59 as as SCONJ cana-733 50 60 listed list VERB cana-733 50 61 below below ADV cana-733 50 62 , , PUNCT cana-733 51 1 ๏ฟฝ ๏ฟฝ PROPN cana-733 51 2 ฬŒ ฬŒ NUM cana-733 51 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 51 4 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 51 5 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 51 6 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ PROPN cana-733 51 7 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ PROPN cana-733 51 8 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 51 9 ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  NOUN cana-733 51 10 0.8 0.8 NUM cana-733 51 11 0.8 0.8 NUM cana-733 51 12 0.8 0.8 NUM cana-733 51 13 0.8 0.8 NUM cana-733 51 14 0.8 0.8 NUM cana-733 51 15 e๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก e๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก NOUN cana-733 51 16 0.4 0.4 NUM cana-733 51 17 0.6 0.6 NUM cana-733 51 18 0.5 0.5 NUM cana-733 51 19 0.5 0.5 NUM cana-733 51 20 0.3 0.3 NUM cana-733 51 21 ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก NOUN cana-733 51 22 0.9 0.9 NUM cana-733 51 23 0.1 0.1 NUM cana-733 51 24 0.7 0.7 NUM cana-733 51 25 0.1 0.1 NUM cana-733 51 26 0.1 0.1 NUM cana-733 51 27 ( ( PUNCT cana-733 51 28 ๏ฟฝ ๏ฟฝ PROPN cana-733 51 29 ฬŒ ฬŒ NUM cana-733 51 30 ๏ฟฝ ๏ฟฝ NOUN cana-733 51 31 ,๐’ฆ ,๐’ฆ PUNCT cana-733 51 32 ) ) PUNCT cana-733 51 33 is be AUX cana-733 51 34 not not PART cana-733 51 35 a a DET cana-733 51 36 fs fs PROPN cana-733 51 37 - - PUNCT cana-733 51 38 w w NOUN cana-733 51 39 - - PUNCT cana-733 51 40 algebras algebras ADJ cana-733 51 41 over over ADP cana-733 51 42 โ„ณ. โ„ณ. PROPN cana-733 51 43 as as ADP cana-733 51 44 ( ( PUNCT cana-733 51 45 ๏ฟฝ ๏ฟฝ PROPN cana-733 51 46 ฬŒ ฬŒ NUM cana-733 51 47 ๏ฟฝ ๏ฟฝ NOUN cana-733 51 48 ,๐’ฆ ,๐’ฆ PUNCT cana-733 51 49 ) ) PUNCT cana-733 51 50 is be AUX cana-733 51 51 not not PART cana-733 51 52 a a DET cana-733 51 53 fs fs PROPN cana-733 51 54 - - PUNCT cana-733 51 55 w w NOUN cana-733 51 56 - - PUNCT cana-733 51 57 algebras algebras X cana-733 51 58 . . PUNCT cana-733 52 1 it it PRON cana-733 52 2 is be AUX cana-733 52 3 based base VERB cana-733 52 4 on on ADP cana-733 52 5 a a DET cana-733 52 6 parameter parameter NOUN cana-733 52 7 โ€œ " PUNCT cana-733 52 8 elegent elegent ADJ cana-733 52 9 โ€ " PUNCT cana-733 52 10 over over ADP cana-733 52 11 โ„ณ. โ„ณ. PROPN cana-733 52 12 infect infect VERB cana-733 52 13 ๏ฟฝ ๏ฟฝ PROPN cana-733 52 14 ฬŒ ฬŒ NUM cana-733 52 15 ๏ฟฝ ๏ฟฝ NOUN cana-733 52 16 [elegent [elegent NOUN cana-733 52 17 ] ] X cana-733 52 18 ( ( PUNCT cana-733 52 19 gray gray ADJ cana-733 52 20 โŠ› โŠ› ADJ cana-733 52 21 olive olive NOUN cana-733 52 22 ) ) PUNCT cana-733 52 23 = = SYM cana-733 52 24 ๏ฟฝ ๏ฟฝ PROPN cana-733 52 25 ฬŒ ฬŒ NUM cana-733 52 26 ๏ฟฝ ๏ฟฝ NOUN cana-733 52 27 [elegent [elegent NOUN cana-733 52 28 ] ] X cana-733 52 29 ( ( PUNCT cana-733 52 30 pink pink ADJ cana-733 52 31 ) ) PUNCT cana-733 52 32 = = SYM cana-733 52 33 0.4 0.4 NUM cana-733 52 34 โ‰ฑ โ‰ฑ PROPN cana-733 52 35 0.5 0.5 NUM cana-733 52 36 = = SYM cana-733 52 37 min min PROPN cana-733 52 38 { { PUNCT cana-733 52 39 ๏ฟฝ ๏ฟฝ PROPN cana-733 52 40 ฬŒ ฬŒ NUM cana-733 52 41 ๏ฟฝ ๏ฟฝ NOUN cana-733 52 42 [elegent](gray [elegent](gray NOUN cana-733 52 43 ) ) PUNCT cana-733 52 44 , , PUNCT cana-733 52 45 ๏ฟฝ ๏ฟฝ PROPN cana-733 52 46 ฬŒ ฬŒ NUM cana-733 52 47 ๏ฟฝ ๏ฟฝ NOUN cana-733 52 48 [elegent [elegent NOUN cana-733 52 49 ] ] X cana-733 52 50 ( ( PUNCT cana-733 52 51 olive olive NOUN cana-733 52 52 ) ) PUNCT cana-733 52 53 } } PUNCT cana-733 52 54 a a DET cana-733 52 55 fs fs PROPN cana-733 52 56 - - PUNCT cana-733 52 57 w w NOUN cana-733 52 58 - - PUNCT cana-733 52 59 algebras algebras NOUN cana-733 52 60 based base VERB cana-733 52 61 on on ADP cana-733 52 62 both both CCONJ cana-733 52 63 a a DET cana-733 52 64 parameter parameter NOUN cana-733 52 65 โ€œ " PUNCT cana-733 52 66 glorious glorious ADJ cana-733 52 67 โ€ " PUNCT cana-733 52 68 and and CCONJ cana-733 52 69 a a DET cana-733 52 70 parameter parameter NOUN cana-733 52 71 โ€œ " PUNCT cana-733 52 72 modest modest ADJ cana-733 52 73 โ€ " PUNCT cana-733 52 74 over over ADP cana-733 52 75 โ„ณ โ„ณ PROPN cana-733 52 76 , , PUNCT cana-733 52 77 we we PRON cana-733 52 78 are be AUX cana-733 52 79 able able ADJ cana-733 52 80 to to PART cana-733 52 81 confirm confirm VERB cana-733 52 82 that( that( PROPN cana-733 52 83 ๏ฟฝ ๏ฟฝ PROPN cana-733 52 84 ฬŒ ฬŒ NUM cana-733 52 85 ๏ฟฝ ๏ฟฝ NOUN cana-733 52 86 ,๐’ฆ ,๐’ฆ PUNCT cana-733 52 87 ) ) PUNCT cana-733 52 88 . . PUNCT cana-733 53 1 example example NOUN cana-733 53 2 3.3 3.3 NUM cana-733 53 3 : : PUNCT cana-733 53 4 think think VERB cana-733 53 5 about about ADP cana-733 53 6 the the DET cana-733 53 7 universe universe ADJ cana-733 53 8 โ„ณ โ„ณ NOUN cana-733 53 9 = = PUNCT cana-733 53 10 { { PUNCT cana-733 53 11 pink pink ADJ cana-733 53 12 , , PUNCT cana-733 53 13 gray gray ADJ cana-733 53 14 , , PUNCT cana-733 53 15 red red ADJ cana-733 53 16 , , PUNCT cana-733 53 17 olive olive NOUN cana-733 53 18 , , PUNCT cana-733 53 19 tan tan PROPN cana-733 53 20 } } PUNCT cana-733 53 21 and and CCONJ cana-733 53 22 examine examine VERB cana-733 53 23 the the DET cana-733 53 24 soft soft ADJ cana-733 53 25 engine engine NOUN cana-733 53 26 โ—ฌ โ—ฌ NOUN cana-733 53 27 that that PRON cana-733 53 28 generates generate VERB cana-733 53 29 the the DET cana-733 53 30 products product NOUN cana-733 53 31 listed list VERB cana-733 53 32 below below ADP cana-733 53 33 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ ADJ cana-733 53 34 โ—ฌ โ—ฌ PROPN cana-733 54 1 ๐œš ๐œš NOUN cana-733 54 2 = = SYM cana-733 54 3 { { PUNCT cana-733 54 4 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 54 5 โˆถ โˆถ NOUN cana-733 54 6 ๐œš ๐œš X cana-733 54 7 โˆˆ โˆˆ PROPN cana-733 54 8 { { PUNCT cana-733 54 9 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ NOUN cana-733 54 10 , , PUNCT cana-733 54 11 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 54 12 , , PUNCT cana-733 54 13 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 54 14 } } PUNCT cana-733 54 15 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 54 16 โˆถ โˆถ NOUN cana-733 54 17 ๐œš ๐œš X cana-733 54 18 โˆˆ โˆˆ NOUN cana-733 54 19 { { PUNCT cana-733 54 20 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 54 21 , , PUNCT cana-733 54 22 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 54 23 } } PUNCT cana-733 54 24 } } PUNCT cana-733 54 25 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ VERB cana-733 54 26 โ—ฌ โ—ฌ ADJ cana-733 54 27 ๐œ ๐œ X cana-733 54 28 = = SYM cana-733 54 29 { { PUNCT cana-733 54 30 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 54 31 โˆถ โˆถ NOUN cana-733 54 32 ๐œ ๐œ X cana-733 54 33 = = SYM cana-733 54 34 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 54 35 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 54 36 โˆถ โˆถ NOUN cana-733 54 37 ๐œ ๐œ ADP cana-733 54 38 = = SYM cana-733 54 39 { { PUNCT cana-733 54 40 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ ADJ cana-733 54 41 , , PUNCT cana-733 54 42 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 54 43 } } PUNCT cana-733 54 44 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 54 45 โˆถ โˆถ NOUN cana-733 54 46 ๐œ ๐œ ADP cana-733 54 47 = = NOUN cana-733 54 48 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 55 1 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 55 2 โˆถ โˆถ VERB cana-733 55 3 ๐œ ๐œ ADP cana-733 55 4 = = SYM cana-733 55 5 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 55 6 } } PUNCT cana-733 55 7 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ VERB cana-733 55 8 โ—ฌ โ—ฌ ADJ cana-733 55 9 ๐‘ง ๐‘ง X cana-733 55 10 = = X cana-733 55 11 { { PUNCT cana-733 55 12 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 55 13 โˆถ โˆถ NOUN cana-733 55 14 ๐‘ง ๐‘ง X cana-733 55 15 = = SYM cana-733 55 16 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 55 17 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 55 18 โˆถ โˆถ PROPN cana-733 55 19 ๐‘ง ๐‘ง PRON cana-733 55 20 โˆˆ โˆˆ PROPN cana-733 55 21 { { PUNCT cana-733 55 22 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ ADJ cana-733 55 23 , , PUNCT cana-733 55 24 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 55 25 } } PUNCT cana-733 55 26 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 55 27 โˆถ โˆถ NOUN cana-733 55 28 ๐‘ง ๐‘ง PRON cana-733 55 29 โˆˆ โˆˆ PROPN cana-733 55 30 { { PUNCT cana-733 55 31 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 55 32 , , PUNCT cana-733 55 33 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 55 34 } } PUNCT cana-733 55 35 } } PUNCT cana-733 55 36 communications communication NOUN cana-733 55 37 on on ADP cana-733 55 38 applied apply VERB cana-733 55 39 nonlinear nonlinear ADJ cana-733 55 40 analysis analysis NOUN cana-733 55 41 issn issn NOUN cana-733 55 42 : : PUNCT cana-733 55 43 1074 1074 NUM cana-733 55 44 - - PUNCT cana-733 55 45 133x 133x NUM cana-733 55 46 vol vol NOUN cana-733 55 47 31 31 NUM cana-733 55 48 no no NOUN cana-733 55 49 . . PUNCT cana-733 56 1 3s 3s NUM cana-733 56 2 ( ( PUNCT cana-733 56 3 2024 2024 NUM cana-733 56 4 ) ) PUNCT cana-733 56 5 85 85 NUM cana-733 56 6 https://internationalpubls.com https://internationalpubls.com X cana-733 56 7 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 56 8 โ—ฌ โ—ฌ ADJ cana-733 56 9 ๐‘ข ๐‘ข X cana-733 56 10 = = PUNCT cana-733 56 11 { { PUNCT cana-733 56 12 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 56 13 โˆถ โˆถ PROPN cana-733 56 14 ๐‘ข ๐‘ข X cana-733 56 15 โˆˆ โˆˆ PROPN cana-733 56 16 { { PUNCT cana-733 56 17 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 56 18 , , PUNCT cana-733 56 19 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 56 20 } } PUNCT cana-733 56 21 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 56 22 โˆถ โˆถ NOUN cana-733 56 23 ๐‘ข ๐‘ข ADP cana-733 56 24 โˆˆ โˆˆ PROPN cana-733 56 25 { { PUNCT cana-733 56 26 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 56 27 , , PUNCT cana-733 56 28 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ADJ cana-733 56 29 , , PUNCT cana-733 56 30 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 56 31 } } PUNCT cana-733 56 32 } } PUNCT cana-733 56 33 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› PUNCT cana-733 57 1 โ—ฌ โ—ฌ ADJ cana-733 57 2 ๐‘ฃ ๐‘ฃ ADP cana-733 57 3 = = SYM cana-733 57 4 { { PUNCT cana-733 57 5 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 57 6 โˆถ โˆถ NOUN cana-733 57 7 ๐‘ฃ ๐‘ฃ ADP cana-733 57 8 = = PUNCT cana-733 57 9 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 57 10 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ VERB cana-733 57 11 โˆถ โˆถ PROPN cana-733 57 12 ๐‘ฃ ๐‘ฃ ADP cana-733 57 13 = = PUNCT cana-733 57 14 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 57 15 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ NOUN cana-733 57 16 โˆถ โˆถ NOUN cana-733 57 17 ๐‘ฃ ๐‘ฃ PRON cana-733 57 18 = = PUNCT cana-733 57 19 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ VERB cana-733 57 20 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› PUNCT cana-733 58 1 โˆถ โˆถ VERB cana-733 58 2 ๐‘ฃ ๐‘ฃ ADP cana-733 58 3 = = PUNCT cana-733 58 4 { { PUNCT cana-733 58 5 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ ADJ cana-733 58 6 , , PUNCT cana-733 58 7 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ NOUN cana-733 58 8 } } PUNCT cana-733 58 9 } } PUNCT cana-733 58 10 then then ADV cana-733 58 11 ( ( PUNCT cana-733 58 12 โ„ณ โ„ณ NOUN cana-733 58 13 , , PUNCT cana-733 58 14 โ—ฌ โ—ฌ ADJ cana-733 58 15 , , PUNCT cana-733 58 16 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ NOUN cana-733 58 17 ) ) PUNCT cana-733 58 18 is be AUX cana-733 58 19 a a DET cana-733 58 20 w w NOUN cana-733 58 21 - - NOUN cana-733 58 22 algebra algebra NOUN cana-733 58 23 . . PUNCT cana-733 59 1 ๐’ฆ ๐’ฆ NOUN cana-733 59 2 = = SYM cana-733 59 3 { { PUNCT cana-733 59 4 ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  NOUN cana-733 59 5 , , PUNCT cana-733 59 6 ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก,๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก,๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก NOUN cana-733 59 7 } } PUNCT cana-733 59 8 . . PUNCT cana-733 60 1 let let AUX cana-733 60 2 ( ( PUNCT cana-733 60 3 ๏ฟฝ ๏ฟฝ NOUN cana-733 60 4 ฬŒ ฬŒ NUM cana-733 60 5 ๏ฟฝ ๏ฟฝ NOUN cana-733 60 6 ,๐’ฆ ,๐’ฆ PUNCT cana-733 60 7 ) ) PUNCT cana-733 60 8 be be AUX cana-733 60 9 a a DET cana-733 60 10 fs fs NOUN cana-733 60 11 - - PUNCT cana-733 60 12 set set VERB cana-733 60 13 over over ADP cana-733 60 14 โ„ณ โ„ณ PROPN cana-733 60 15 , , PUNCT cana-733 60 16 then then ADV cana-733 60 17 ๏ฟฝ ๏ฟฝ PROPN cana-733 60 18 ฬŒ ฬŒ NUM cana-733 60 19 ๏ฟฝ ๏ฟฝ PROPN cana-733 60 20 [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  [๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  X cana-733 60 21 ] ] X cana-733 60 22 , , PUNCT cana-733 60 23 ๏ฟฝ ๏ฟฝ PROPN cana-733 60 24 ฬŒ ฬŒ NUM cana-733 60 25 ๏ฟฝ ๏ฟฝ NOUN cana-733 60 26 [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก [๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก X cana-733 60 27 ] ] PUNCT cana-733 60 28 & & CCONJ cana-733 60 29 ๏ฟฝ ๏ฟฝ PROPN cana-733 60 30 ฬŒ ฬŒ NUM cana-733 60 31 ๏ฟฝ ๏ฟฝ PROPN cana-733 60 32 [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก [๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก X cana-733 60 33 ] ] X cana-733 60 34 are be AUX cana-733 60 35 fuzzy fuzzy ADJ cana-733 60 36 sets set NOUN cana-733 60 37 in in ADP cana-733 60 38 โ„ณ. โ„ณ. PROPN cana-733 60 39 we we PRON cana-733 60 40 define define VERB cana-733 60 41 , , PUNCT cana-733 61 1 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 2 ฬŒ ฬŒ NUM cana-733 61 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 4 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 61 5 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 61 6 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ PROPN cana-733 61 7 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ PROPN cana-733 61 8 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 61 9 ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  NOUN cana-733 61 10 0.9 0.9 NUM cana-733 61 11 0.6 0.6 NUM cana-733 61 12 0.2 0.2 NUM cana-733 61 13 0.1 0.1 NUM cana-733 61 14 0.1 0.1 NUM cana-733 61 15 ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก NOUN cana-733 61 16 0.6 0.6 NUM cana-733 61 17 0.4 0.4 NUM cana-733 61 18 0.6 0.6 NUM cana-733 61 19 0.5 0.5 NUM cana-733 61 20 0.4 0.4 NUM cana-733 61 21 ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก NOUN cana-733 61 22 0.7 0.7 NUM cana-733 61 23 0.1 0.1 NUM cana-733 61 24 0.5 0.5 NUM cana-733 61 25 0.4 0.4 NUM cana-733 61 26 0.1 0.1 NUM cana-733 61 27 then then ADV cana-733 61 28 ( ( PUNCT cana-733 61 29 ๏ฟฝ ๏ฟฝ NOUN cana-733 61 30 ฬŒ ฬŒ NUM cana-733 61 31 ๏ฟฝ ๏ฟฝ NOUN cana-733 61 32 ,๐’ฆ ,๐’ฆ PUNCT cana-733 61 33 ) ) PUNCT cana-733 61 34 is be AUX cana-733 61 35 a a DET cana-733 61 36 fs fs PROPN cana-733 61 37 - - PUNCT cana-733 61 38 w w NOUN cana-733 61 39 - - PUNCT cana-733 61 40 algebras algebras ADJ cana-733 61 41 over over ADP cana-733 61 42 โ„ณ. โ„ณ. PROPN cana-733 61 43 proposition proposition NOUN cana-733 61 44 3.4 3.4 NUM cana-733 61 45 : : PUNCT cana-733 61 46 a a DET cana-733 61 47 fs fs PROPN cana-733 61 48 - - PUNCT cana-733 61 49 w w NOUN cana-733 61 50 - - PUNCT cana-733 61 51 algebras algebras X cana-733 61 52 ( ( PUNCT cana-733 61 53 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 54 ฬŒ ฬŒ NUM cana-733 61 55 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 56 , , PUNCT cana-733 61 57 ๐ผ)over ๐ผ)over SCONJ cana-733 61 58 ๐’ณ ๐’ณ PROPN cana-733 61 59 is be AUX cana-733 61 60 defined define VERB cana-733 61 61 as as ADP cana-733 61 62 ( ( PUNCT cana-733 61 63 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 64 ฬŒ ฬŒ NUM cana-733 61 65 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 66 (๐“‚)(0 (๐“‚)(0 NUM cana-733 61 67 ) ) PUNCT cana-733 61 68 โ‰ฅ โ‰ฅ NOUN cana-733 61 69 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 70 ฬŒ ฬŒ NUM cana-733 61 71 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 72 (๐“‚)(ฯฑ (๐“‚)(ฯฑ NUM cana-733 61 73 ) ) PUNCT cana-733 61 74 for for ADP cana-733 61 75 every every DET cana-733 61 76 ฯฑ ฯฑ PROPN cana-733 61 77 โˆˆ โˆˆ PROPN cana-733 61 78 ๐’ณ ๐’ณ PROPN cana-733 61 79 where where SCONJ cana-733 61 80 ๐“‚ ๐“‚ NOUN cana-733 61 81 is be AUX cana-733 61 82 any any DET cana-733 61 83 parameter parameter NOUN cana-733 61 84 in in ADP cana-733 61 85 ๐ผ. ๐ผ. PROPN cana-733 61 86 proof proof NOUN cana-733 61 87 : : PUNCT cana-733 61 88 let let VERB cana-733 61 89 ฯฑ ฯฑ ADP cana-733 61 90 โˆˆ โˆˆ PROPN cana-733 61 91 ๐’ณ ๐’ณ PROPN cana-733 61 92 and and CCONJ cana-733 61 93 ๐“‚ ๐“‚ PROPN cana-733 61 94 โˆˆ โˆˆ PROPN cana-733 61 95 ๐ผ ๐ผ PROPN cana-733 61 96 , , PUNCT cana-733 61 97 then then ADV cana-733 61 98 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 99 ฬŒ ฬŒ NUM cana-733 61 100 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 101 (๐“‚)(0 (๐“‚)(0 NUM cana-733 61 102 ) ) PUNCT cana-733 61 103 = = SYM cana-733 61 104 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 105 ฬŒ ฬŒ NUM cana-733 61 106 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 107 (๐“‚)(ฯฑ (๐“‚)(ฯฑ PROPN cana-733 61 108 โ†’ โ†’ SYM cana-733 61 109 ฯฑ ฯฑ NOUN cana-733 61 110 ) ) PUNCT cana-733 61 111 โ‰ฅ โ‰ฅ PROPN cana-733 61 112 min min PROPN cana-733 61 113 { { PUNCT cana-733 61 114 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 115 ฬŒ ฬŒ NUM cana-733 61 116 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 117 (๐“‚)(ฯฑ (๐“‚)(ฯฑ NUM cana-733 61 118 ) ) PUNCT cana-733 61 119 , , PUNCT cana-733 61 120 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 121 ฬŒ ฬŒ NUM cana-733 61 122 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 123 (๐“‚)(ฯฑ (๐“‚)(ฯฑ NUM cana-733 61 124 ) ) PUNCT cana-733 61 125 } } PUNCT cana-733 61 126 = = SYM cana-733 61 127 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 128 ฬŒ ฬŒ NUM cana-733 61 129 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 130 (๐“‚)(ฯฑ (๐“‚)(ฯฑ NUM cana-733 61 131 ) ) PUNCT cana-733 61 132 hence hence ADV cana-733 61 133 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 134 ฬŒ ฬŒ NUM cana-733 61 135 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 136 (๐“‚)(0 (๐“‚)(0 NUM cana-733 61 137 ) ) PUNCT cana-733 61 138 โ‰ฅ โ‰ฅ NOUN cana-733 61 139 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 140 ฬŒ ฬŒ NUM cana-733 61 141 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 142 (๐“‚)(ฯฑ (๐“‚)(ฯฑ NUM cana-733 61 143 ) ) PUNCT cana-733 61 144 for for ADP cana-733 61 145 all all PRON cana-733 61 146 ฯฑ ฯฑ PROPN cana-733 61 147 โˆˆ โˆˆ PROPN cana-733 61 148 ๐’ณ ๐’ณ PROPN cana-733 61 149 and and CCONJ cana-733 61 150 any any DET cana-733 61 151 parameter parameter NOUN cana-733 61 152 ๐“‚ ๐“‚ PROPN cana-733 61 153 in in ADP cana-733 61 154 ๐ผ. ๐ผ. PROPN cana-733 61 155 theorem theorem VERB cana-733 61 156 3.5 3.5 NUM cana-733 61 157 : : PUNCT cana-733 61 158 let let VERB cana-733 61 159 ( ( PUNCT cana-733 61 160 ๏ฟฝ ๏ฟฝ NOUN cana-733 61 161 ฬŒ ฬŒ NUM cana-733 61 162 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 163 , , PUNCT cana-733 61 164 ๐ผ ๐ผ PROPN cana-733 61 165 ) ) PUNCT cana-733 61 166 be be VERB cana-733 61 167 a a DET cana-733 61 168 fs fs PROPN cana-733 61 169 - - PUNCT cana-733 61 170 w w NOUN cana-733 61 171 - - PUNCT cana-733 61 172 algebras algebras ADJ cana-733 61 173 over over ADP cana-733 61 174 ๐’ณ. ๐’ณ. PROPN cana-733 61 175 if if SCONJ cana-733 61 176 ๐’ฅ ๐’ฅ PRON cana-733 61 177 is be AUX cana-733 61 178 a a DET cana-733 61 179 subset subset NOUN cana-733 61 180 of of ADP cana-733 61 181 ๐ผ ๐ผ PROPN cana-733 61 182 , , PUNCT cana-733 61 183 then then ADV cana-733 61 184 ( ( PUNCT cana-733 61 185 ๏ฟฝ ๏ฟฝ NOUN cana-733 61 186 ฬŒ ฬŒ NUM cana-733 61 187 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 188 ๐’ฅโ„ ๐’ฅโ„ PROPN cana-733 61 189 , , PUNCT cana-733 61 190 ๐’ฅ ๐’ฅ PROPN cana-733 61 191 ) ) PUNCT cana-733 61 192 is be AUX cana-733 61 193 a a DET cana-733 61 194 fsw fsw PROPN cana-733 61 195 - - PUNCT cana-733 61 196 algebras algebras PROPN cana-733 61 197 over over ADP cana-733 61 198 ๐’ณ. ๐’ณ. PROPN cana-733 61 199 the the DET cana-733 61 200 example example NOUN cana-733 61 201 that that PRON cana-733 61 202 follows follow VERB cana-733 61 203 demonstrates demonstrate VERB cana-733 61 204 that that SCONJ cana-733 61 205 a a DET cana-733 61 206 fs fs NOUN cana-733 61 207 - - PUNCT cana-733 61 208 set set ADJ cana-733 61 209 ( ( PUNCT cana-733 61 210 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 211 ฬŒ ฬŒ NUM cana-733 61 212 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 213 , , PUNCT cana-733 61 214 ๐ผ ๐ผ PROPN cana-733 61 215 ) ) PUNCT cana-733 61 216 exists exist VERB cana-733 61 217 over over ADP cana-733 61 218 a a DET cana-733 61 219 w w NOUN cana-733 61 220 - - PUNCT cana-733 61 221 algebra algebra NOUN cana-733 61 222 ๐’ณ ๐’ณ NOUN cana-733 61 223 in in ADP cana-733 61 224 such such DET cana-733 61 225 a a DET cana-733 61 226 way way NOUN cana-733 61 227 that that PRON cana-733 61 228 , , PUNCT cana-733 61 229 ( ( PUNCT cana-733 61 230 i i NOUN cana-733 61 231 ) ) PUNCT cana-733 61 232 ( ( PUNCT cana-733 61 233 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 234 ฬŒ ฬŒ NUM cana-733 61 235 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 236 , , PUNCT cana-733 61 237 ๐ผ ๐ผ PROPN cana-733 61 238 ) ) PUNCT cana-733 61 239 is be AUX cana-733 61 240 not not PART cana-733 61 241 a a DET cana-733 61 242 fs fs VERB cana-733 61 243 - - PUNCT cana-733 61 244 w w NOUN cana-733 61 245 - - PUNCT cana-733 61 246 algebra algebra NOUN cana-733 61 247 over over ADP cana-733 61 248 ๐’ณ. ๐’ณ. PROPN cana-733 61 249 ( ( PUNCT cana-733 61 250 ii ii NOUN cana-733 61 251 ) ) PUNCT cana-733 61 252 there there PRON cana-733 61 253 exists exist VERB cana-733 61 254 a a DET cana-733 61 255 subset subset NOUN cana-733 61 256 โ„ฌ โ„ฌ NOUN cana-733 61 257 of of ADP cana-733 61 258 ๐ผ ๐ผ PROPN cana-733 61 259 such such ADJ cana-733 61 260 that that PRON cana-733 61 261 ( ( PUNCT cana-733 61 262 ๏ฟฝ ๏ฟฝ NOUN cana-733 61 263 ฬŒ ฬŒ NUM cana-733 61 264 ๏ฟฝ ๏ฟฝ PROPN cana-733 61 265 ๐’ฅโ„ ๐’ฅโ„ PROPN cana-733 61 266 , , PUNCT cana-733 61 267 ๐’ฅ ๐’ฅ PROPN cana-733 61 268 ) ) PUNCT cana-733 61 269 is be AUX cana-733 61 270 a a DET cana-733 61 271 fs fs PROPN cana-733 61 272 - - PUNCT cana-733 61 273 w w NOUN cana-733 61 274 - - PUNCT cana-733 61 275 algebra algebra NOUN cana-733 61 276 over over ADP cana-733 61 277 ๐’ณ. ๐’ณ. PROPN cana-733 61 278 example example NOUN cana-733 61 279 3.6 3.6 NUM cana-733 61 280 : : PUNCT cana-733 61 281 let let VERB cana-733 61 282 ( ( PUNCT cana-733 61 283 โ„ณ,โŠ›,pink โ„ณ,โŠ›,pink NOUN cana-733 61 284 ) ) PUNCT cana-733 61 285 is be AUX cana-733 61 286 a a DET cana-733 61 287 w w NOUN cana-733 61 288 - - PUNCT cana-733 61 289 algebra algebra NOUN cana-733 61 290 as as ADP cana-733 61 291 in in ADP cana-733 61 292 example-3.2 example-3.2 NOUN cana-733 61 293 define define VERB cana-733 61 294 parameters parameter NOUN cana-733 61 295 ๐ผ ๐ผ ADP cana-733 61 296 = = PUNCT cana-733 61 297 { { PUNCT cana-733 61 298 glorious glorious ADJ cana-733 61 299 , , PUNCT cana-733 61 300 elegant elegant ADJ cana-733 61 301 , , PUNCT cana-733 61 302 modest modest ADJ cana-733 61 303 , , PUNCT cana-733 61 304 clever clever ADJ cana-733 61 305 , , PUNCT cana-733 61 306 gentle gentle ADJ cana-733 61 307 } } PUNCT cana-733 61 308 . . PUNCT cana-733 62 1 if if SCONJ cana-733 62 2 ( ( PUNCT cana-733 62 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 4 ฬŒ ฬŒ NUM cana-733 62 5 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 6 , , PUNCT cana-733 62 7 ๐ผ ๐ผ PROPN cana-733 62 8 ) ) PUNCT cana-733 62 9 be be VERB cana-733 62 10 a a DET cana-733 62 11 fs fs NOUN cana-733 62 12 - - PUNCT cana-733 62 13 set set VERB cana-733 62 14 over over ADP cana-733 62 15 โ„ณ โ„ณ PROPN cana-733 62 16 , , PUNCT cana-733 62 17 then then ADV cana-733 62 18 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 19 ฬŒ ฬŒ NUM cana-733 62 20 ๏ฟฝ ๏ฟฝ NOUN cana-733 62 21 [glorious [glorious X cana-733 62 22 ] ] X cana-733 62 23 , , PUNCT cana-733 62 24 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 25 ฬŒ ฬŒ NUM cana-733 62 26 ๏ฟฝ ๏ฟฝ NOUN cana-733 62 27 [elegant [elegant X cana-733 62 28 ] ] X cana-733 62 29 , , PUNCT cana-733 62 30 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 31 ฬŒ ฬŒ NUM cana-733 62 32 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 33 [modest [modest X cana-733 62 34 ] ] X cana-733 62 35 , , PUNCT cana-733 62 36 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 37 ฬŒ ฬŒ NUM cana-733 62 38 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 39 [clever [clever X cana-733 62 40 ] ] PUNCT cana-733 62 41 & & CCONJ cana-733 62 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 43 ฬŒ ฬŒ NUM cana-733 62 44 ๏ฟฝ ๏ฟฝ NOUN cana-733 62 45 [gentle [gentle X cana-733 62 46 ] ] X cana-733 62 47 defined define VERB cana-733 62 48 as as ADP cana-733 62 49 ๏ฟฝ ๏ฟฝ PROPN cana-733 62 50 ฬŒ ฬŒ NUM cana-733 62 51 ๏ฟฝ ๏ฟฝ NOUN cana-733 62 52 pink pink ADJ cana-733 62 53 gray gray ADJ cana-733 62 54 red red ADJ cana-733 62 55 olive olive NOUN cana-733 62 56 tan tan PROPN cana-733 62 57 glorious glorious ADJ cana-733 62 58 0.7 0.7 NUM cana-733 62 59 0.7 0.7 NUM cana-733 62 60 0.7 0.7 NUM cana-733 62 61 0.4 0.4 NUM cana-733 62 62 0.4 0.4 NUM cana-733 62 63 elegant elegant ADJ cana-733 62 64 0.8 0.8 NUM cana-733 62 65 0.7 0.7 NUM cana-733 62 66 0.4 0.4 NUM cana-733 62 67 0.6 0.6 NUM cana-733 62 68 0.4 0.4 NUM cana-733 62 69 modest modest ADJ cana-733 62 70 0.6 0.6 NUM cana-733 62 71 0.2 0.2 NUM cana-733 62 72 0.6 0.6 NUM cana-733 62 73 0.2 0.2 NUM cana-733 62 74 0.2 0.2 NUM cana-733 62 75 clever clever ADJ cana-733 62 76 0.2 0.2 NUM cana-733 62 77 0.3 0.3 NUM cana-733 62 78 0.4 0.4 NUM cana-733 62 79 0.5 0.5 NUM cana-733 62 80 0.5 0.5 NUM cana-733 62 81 gentle gentle ADJ cana-733 62 82 0.3 0.3 NUM cana-733 62 83 0.2 0.2 NUM cana-733 62 84 0.6 0.6 NUM cana-733 62 85 0.6 0.6 NUM cana-733 62 86 0.2 0.2 NUM cana-733 62 87 communications communication NOUN cana-733 62 88 on on ADP cana-733 62 89 applied apply VERB cana-733 62 90 nonlinear nonlinear ADJ cana-733 62 91 analysis analysis NOUN cana-733 62 92 issn issn NOUN cana-733 62 93 : : PUNCT cana-733 62 94 1074 1074 NUM cana-733 62 95 - - PUNCT cana-733 62 96 133x 133x NUM cana-733 62 97 vol vol NOUN cana-733 62 98 31 31 NUM cana-733 62 99 no no NOUN cana-733 62 100 . . PUNCT cana-733 63 1 3s 3s NUM cana-733 63 2 ( ( PUNCT cana-733 63 3 2024 2024 NUM cana-733 63 4 ) ) PUNCT cana-733 63 5 86 86 NUM cana-733 63 6 https://internationalpubls.com https://internationalpubls.com X cana-733 63 7 then then ADV cana-733 63 8 ( ( PUNCT cana-733 63 9 ๏ฟฝ ๏ฟฝ PROPN cana-733 63 10 ฬŒ ฬŒ NUM cana-733 63 11 ๏ฟฝ ๏ฟฝ PROPN cana-733 63 12 , , PUNCT cana-733 63 13 ๐ผ ๐ผ PROPN cana-733 63 14 ) ) PUNCT cana-733 63 15 is be AUX cana-733 63 16 not not PART cana-733 63 17 fs f NOUN cana-733 63 18 - - PUNCT cana-733 63 19 w w NOUN cana-733 63 20 - - PUNCT cana-733 63 21 algebra algebra NOUN cana-733 63 22 over over ADP cana-733 63 23 โ„ณ. โ„ณ. PROPN cana-733 63 24 since since SCONJ cana-733 63 25 ๏ฟฝ ๏ฟฝ PROPN cana-733 63 26 ฬŒ ฬŒ NUM cana-733 63 27 ๏ฟฝ ๏ฟฝ PROPN cana-733 63 28 [clever [clever X cana-733 63 29 ] ] PUNCT cana-733 63 30 & & CCONJ cana-733 63 31 ๏ฟฝ ๏ฟฝ PROPN cana-733 63 32 ฬŒ ฬŒ NUM cana-733 63 33 ๏ฟฝ ๏ฟฝ NOUN cana-733 63 34 [gentle [gentle X cana-733 63 35 ] ] X cana-733 63 36 are be AUX cana-733 63 37 not not PART cana-733 63 38 fuzzy fuzzy ADJ cana-733 63 39 w w NOUN cana-733 63 40 - - NOUN cana-733 63 41 algebra algebra NOUN cana-733 63 42 in in ADP cana-733 63 43 โ„ณ. โ„ณ. PROPN cana-733 63 44 but but CCONJ cana-733 63 45 ๐’ฅ ๐’ฅ NOUN cana-733 63 46 = = PROPN cana-733 63 47 { { PUNCT cana-733 63 48 glorious glorious ADJ cana-733 63 49 , , PUNCT cana-733 63 50 elegant elegant ADJ cana-733 63 51 , , PUNCT cana-733 63 52 modest modest ADJ cana-733 63 53 } } PUNCT cana-733 63 54 then then ADV cana-733 63 55 ( ( PUNCT cana-733 63 56 ๏ฟฝ ๏ฟฝ NOUN cana-733 63 57 ฬŒ ฬŒ NUM cana-733 63 58 ๏ฟฝ ๏ฟฝ PROPN cana-733 63 59 ๐’ฅโ„ ๐’ฅโ„ PROPN cana-733 63 60 , , PUNCT cana-733 63 61 ๐’ฅ ๐’ฅ PROPN cana-733 63 62 ) ) PUNCT cana-733 63 63 is be AUX cana-733 63 64 a a DET cana-733 63 65 fs fs PROPN cana-733 63 66 - - PUNCT cana-733 63 67 w w NOUN cana-733 63 68 - - PUNCT cana-733 63 69 algebra algebra NOUN cana-733 63 70 over over ADP cana-733 63 71 โ„ณ. โ„ณ. PROPN cana-733 63 72 definition definition NOUN cana-733 63 73 3.7 3.7 NUM cana-733 63 74 : : PUNCT cana-733 64 1 [ [ X cana-733 64 2 1 1 X cana-733 64 3 ] ] PUNCT cana-733 64 4 the the DET cana-733 64 5 soft soft ADJ cana-733 64 6 set set NOUN cana-733 64 7 ( ( PUNCT cana-733 64 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 64 9 ฬŒ ฬŒ NUM cana-733 64 10 ๏ฟฝ ๏ฟฝ PROPN cana-733 64 11 , , PUNCT cana-733 64 12 ๐’Ÿ ๐’Ÿ PROPN cana-733 64 13 ) ) PUNCT cana-733 65 1 where where SCONJ cana-733 65 2 ๐’Ÿ ๐’Ÿ NOUN cana-733 65 3 = = PUNCT cana-733 65 4 ๐ผ ๐ผ ADP cana-733 65 5 โˆช โˆช VERB cana-733 65 6 ๐’ฅ ๐’ฅ PROPN cana-733 65 7 and and CCONJ cana-733 65 8 for for ADP cana-733 65 9 every every DET cana-733 65 10 t t NOUN cana-733 65 11 โˆˆ โˆˆ PROPN cana-733 65 12 ๐’Ÿ ๐’Ÿ NOUN cana-733 65 13 is be AUX cana-733 65 14 the the DET cana-733 65 15 extended extended ADJ cana-733 65 16 intersection intersection NOUN cana-733 65 17 ( ( PUNCT cana-733 65 18 ei ei NOUN cana-733 65 19 ) ) PUNCT cana-733 65 20 of of ADP cana-733 65 21 two two NUM cana-733 65 22 soft soft ADJ cana-733 65 23 sets set NOUN cana-733 65 24 ( ( PUNCT cana-733 65 25 ๏ฟฝ ๏ฟฝ PROPN cana-733 65 26 ฬŒ ฬŒ NUM cana-733 65 27 ๏ฟฝ ๏ฟฝ PROPN cana-733 65 28 , , PUNCT cana-733 65 29 ๐ผ ๐ผ PROPN cana-733 65 30 ) ) PUNCT cana-733 65 31 and and CCONJ cana-733 65 32 ( ( PUNCT cana-733 65 33 ๏ฟฝ ๏ฟฝ PROPN cana-733 65 34 ฬŒ ฬŒ NUM cana-733 65 35 ๏ฟฝ ๏ฟฝ PROPN cana-733 65 36 , , PUNCT cana-733 65 37 ๐’ฅ ๐’ฅ PROPN cana-733 65 38 ) ) PUNCT cana-733 65 39 over over ADP cana-733 65 40 โ„ณ. โ„ณ. PROPN cana-733 65 41 ๏ฟฝ ๏ฟฝ PROPN cana-733 65 42 ฬŒ ฬŒ NUM cana-733 65 43 ๏ฟฝ ๏ฟฝ NOUN cana-733 65 44 [t [t X cana-733 65 45 ] ] X cana-733 65 46 = = SYM cana-733 65 47 { { PUNCT cana-733 65 48 ๏ฟฝ ๏ฟฝ PROPN cana-733 65 49 ฬŒ ฬŒ NUM cana-733 65 50 ๏ฟฝ ๏ฟฝ NOUN cana-733 65 51 [t [t X cana-733 65 52 ] ] X cana-733 65 53 โˆถ โˆถ NOUN cana-733 65 54 t t X cana-733 65 55 โˆˆ โˆˆ NOUN cana-733 66 1 ๐ผ ๐ผ ADP cana-733 66 2 โˆ– โˆ– PROPN cana-733 67 1 ๐’ฅ ๐’ฅ PROPN cana-733 67 2 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 3 ฬŒ ฬŒ NUM cana-733 67 4 ๏ฟฝ ๏ฟฝ NOUN cana-733 67 5 [t [t X cana-733 67 6 ] ] X cana-733 67 7 โˆถ โˆถ NOUN cana-733 67 8 t t NOUN cana-733 67 9 โˆˆ โˆˆ PROPN cana-733 67 10 ๐’ฅ ๐’ฅ PROPN cana-733 67 11 โˆ– โˆ– X cana-733 67 12 ๐ผ ๐ผ ADP cana-733 67 13 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 14 ฬŒ ฬŒ NUM cana-733 67 15 ๏ฟฝ ๏ฟฝ NOUN cana-733 67 16 [t [t X cana-733 67 17 ] ] X cana-733 67 18 โˆฉ โˆฉ X cana-733 67 19 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 20 ฬŒ ฬŒ NUM cana-733 67 21 ๏ฟฝ ๏ฟฝ NOUN cana-733 67 22 [t [t X cana-733 67 23 ] ] X cana-733 67 24 โˆถ โˆถ NOUN cana-733 67 25 t t X cana-733 67 26 โˆˆ โˆˆ NOUN cana-733 67 27 ๐ผ ๐ผ PROPN cana-733 67 28 โˆฉ โˆฉ ADJ cana-733 67 29 ๐’ฅ ๐’ฅ PROPN cana-733 67 30 } } PUNCT cana-733 67 31 we we PRON cana-733 67 32 write write VERB cana-733 67 33 ( ( PUNCT cana-733 67 34 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 35 ฬŒ ฬŒ NUM cana-733 67 36 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 37 , , PUNCT cana-733 67 38 ๐ผ ๐ผ PROPN cana-733 67 39 ) ) PUNCT cana-733 67 40 โˆฉฬŒt โˆฉฬŒt PROPN cana-733 67 41 ( ( PUNCT cana-733 67 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 43 ฬŒ ฬŒ NUM cana-733 67 44 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 45 , , PUNCT cana-733 67 46 ๐’ฅ ๐’ฅ NOUN cana-733 67 47 ) ) PUNCT cana-733 67 48 =( =( PROPN cana-733 67 49 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 50 ฬŒ ฬŒ NUM cana-733 67 51 ๏ฟฝ ๏ฟฝ PROPN cana-733 67 52 , , PUNCT cana-733 67 53 ๐’Ÿ ๐’Ÿ PROPN cana-733 67 54 ) ) PUNCT cana-733 67 55 . . PUNCT cana-733 68 1 definition definition NOUN cana-733 68 2 3.8 3.8 NUM cana-733 68 3 : : PUNCT cana-733 68 4 let let VERB cana-733 68 5 ( ( PUNCT cana-733 68 6 ๏ฟฝ ๏ฟฝ NOUN cana-733 68 7 ฬŒ ฬŒ NUM cana-733 68 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 9 , , PUNCT cana-733 68 10 ๐ผ ๐ผ PROPN cana-733 68 11 ) ) PUNCT cana-733 68 12 & & CCONJ cana-733 68 13 ( ( PUNCT cana-733 68 14 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 15 ฬŒ ฬŒ NUM cana-733 68 16 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 17 , , PUNCT cana-733 68 18 ๐’ฅ ๐’ฅ PROPN cana-733 68 19 ) ) PUNCT cana-733 68 20 be be VERB cana-733 68 21 two two NUM cana-733 68 22 soft soft ADJ cana-733 68 23 sets set NOUN cana-733 68 24 over over ADP cana-733 68 25 โ„ณ โ„ณ PROPN cana-733 68 26 such such ADJ cana-733 68 27 that that SCONJ cana-733 68 28 ๐ผ ๐ผ ADP cana-733 68 29 โˆฉ โˆฉ NOUN cana-733 68 30 ๐’ฅ ๐’ฅ PROPN cana-733 68 31 โ‰  โ‰  PROPN cana-733 68 32 ฯ• ฯ• PROPN cana-733 68 33 the the DET cana-733 68 34 ei ei X cana-733 68 35 of of ADP cana-733 68 36 ( ( PUNCT cana-733 68 37 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 38 ฬŒ ฬŒ NUM cana-733 68 39 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 40 , , PUNCT cana-733 68 41 ๐ผ ๐ผ PROPN cana-733 68 42 ) ) PUNCT cana-733 68 43 and and CCONJ cana-733 68 44 ( ( PUNCT cana-733 68 45 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 46 ฬŒ ฬŒ NUM cana-733 68 47 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 48 , , PUNCT cana-733 68 49 ๐’ฅ ๐’ฅ PROPN cana-733 68 50 ) ) PUNCT cana-733 68 51 is be AUX cana-733 68 52 denoted denote VERB cana-733 68 53 by by ADP cana-733 68 54 ( ( PUNCT cana-733 68 55 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 56 ฬŒ ฬŒ NUM cana-733 68 57 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 58 , , PUNCT cana-733 68 59 ๐ผ ๐ผ PROPN cana-733 68 60 ) ) PUNCT cana-733 68 61 โˆฉฬŒ๐ฌ โˆฉฬŒ๐ฌ X cana-733 68 62 ( ( PUNCT cana-733 68 63 ( ( PUNCT cana-733 68 64 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 65 ฬŒ ฬŒ NUM cana-733 68 66 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 67 , , PUNCT cana-733 68 68 ๐’ฅ ๐’ฅ PROPN cana-733 68 69 ) ) PUNCT cana-733 68 70 and and CCONJ cana-733 68 71 is be AUX cana-733 68 72 defined define VERB cana-733 68 73 as as ADP cana-733 68 74 ( ( PUNCT cana-733 68 75 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 76 ฬŒ ฬŒ NUM cana-733 68 77 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 78 , , PUNCT cana-733 68 79 ๐ผ ๐ผ PROPN cana-733 68 80 ) ) PUNCT cana-733 68 81 โˆฉฬŒ๐ฌ โˆฉฬŒ๐ฌ PUNCT cana-733 68 82 ( ( PUNCT cana-733 68 83 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 84 ฬŒ ฬŒ NUM cana-733 68 85 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 86 , , PUNCT cana-733 68 87 ๐’ฅ ๐’ฅ PROPN cana-733 68 88 ) ) PUNCT cana-733 68 89 = = SYM cana-733 68 90 ( ( PUNCT cana-733 68 91 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 92 ฬŒ ฬŒ NUM cana-733 68 93 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 94 , , PUNCT cana-733 68 95 ๐’Ÿ ๐’Ÿ PROPN cana-733 68 96 ) ) PUNCT cana-733 68 97 where where SCONJ cana-733 68 98 ๐’Ÿ ๐’Ÿ NOUN cana-733 68 99 = = SYM cana-733 68 100 ๐ผ ๐ผ PROPN cana-733 68 101 โˆฉ โˆฉ ADJ cana-733 68 102 ๐’ฅ ๐’ฅ PROPN cana-733 68 103 and and CCONJ cana-733 68 104 for for ADP cana-733 68 105 all all DET cana-733 68 106 u u PRON cana-733 68 107 โˆˆ โˆˆ PROPN cana-733 68 108 ๐’Ÿ ๐’Ÿ PROPN cana-733 68 109 , , PUNCT cana-733 68 110 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 111 ฬŒ ฬŒ NUM cana-733 68 112 ๏ฟฝ ๏ฟฝ NOUN cana-733 68 113 [u [u X cana-733 68 114 ] ] X cana-733 68 115 = = PUNCT cana-733 68 116 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 117 ฬŒ ฬŒ NUM cana-733 68 118 ๏ฟฝ ๏ฟฝ NOUN cana-733 68 119 [u [u X cana-733 68 120 ] ] X cana-733 68 121 โˆฉ โˆฉ PROPN cana-733 68 122 ๏ฟฝ ๏ฟฝ PROPN cana-733 68 123 ฬŒ ฬŒ NUM cana-733 68 124 ๏ฟฝ ๏ฟฝ NOUN cana-733 68 125 [u [u NOUN cana-733 68 126 ] ] PUNCT cana-733 68 127 . . PUNCT cana-733 69 1 theorem theorem VERB cana-733 69 2 3.9 3.9 NUM cana-733 69 3 : : PUNCT cana-733 69 4 the the DET cana-733 69 5 ei ei X cana-733 69 6 of of ADP cana-733 69 7 ( ( PUNCT cana-733 69 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 9 ฬŒ ฬŒ NUM cana-733 69 10 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 11 , , PUNCT cana-733 69 12 ๐ผ ๐ผ PROPN cana-733 69 13 ) ) PUNCT cana-733 69 14 and and CCONJ cana-733 69 15 ( ( PUNCT cana-733 69 16 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 17 ฬŒ ฬŒ NUM cana-733 69 18 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 19 , , PUNCT cana-733 69 20 ๐’ฅ ๐’ฅ PROPN cana-733 69 21 ) ) PUNCT cana-733 69 22 is be AUX cana-733 69 23 a a DET cana-733 69 24 fs fs PROPN cana-733 69 25 - - PUNCT cana-733 69 26 w w NOUN cana-733 69 27 - - PUNCT cana-733 69 28 algebra algebra NOUN cana-733 69 29 over over ADP cana-733 69 30 ๐’ณ ๐’ณ PROPN cana-733 69 31 , , PUNCT cana-733 69 32 if if SCONJ cana-733 69 33 ( ( PUNCT cana-733 69 34 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 35 ฬŒ ฬŒ NUM cana-733 69 36 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 37 , , PUNCT cana-733 69 38 ๐ผ ๐ผ PROPN cana-733 69 39 ) ) PUNCT cana-733 69 40 and and CCONJ cana-733 69 41 ( ( PUNCT cana-733 69 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 43 ฬŒ ฬŒ NUM cana-733 69 44 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 45 , , PUNCT cana-733 69 46 ๐’ฅ ๐’ฅ PROPN cana-733 69 47 ) ) PUNCT cana-733 69 48 are be AUX cana-733 69 49 fsw fsw PROPN cana-733 69 50 - - PUNCT cana-733 69 51 algebras algebras PROPN cana-733 69 52 over over ADP cana-733 69 53 ๐’ณ. ๐’ณ. PROPN cana-733 69 54 proof proof NOUN cana-733 69 55 : : PUNCT cana-733 69 56 the the DET cana-733 69 57 ei ei X cana-733 69 58 of of ADP cana-733 69 59 ( ( PUNCT cana-733 69 60 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 61 ฬŒ ฬŒ NUM cana-733 69 62 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 63 , , PUNCT cana-733 69 64 ๐ผ ๐ผ PROPN cana-733 69 65 ) ) PUNCT cana-733 69 66 and and CCONJ cana-733 69 67 ( ( PUNCT cana-733 69 68 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 69 ฬŒ ฬŒ NUM cana-733 69 70 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 71 , , PUNCT cana-733 69 72 ๐’ฅ ๐’ฅ PROPN cana-733 69 73 ) ) PUNCT cana-733 69 74 is be AUX cana-733 69 75 ( ( PUNCT cana-733 69 76 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 77 ฬŒ ฬŒ NUM cana-733 69 78 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 79 , , PUNCT cana-733 69 80 ๐ผ ๐ผ PROPN cana-733 69 81 ) ) PUNCT cana-733 69 82 โˆฉฬŒt โˆฉฬŒt PROPN cana-733 69 83 ( ( PUNCT cana-733 69 84 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 85 ฬŒ ฬŒ NUM cana-733 69 86 ๏ฟฝ ๏ฟฝ PROPN cana-733 69 87 , , PUNCT cana-733 69 88 ๐’ฅ ๐’ฅ PROPN cana-733 69 89 ) ) PUNCT cana-733 70 1 = = SYM cana-733 70 2 ( ( PUNCT cana-733 70 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 70 4 ฬŒ ฬŒ NUM cana-733 70 5 ๏ฟฝ ๏ฟฝ NOUN cana-733 70 6 ,๐’Ÿ ,๐’Ÿ PUNCT cana-733 70 7 ) ) PUNCT cana-733 70 8 then then ADV cana-733 70 9 ๐’Ÿ ๐’Ÿ NOUN cana-733 70 10 = = PUNCT cana-733 70 11 ๐ผ ๐ผ PROPN cana-733 70 12 โˆช โˆช VERB cana-733 70 13 ๐’ฅ ๐’ฅ PROPN cana-733 70 14 for for ADP cana-733 70 15 any any DET cana-733 70 16 u u PROPN cana-733 70 17 โˆˆ โˆˆ PROPN cana-733 70 18 ๐’Ÿ. ๐’Ÿ. PROPN cana-733 70 19 ๏ฟฝ ๏ฟฝ PROPN cana-733 70 20 ฬŒ ฬŒ NUM cana-733 70 21 ๏ฟฝ ๏ฟฝ NOUN cana-733 70 22 (u (u NOUN cana-733 70 23 ) ) PUNCT cana-733 70 24 = = SYM cana-733 70 25 ๏ฟฝ ๏ฟฝ PROPN cana-733 70 26 ฬŒ ฬŒ NUM cana-733 70 27 ๏ฟฝ ๏ฟฝ NOUN cana-733 70 28 (u (u NOUN cana-733 70 29 ) ) PUNCT cana-733 70 30 ( ( PUNCT cana-733 70 31 resp resp PROPN cana-733 70 32 ๏ฟฝ ๏ฟฝ PROPN cana-733 70 33 ฬŒ ฬŒ NUM cana-733 70 34 ๏ฟฝ ๏ฟฝ NOUN cana-733 70 35 (u (u NOUN cana-733 70 36 ) ) PUNCT cana-733 70 37 = = SYM cana-733 70 38 ๏ฟฝ ๏ฟฝ PROPN cana-733 70 39 ฬŒ ฬŒ NUM cana-733 70 40 ๏ฟฝ ๏ฟฝ NOUN cana-733 70 41 (u (u NOUN cana-733 70 42 ) ) PUNCT cana-733 70 43 ) ) PUNCT cana-733 70 44 is be AUX cana-733 70 45 a a DET cana-733 70 46 fuzzy fuzzy ADJ cana-733 70 47 w w NOUN cana-733 70 48 - - NOUN cana-733 70 49 algebra algebra NOUN cana-733 70 50 if if SCONJ cana-733 70 51 u u PROPN cana-733 70 52 โˆˆ โˆˆ NOUN cana-733 70 53 ๐ผ ๐ผ ADP cana-733 70 54 โˆ– โˆ– PROPN cana-733 70 55 ๐’ฅ ๐’ฅ PROPN cana-733 70 56 ( ( PUNCT cana-733 70 57 resp resp PROPN cana-733 70 58 โˆˆ โˆˆ PROPN cana-733 70 59 ๐’ฅ ๐’ฅ PROPN cana-733 70 60 โˆ– โˆ– PROPN cana-733 71 1 ๐ผ ๐ผ PROPN cana-733 71 2 ) ) PUNCT cana-733 71 3 . . PUNCT cana-733 72 1 ๏ฟฝ ๏ฟฝ PROPN cana-733 72 2 ฬŒ ฬŒ NUM cana-733 72 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 72 4 [u [u X cana-733 72 5 ] ] X cana-733 72 6 = = PUNCT cana-733 72 7 ๏ฟฝ ๏ฟฝ PROPN cana-733 72 8 ฬŒ ฬŒ NUM cana-733 72 9 ๏ฟฝ ๏ฟฝ NOUN cana-733 72 10 [u [u X cana-733 72 11 ] ] X cana-733 72 12 โˆฉ โˆฉ PROPN cana-733 72 13 ๏ฟฝ ๏ฟฝ PROPN cana-733 72 14 ฬŒ ฬŒ NUM cana-733 72 15 ๏ฟฝ ๏ฟฝ NOUN cana-733 72 16 [u [u X cana-733 72 17 ] ] X cana-733 72 18 is be AUX cana-733 72 19 a a DET cana-733 72 20 fuzzy fuzzy ADJ cana-733 72 21 w w NOUN cana-733 72 22 - - NOUN cana-733 72 23 algebra algebra NOUN cana-733 72 24 for for ADP cana-733 72 25 all all DET cana-733 72 26 u u NOUN cana-733 72 27 โˆˆ โˆˆ NOUN cana-733 72 28 ๐ผ ๐ผ ADP cana-733 72 29 โˆฉ โˆฉ NOUN cana-733 72 30 ๐’ฅ ๐’ฅ PROPN cana-733 72 31 if if SCONJ cana-733 72 32 ๐ผ ๐ผ PROPN cana-733 72 33 โˆฉ โˆฉ NOUN cana-733 72 34 ๐’ฅ ๐’ฅ PROPN cana-733 72 35 โ‰  โ‰  PROPN cana-733 72 36 ฯ•. ฯ•. NOUN cana-733 72 37 given give VERB cana-733 72 38 that that DET cana-733 72 39 two two NUM cana-733 72 40 fuzzy fuzzy ADJ cana-733 72 41 w w NOUN cana-733 72 42 - - PUNCT cana-733 72 43 algebra algebra NOUN cana-733 72 44 intersect intersect NOUN cana-733 72 45 to to PART cana-733 72 46 form form VERB cana-733 72 47 a a DET cana-733 72 48 fuzzy fuzzy ADJ cana-733 72 49 w w NOUN cana-733 72 50 - - NOUN cana-733 72 51 algebra algebra NOUN cana-733 72 52 . . PUNCT cana-733 73 1 therefore therefore ADV cana-733 73 2 , , PUNCT cana-733 73 3 over over ADP cana-733 73 4 w w NOUN cana-733 73 5 - - PUNCT cana-733 73 6 algebra algebra NOUN cana-733 73 7 ๐’ณ ๐’ณ PROPN cana-733 73 8 , , PUNCT cana-733 73 9 ( ( PUNCT cana-733 73 10 ๏ฟฝ ๏ฟฝ PROPN cana-733 73 11 ฬŒ ฬŒ NUM cana-733 73 12 ๏ฟฝ ๏ฟฝ PROPN cana-733 73 13 , , PUNCT cana-733 73 14 ๐’Ÿ ๐’Ÿ PROPN cana-733 73 15 ) ) PUNCT cana-733 73 16 is be AUX cana-733 73 17 a a DET cana-733 73 18 fs fs NOUN cana-733 73 19 - - PUNCT cana-733 73 20 walgebra walgebra NOUN cana-733 73 21 . . PUNCT cana-733 74 1 corollary corollary ADJ cana-733 74 2 3.10 3.10 NUM cana-733 74 3 : : PUNCT cana-733 74 4 if if SCONJ cana-733 74 5 ( ( PUNCT cana-733 74 6 ๏ฟฝ ๏ฟฝ NOUN cana-733 74 7 ฬŒ ฬŒ NUM cana-733 74 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 9 , , PUNCT cana-733 74 10 ๐ผ ๐ผ PROPN cana-733 74 11 ) ) PUNCT cana-733 74 12 and and CCONJ cana-733 74 13 ( ( PUNCT cana-733 74 14 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 15 ฬŒ ฬŒ NUM cana-733 74 16 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 17 , , PUNCT cana-733 74 18 ๐’ฅ ๐’ฅ PROPN cana-733 74 19 ) ) PUNCT cana-733 74 20 are be AUX cana-733 74 21 two two NUM cana-733 74 22 fs f NOUN cana-733 74 23 - - PUNCT cana-733 74 24 w w NOUN cana-733 74 25 - - PUNCT cana-733 74 26 algebras algebras NOUN cana-733 74 27 over over ADP cana-733 74 28 ๐’ณ ๐’ณ PROPN cana-733 74 29 , , PUNCT cana-733 74 30 then then ADV cana-733 74 31 ( ( PUNCT cana-733 74 32 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 33 ฬŒ ฬŒ NUM cana-733 74 34 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 35 , , PUNCT cana-733 74 36 ๐ผ ๐ผ PROPN cana-733 74 37 ) ) PUNCT cana-733 74 38 โˆฉฬŒ โˆฉฬŒ NOUN cana-733 74 39 ( ( PUNCT cana-733 74 40 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 41 ฬŒ ฬŒ NUM cana-733 74 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 74 43 , , PUNCT cana-733 74 44 ๐’ฅ ๐’ฅ PROPN cana-733 74 45 ) ) PUNCT cana-733 74 46 is be AUX cana-733 74 47 a a DET cana-733 74 48 fs fs PROPN cana-733 74 49 - - PUNCT cana-733 74 50 w w NOUN cana-733 74 51 - - PUNCT cana-733 74 52 algebra algebra NOUN cana-733 74 53 over over ADP cana-733 74 54 ๐’ณ ๐’ณ PROPN cana-733 74 55 through through ADP cana-733 74 56 its its PRON cana-733 74 57 ei ei PROPN cana-733 74 58 . . PROPN cana-733 74 59 corollary corollary NOUN cana-733 74 60 3.11 3.11 NUM cana-733 74 61 : : PUNCT cana-733 74 62 a a DET cana-733 74 63 fs fs PROPN cana-733 74 64 - - PUNCT cana-733 74 65 w w NOUN cana-733 74 66 - - PUNCT cana-733 74 67 algebra algebra NOUN cana-733 74 68 is be AUX cana-733 74 69 the the DET cana-733 74 70 limited limited ADJ cana-733 74 71 ei ei NOUN cana-733 74 72 of of ADP cana-733 74 73 two two NUM cana-733 74 74 fs fs PROPN cana-733 74 75 - - PUNCT cana-733 74 76 w w NOUN cana-733 74 77 - - PUNCT cana-733 74 78 algebras algebras NOUN cana-733 74 79 . . PUNCT cana-733 75 1 theorem theorem VERB cana-733 75 2 3.12 3.12 NUM cana-733 75 3 : : PUNCT cana-733 75 4 a a DET cana-733 75 5 w w NOUN cana-733 75 6 - - PUNCT cana-733 75 7 algebra algebra NOUN cana-733 75 8 ๐’ณ ๐’ณ PROPN cana-733 75 9 has have VERB cana-733 75 10 two two NUM cana-733 75 11 fs fs ADJ cana-733 75 12 - - PUNCT cana-733 75 13 w w NOUN cana-733 75 14 - - PUNCT cana-733 75 15 algebras algebras ADV cana-733 75 16 : : PUNCT cana-733 75 17 ( ( PUNCT cana-733 75 18 ๏ฟฝ ๏ฟฝ PROPN cana-733 75 19 ฬŒ ฬŒ NUM cana-733 75 20 ๏ฟฝ ๏ฟฝ PROPN cana-733 75 21 , , PUNCT cana-733 75 22 ๐ผ ๐ผ PROPN cana-733 75 23 ) ) PUNCT cana-733 75 24 and and CCONJ cana-733 75 25 ( ( PUNCT cana-733 75 26 ๏ฟฝ ๏ฟฝ PROPN cana-733 75 27 ฬŒ ฬŒ NUM cana-733 75 28 ๏ฟฝ ๏ฟฝ PROPN cana-733 75 29 , , PUNCT cana-733 75 30 ๐’ฅ ๐’ฅ PROPN cana-733 75 31 ) ) PUNCT cana-733 75 32 . . PUNCT cana-733 76 1 the the DET cana-733 76 2 union union PROPN cana-733 76 3 ( ( PUNCT cana-733 76 4 ๏ฟฝ ๏ฟฝ PROPN cana-733 76 5 ฬŒ ฬŒ NUM cana-733 76 6 ๏ฟฝ ๏ฟฝ PROPN cana-733 76 7 , , PUNCT cana-733 76 8 ๐ผ ๐ผ PROPN cana-733 76 9 ) ) PUNCT cana-733 76 10 โˆชฬŒ โˆชฬŒ NOUN cana-733 76 11 ( ( PUNCT cana-733 76 12 ๏ฟฝ ๏ฟฝ PROPN cana-733 76 13 ฬŒ ฬŒ NUM cana-733 76 14 ๏ฟฝ ๏ฟฝ PROPN cana-733 76 15 , , PUNCT cana-733 76 16 ๐’ฅ ๐’ฅ PROPN cana-733 76 17 ) ) PUNCT cana-733 76 18 is be AUX cana-733 76 19 a a DET cana-733 76 20 fuzzy fuzzy ADJ cana-733 76 21 w w NOUN cana-733 76 22 - - NOUN cana-733 76 23 algebra algebra NOUN cana-733 76 24 over over ADP cana-733 76 25 ๐’ณ ๐’ณ PROPN cana-733 76 26 , , PUNCT cana-733 76 27 if if SCONJ cana-733 76 28 ๐ผ ๐ผ PROPN cana-733 76 29 & & CCONJ cana-733 76 30 ๐’ฅ ๐’ฅ PROPN cana-733 76 31 are be AUX cana-733 76 32 disjoint disjoint ADJ cana-733 76 33 . . PUNCT cana-733 77 1 proof proof NOUN cana-733 77 2 : : PUNCT cana-733 77 3 we we PRON cana-733 77 4 can can AUX cana-733 77 5 write write VERB cana-733 77 6 ( ( PUNCT cana-733 77 7 ๏ฟฝ ๏ฟฝ PROPN cana-733 77 8 ฬŒ ฬŒ NUM cana-733 77 9 ๏ฟฝ ๏ฟฝ PROPN cana-733 77 10 , , PUNCT cana-733 77 11 ๐ผ ๐ผ PROPN cana-733 77 12 ) ) PUNCT cana-733 77 13 โˆชฬŒ โˆชฬŒ NOUN cana-733 78 1 ( ( PUNCT cana-733 78 2 ๏ฟฝ ๏ฟฝ PROPN cana-733 78 3 ฬŒ ฬŒ NUM cana-733 78 4 ๏ฟฝ ๏ฟฝ PROPN cana-733 78 5 , , PUNCT cana-733 78 6 ๐’ฅ ๐’ฅ PROPN cana-733 78 7 ) ) PUNCT cana-733 78 8 = = SYM cana-733 78 9 ( ( PUNCT cana-733 78 10 ๏ฟฝ ๏ฟฝ PROPN cana-733 78 11 ฬŒ ฬŒ NUM cana-733 78 12 ๏ฟฝ ๏ฟฝ PROPN cana-733 78 13 , , PUNCT cana-733 78 14 ๐’Ÿ ๐’Ÿ PROPN cana-733 78 15 ) ) PUNCT cana-733 79 1 where where SCONJ cana-733 79 2 ๐’Ÿ ๐’Ÿ NOUN cana-733 79 3 = = PUNCT cana-733 79 4 ๐ผ ๐ผ ADP cana-733 79 5 โˆช โˆช VERB cana-733 79 6 ๐’ฅ ๐’ฅ PROPN cana-733 79 7 and and CCONJ cana-733 79 8 for for ADP cana-733 79 9 all all DET cana-733 79 10 t t NOUN cana-733 79 11 โˆˆ โˆˆ PROPN cana-733 79 12 ๐’Ÿ ๐’Ÿ PROPN cana-733 79 13 ๏ฟฝ ๏ฟฝ PROPN cana-733 79 14 ฬŒ ฬŒ NUM cana-733 79 15 ๏ฟฝ ๏ฟฝ NOUN cana-733 79 16 [t [t X cana-733 79 17 ] ] X cana-733 79 18 = = SYM cana-733 79 19 { { PUNCT cana-733 79 20 ๏ฟฝ ๏ฟฝ PROPN cana-733 79 21 ฬŒ ฬŒ NUM cana-733 79 22 ๏ฟฝ ๏ฟฝ NOUN cana-733 79 23 [t [t X cana-733 79 24 ] ] X cana-733 79 25 โˆถ โˆถ NOUN cana-733 79 26 t t X cana-733 79 27 โˆˆ โˆˆ NOUN cana-733 79 28 ๐ผ ๐ผ ADP cana-733 79 29 โˆ– โˆ– PROPN cana-733 79 30 ๐’ฅ ๐’ฅ PROPN cana-733 79 31 ๏ฟฝ ๏ฟฝ PROPN cana-733 79 32 ฬŒ ฬŒ NUM cana-733 79 33 ๏ฟฝ ๏ฟฝ NOUN cana-733 79 34 [t [t X cana-733 79 35 ] ] X cana-733 79 36 โˆถ โˆถ NOUN cana-733 79 37 t t NOUN cana-733 79 38 โˆˆ โˆˆ PROPN cana-733 80 1 ๐’ฅ ๐’ฅ PROPN cana-733 80 2 โˆ– โˆ– X cana-733 81 1 ๐ผ ๐ผ ADP cana-733 81 2 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 3 ฬŒ ฬŒ NUM cana-733 81 4 ๏ฟฝ ๏ฟฝ NOUN cana-733 81 5 [t [t X cana-733 81 6 ] ] X cana-733 81 7 โˆฉ โˆฉ X cana-733 81 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 9 ฬŒ ฬŒ NUM cana-733 81 10 ๏ฟฝ ๏ฟฝ NOUN cana-733 81 11 [t [t X cana-733 81 12 ] ] X cana-733 81 13 โˆถ โˆถ NOUN cana-733 81 14 t t X cana-733 81 15 โˆˆ โˆˆ NOUN cana-733 81 16 ๐ผ ๐ผ ADP cana-733 81 17 โˆฉ โˆฉ ADJ cana-733 81 18 ๐’ฅ ๐’ฅ PROPN cana-733 81 19 } } PUNCT cana-733 81 20 since since SCONJ cana-733 81 21 ๐ผ ๐ผ ADP cana-733 81 22 โˆฉ โˆฉ NOUN cana-733 81 23 ๐’ฅ ๐’ฅ PROPN cana-733 81 24 = = SYM cana-733 81 25 ฯ• ฯ• PROPN cana-733 81 26 , , PUNCT cana-733 81 27 for for ADP cana-733 81 28 every every DET cana-733 81 29 u u PROPN cana-733 81 30 โˆˆ โˆˆ PROPN cana-733 81 31 ๐’Ÿ ๐’Ÿ PROPN cana-733 81 32 , , PUNCT cana-733 81 33 either either CCONJ cana-733 81 34 u u PROPN cana-733 81 35 โˆˆ โˆˆ PROPN cana-733 81 36 ๐ผ ๐ผ ADP cana-733 81 37 โˆ– โˆ– X cana-733 81 38 ๐’ฅ ๐’ฅ PROPN cana-733 81 39 ( ( PUNCT cana-733 81 40 or or CCONJ cana-733 81 41 ) ) PUNCT cana-733 81 42 u u NOUN cana-733 81 43 โˆˆ โˆˆ PROPN cana-733 81 44 ๐’ฅ ๐’ฅ PROPN cana-733 81 45 โˆ– โˆ– X cana-733 81 46 ๐ผ. ๐ผ. PROPN cana-733 81 47 because because SCONJ cana-733 81 48 ( ( PUNCT cana-733 81 49 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 50 ฬŒ ฬŒ NUM cana-733 81 51 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 52 , , PUNCT cana-733 81 53 ๐ผ ๐ผ PROPN cana-733 81 54 ) ) PUNCT cana-733 81 55 is be AUX cana-733 81 56 a a DET cana-733 81 57 fuzzy fuzzy ADJ cana-733 81 58 walgebra walgebra NOUN cana-733 81 59 over over ADP cana-733 81 60 ๐’ณ. ๐’ณ. PROPN cana-733 81 61 if if SCONJ cana-733 81 62 u u PROPN cana-733 81 63 โˆˆ โˆˆ NOUN cana-733 81 64 ๐ผ ๐ผ ADP cana-733 81 65 โˆ– โˆ– PROPN cana-733 81 66 ๐’ฅ ๐’ฅ PROPN cana-733 81 67 , , PUNCT cana-733 81 68 then then ADV cana-733 81 69 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 70 ฬŒ ฬŒ NUM cana-733 81 71 ๏ฟฝ ๏ฟฝ NOUN cana-733 81 72 (u (u NOUN cana-733 81 73 ) ) PUNCT cana-733 81 74 = = SYM cana-733 81 75 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 76 ฬŒ ฬŒ NUM cana-733 81 77 ๏ฟฝ ๏ฟฝ NOUN cana-733 81 78 (u (u NOUN cana-733 81 79 ) ) PUNCT cana-733 81 80 is be AUX cana-733 81 81 a a DET cana-733 81 82 fuzzy fuzzy ADJ cana-733 81 83 w w NOUN cana-733 81 84 - - NOUN cana-733 81 85 algebra algebra NOUN cana-733 81 86 in in ADP cana-733 81 87 a a DET cana-733 81 88 ๐’ณ. ๐’ณ. PROPN cana-733 81 89 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 90 ฬŒ ฬŒ NUM cana-733 81 91 ๏ฟฝ ๏ฟฝ NOUN cana-733 81 92 (u (u NOUN cana-733 81 93 ) ) PUNCT cana-733 81 94 = = SYM cana-733 81 95 ๏ฟฝ ๏ฟฝ PROPN cana-733 81 96 ฬŒ ฬŒ NUM cana-733 81 97 ๏ฟฝ ๏ฟฝ NOUN cana-733 81 98 (u (u NOUN cana-733 81 99 ) ) PUNCT cana-733 81 100 is be AUX cana-733 81 101 a a DET cana-733 81 102 fuzzy fuzzy ADJ cana-733 81 103 w w NOUN cana-733 81 104 - - NOUN cana-733 81 105 algebra algebra NOUN cana-733 81 106 in in ADP cana-733 81 107 a a DET cana-733 81 108 ๐’ณ ๐’ณ PROPN cana-733 81 109 , , PUNCT cana-733 82 1 if if SCONJ cana-733 82 2 u u PROPN cana-733 82 3 โˆˆ โˆˆ PROPN cana-733 82 4 ๐’ฅ ๐’ฅ PROPN cana-733 82 5 โˆ– โˆ– PUNCT cana-733 82 6 ๐ผ ๐ผ PROPN cana-733 82 7 , , PUNCT cana-733 82 8 for for ADP cana-733 82 9 ( ( PUNCT cana-733 82 10 ๏ฟฝ ๏ฟฝ PROPN cana-733 82 11 ฬŒ ฬŒ NUM cana-733 82 12 ๏ฟฝ ๏ฟฝ PROPN cana-733 82 13 , , PUNCT cana-733 82 14 ๐’ฅ ๐’ฅ PROPN cana-733 82 15 ) ) PUNCT cana-733 82 16 . . PUNCT cana-733 83 1 hence hence ADV cana-733 83 2 ( ( PUNCT cana-733 83 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 83 4 ฬŒ ฬŒ NUM cana-733 83 5 ๏ฟฝ ๏ฟฝ PROPN cana-733 83 6 , , PUNCT cana-733 83 7 ๐’Ÿ ๐’Ÿ PROPN cana-733 83 8 ) ) PUNCT cana-733 83 9 = = SYM cana-733 83 10 ( ( PUNCT cana-733 83 11 ๏ฟฝ ๏ฟฝ PROPN cana-733 83 12 ฬŒ ฬŒ NUM cana-733 83 13 ๏ฟฝ ๏ฟฝ PROPN cana-733 83 14 , , PUNCT cana-733 83 15 ๐ผ ๐ผ PROPN cana-733 83 16 ) ) PUNCT cana-733 83 17 โˆชฬŒ โˆชฬŒ NOUN cana-733 83 18 ( ( PUNCT cana-733 83 19 ๏ฟฝ ๏ฟฝ PROPN cana-733 83 20 ฬŒ ฬŒ NUM cana-733 83 21 ๏ฟฝ ๏ฟฝ PROPN cana-733 83 22 , , PUNCT cana-733 83 23 ๐’ฅ ๐’ฅ PROPN cana-733 83 24 ) ) PUNCT cana-733 83 25 is be AUX cana-733 83 26 a a DET cana-733 83 27 fuzzy fuzzy ADJ cana-733 83 28 w w NOUN cana-733 83 29 - - NOUN cana-733 83 30 algebra algebra NOUN cana-733 83 31 over over ADP cana-733 83 32 ๐’ณ. ๐’ณ. PROPN cana-733 83 33 if if SCONJ cana-733 83 34 ๐ผ ๐ผ PROPN cana-733 83 35 & & CCONJ cana-733 83 36 ๐’ฅ ๐’ฅ PROPN cana-733 83 37 are be AUX cana-733 83 38 not not PART cana-733 83 39 disjoint disjoint ADJ cana-733 83 40 , , PUNCT cana-733 83 41 theorem theorem VERB cana-733 83 42 3.12 3.12 NUM cana-733 83 43 is be AUX cana-733 83 44 not not PART cana-733 83 45 valid valid ADJ cana-733 83 46 as as ADP cana-733 83 47 the the DET cana-733 83 48 following following ADJ cana-733 83 49 example example NOUN cana-733 83 50 displays display NOUN cana-733 83 51 . . PUNCT cana-733 84 1 example example NOUN cana-733 84 2 3.13 3.13 NUM cana-733 84 3 : : PUNCT cana-733 84 4 let let VERB cana-733 84 5 โ„ณ โ„ณ PROPN cana-733 84 6 = = SYM cana-733 84 7 { { PUNCT cana-733 84 8 pink pink ADJ cana-733 84 9 , , PUNCT cana-733 84 10 gray gray ADJ cana-733 84 11 , , PUNCT cana-733 84 12 red red ADJ cana-733 84 13 , , PUNCT cana-733 84 14 olive olive NOUN cana-733 84 15 , , PUNCT cana-733 84 16 tan tan PROPN cana-733 84 17 } } PUNCT cana-733 84 18 be be AUX cana-733 84 19 a a DET cana-733 84 20 universe universe NOUN cana-733 84 21 , , PUNCT cana-733 84 22 and and CCONJ cana-733 84 23 determine determine NOUN cana-733 84 24 of of ADP cana-733 84 25 a a DET cana-733 84 26 soft soft ADJ cana-733 84 27 engine engine NOUN cana-733 84 28 โŸ โŸ NOUN cana-733 84 29 that that PRON cana-733 84 30 generates generate VERB cana-733 84 31 the the DET cana-733 84 32 items item NOUN cana-733 84 33 listed list VERB cana-733 84 34 below below ADV cana-733 84 35 . . PUNCT cana-733 85 1 communications communication NOUN cana-733 85 2 on on ADP cana-733 85 3 applied apply VERB cana-733 85 4 nonlinear nonlinear ADJ cana-733 85 5 analysis analysis NOUN cana-733 85 6 issn issn NOUN cana-733 85 7 : : PUNCT cana-733 85 8 1074 1074 NUM cana-733 85 9 - - PUNCT cana-733 85 10 133x 133x NUM cana-733 85 11 vol vol NOUN cana-733 85 12 31 31 NUM cana-733 85 13 no no NOUN cana-733 85 14 . . PUNCT cana-733 86 1 3s 3s NUM cana-733 86 2 ( ( PUNCT cana-733 86 3 2024 2024 NUM cana-733 86 4 ) ) PUNCT cana-733 86 5 87 87 NUM cana-733 86 6 https://internationalpubls.com https://internationalpubls.com X cana-733 86 7 pink pink ADJ cana-733 86 8 โŸ โŸ NOUN cana-733 86 9 ฯฑ ฯฑ X cana-733 86 10 = = PUNCT cana-733 86 11 { { PUNCT cana-733 86 12 pink pink ADJ cana-733 86 13 โˆถ โˆถ NOUN cana-733 86 14 ฯฑ ฯฑ ADP cana-733 86 15 โˆˆ โˆˆ PROPN cana-733 86 16 { { PUNCT cana-733 86 17 pink pink ADJ cana-733 86 18 , , PUNCT cana-733 86 19 gray gray ADJ cana-733 86 20 } } PUNCT cana-733 86 21 red red ADJ cana-733 86 22 โˆถ โˆถ PROPN cana-733 86 23 ฯฑ ฯฑ X cana-733 86 24 = = SYM cana-733 86 25 red red ADJ cana-733 86 26 olive olive PROPN cana-733 86 27 โˆถ โˆถ PROPN cana-733 86 28 ฯฑ ฯฑ NOUN cana-733 86 29 = = ADJ cana-733 86 30 olive olive NOUN cana-733 86 31 tan tan PROPN cana-733 86 32 โˆถ โˆถ PROPN cana-733 86 33 ฯฑ ฯฑ ADP cana-733 86 34 = = ADJ cana-733 86 35 tan tan ADJ cana-733 86 36 } } PUNCT cana-733 86 37 gray gray PROPN cana-733 86 38 โŸ โŸ NOUN cana-733 86 39 ฯ‚ ฯ‚ X cana-733 86 40 = = PUNCT cana-733 86 41 { { PUNCT cana-733 86 42 gray gray ADJ cana-733 86 43 โˆถ โˆถ NOUN cana-733 86 44 ฯ‚ ฯ‚ X cana-733 87 1 = = PUNCT cana-733 87 2 pink pink ADV cana-733 87 3 pink pink ADJ cana-733 87 4 โˆถ โˆถ NOUN cana-733 87 5 ฯ‚ ฯ‚ NOUN cana-733 87 6 = = NOUN cana-733 87 7 gray gray ADJ cana-733 87 8 red red ADJ cana-733 87 9 โˆถ โˆถ PROPN cana-733 87 10 ฯ‚ ฯ‚ PROPN cana-733 87 11 = = ADJ cana-733 87 12 red red ADJ cana-733 87 13 olive olive PROPN cana-733 87 14 โˆถ โˆถ PROPN cana-733 87 15 ฯ‚ ฯ‚ PROPN cana-733 88 1 = = PUNCT cana-733 88 2 olive olive PROPN cana-733 88 3 tan tan PROPN cana-733 88 4 โˆถ โˆถ NOUN cana-733 88 5 ฯ‚ ฯ‚ PROPN cana-733 88 6 = = ADJ cana-733 88 7 tan tan PROPN cana-733 88 8 } } PUNCT cana-733 88 9 red red PROPN cana-733 88 10 โŸ โŸ PROPN cana-733 88 11 z z NOUN cana-733 88 12 = = NOUN cana-733 88 13 { { PUNCT cana-733 88 14 pink pink ADJ cana-733 88 15 โˆถ โˆถ NOUN cana-733 88 16 z z NOUN cana-733 88 17 = = SYM cana-733 88 18 red red ADJ cana-733 88 19 red red PROPN cana-733 88 20 โˆถ โˆถ PROPN cana-733 88 21 z z PROPN cana-733 88 22 โˆˆ โˆˆ PROPN cana-733 88 23 { { PUNCT cana-733 88 24 pink pink ADJ cana-733 88 25 , , PUNCT cana-733 88 26 gray gray ADJ cana-733 88 27 } } PUNCT cana-733 88 28 tan tan NOUN cana-733 88 29 โˆถ โˆถ NOUN cana-733 88 30 z z NOUN cana-733 89 1 = = PUNCT cana-733 89 2 olive olive ADJ cana-733 89 3 olive olive NOUN cana-733 89 4 โˆถ โˆถ PROPN cana-733 89 5 z z PROPN cana-733 90 1 = = SYM cana-733 90 2 tan tan ADJ cana-733 90 3 } } PUNCT cana-733 90 4 olive olive NOUN cana-733 90 5 โŸ โŸ NOUN cana-733 90 6 u u NOUN cana-733 90 7 = = PUNCT cana-733 90 8 { { PUNCT cana-733 90 9 pink pink ADJ cana-733 90 10 โˆถ โˆถ NOUN cana-733 90 11 u u X cana-733 90 12 = = NOUN cana-733 90 13 olive olive ADJ cana-733 90 14 olive olive PROPN cana-733 90 15 โˆถ โˆถ PROPN cana-733 90 16 u u X cana-733 90 17 โˆˆ โˆˆ PROPN cana-733 90 18 { { PUNCT cana-733 90 19 pink pink ADJ cana-733 90 20 , , PUNCT cana-733 90 21 tan tan PROPN cana-733 90 22 } } PUNCT cana-733 90 23 tan tan PROPN cana-733 90 24 โˆถ โˆถ NOUN cana-733 90 25 u u X cana-733 90 26 = = ADJ cana-733 90 27 red red ADJ cana-733 90 28 red red PROPN cana-733 90 29 โˆถ โˆถ PROPN cana-733 90 30 u u X cana-733 90 31 = = PROPN cana-733 90 32 tan tan PROPN cana-733 90 33 } } PUNCT cana-733 90 34 tan tan PROPN cana-733 90 35 โŸ โŸ PROPN cana-733 90 36 v v NOUN cana-733 90 37 = = PUNCT cana-733 90 38 { { PUNCT cana-733 90 39 pink pink ADJ cana-733 90 40 โˆถ โˆถ NOUN cana-733 90 41 v v ADP cana-733 90 42 = = PUNCT cana-733 90 43 tan tan ADJ cana-733 90 44 red red ADJ cana-733 90 45 โˆถ โˆถ PROPN cana-733 90 46 v v NOUN cana-733 90 47 = = NOUN cana-733 90 48 olive olive NOUN cana-733 90 49 olive olive NOUN cana-733 90 50 โˆถ โˆถ PROPN cana-733 90 51 v v ADP cana-733 90 52 = = SYM cana-733 90 53 red red ADJ cana-733 90 54 tan tan PROPN cana-733 90 55 โˆถ โˆถ PROPN cana-733 90 56 v v ADP cana-733 90 57 โˆˆ โˆˆ NOUN cana-733 90 58 { { PUNCT cana-733 90 59 pink pink ADJ cana-733 90 60 , , PUNCT cana-733 90 61 tan tan PROPN cana-733 90 62 } } PUNCT cana-733 90 63 } } PUNCT cana-733 90 64 then then ADV cana-733 90 65 ( ( PUNCT cana-733 90 66 โ„ณ โ„ณ PROPN cana-733 90 67 , , PUNCT cana-733 90 68 โŸ โŸ NOUN cana-733 90 69 , , PUNCT cana-733 90 70 pink pink ADJ cana-733 90 71 ) ) PUNCT cana-733 90 72 is be AUX cana-733 90 73 a a DET cana-733 90 74 w w NOUN cana-733 90 75 - - PUNCT cana-733 90 76 algebra algebra NOUN cana-733 90 77 , , PUNCT cana-733 90 78 define define VERB cana-733 90 79 ๐ผ ๐ผ PROPN cana-733 90 80 & & CCONJ cana-733 90 81 ๐’ฅ ๐’ฅ PROPN cana-733 90 82 as as ADP cana-733 90 83 , , PUNCT cana-733 90 84 ๐ผ ๐ผ PROPN cana-733 90 85 = = PUNCT cana-733 90 86 { { PUNCT cana-733 90 87 glorious glorious ADJ cana-733 90 88 , , PUNCT cana-733 90 89 elegant elegant ADJ cana-733 90 90 , , PUNCT cana-733 90 91 modest modest ADJ cana-733 90 92 , , PUNCT cana-733 90 93 clever clever ADJ cana-733 90 94 } } PUNCT cana-733 90 95 ๐’ฅ ๐’ฅ PROPN cana-733 90 96 = = X cana-733 90 97 { { PUNCT cana-733 90 98 modest modest ADJ cana-733 90 99 , , PUNCT cana-733 90 100 clever clever ADJ cana-733 90 101 , , PUNCT cana-733 90 102 gentle gentle ADJ cana-733 90 103 } } PUNCT cana-733 90 104 ๐ผ ๐ผ PROPN cana-733 90 105 and and CCONJ cana-733 90 106 ๐’ฅ ๐’ฅ PRON cana-733 90 107 are be AUX cana-733 90 108 therefore therefore ADV cana-733 90 109 not not PART cana-733 90 110 disjoint disjoint VERB cana-733 90 111 . . PUNCT cana-733 91 1 if if SCONJ cana-733 91 2 ( ( PUNCT cana-733 91 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 4 ฬŒ ฬŒ NUM cana-733 91 5 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 6 , , PUNCT cana-733 91 7 ๐ผ ๐ผ PROPN cana-733 91 8 ) ) PUNCT cana-733 91 9 be be VERB cana-733 91 10 a a DET cana-733 91 11 fs fs NOUN cana-733 91 12 - - PUNCT cana-733 91 13 set set VERB cana-733 91 14 over over ADP cana-733 91 15 โ„ณ โ„ณ PROPN cana-733 91 16 , , PUNCT cana-733 91 17 then then ADV cana-733 91 18 fuzzy fuzzy ADJ cana-733 91 19 sets set NOUN cana-733 91 20 in in ADP cana-733 91 21 โ„ณ โ„ณ PROPN cana-733 91 22 include include VERB cana-733 91 23 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 24 ฬŒ ฬŒ NUM cana-733 91 25 ๏ฟฝ ๏ฟฝ NOUN cana-733 91 26 [glorious [glorious X cana-733 91 27 ] ] X cana-733 91 28 , , PUNCT cana-733 91 29 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 30 ฬŒ ฬŒ NUM cana-733 91 31 ๏ฟฝ ๏ฟฝ NOUN cana-733 91 32 [elegant [elegant X cana-733 91 33 ] ] X cana-733 91 34 , , PUNCT cana-733 91 35 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 36 ฬŒ ฬŒ NUM cana-733 91 37 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 38 [modest [modest X cana-733 91 39 ] ] PUNCT cana-733 91 40 & & CCONJ cana-733 91 41 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 42 ฬŒ ฬŒ NUM cana-733 91 43 ๏ฟฝ ๏ฟฝ PROPN cana-733 91 44 [clever [clever X cana-733 91 45 ] ] PUNCT cana-733 91 46 . . PUNCT cana-733 92 1 then then ADV cana-733 92 2 , , PUNCT cana-733 92 3 define define VERB cana-733 92 4 as as ADP cana-733 92 5 : : PUNCT cana-733 92 6 ๏ฟฝ ๏ฟฝ PROPN cana-733 92 7 ฬŒ ฬŒ NUM cana-733 92 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 92 9 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 92 10 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 92 11 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ PROPN cana-733 92 12 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ PROPN cana-733 92 13 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 92 14 ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  ๐‘”๐‘™๐‘œ๐‘Ÿ๐‘–๐‘œ๐‘ข๐‘  NOUN cana-733 92 15 0.8 0.8 NUM cana-733 92 16 0.7 0.7 NUM cana-733 92 17 0.4 0.4 NUM cana-733 92 18 0.4 0.4 NUM cana-733 92 19 0.4 0.4 NUM cana-733 92 20 ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก ๐‘’๐‘™๐‘’๐‘”๐‘Ž๐‘›๐‘ก NOUN cana-733 92 21 0.7 0.7 NUM cana-733 92 22 0.6 0.6 NUM cana-733 92 23 0.5 0.5 NUM cana-733 92 24 0.3 0.3 NUM cana-733 92 25 0.3 0.3 NUM cana-733 92 26 ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก NOUN cana-733 92 27 0.9 0.9 NUM cana-733 92 28 0.6 0.6 NUM cana-733 92 29 0.2 0.2 NUM cana-733 92 30 0.4 0.4 NUM cana-733 92 31 0.2 0.2 NUM cana-733 92 32 ๐‘๐‘™๐‘’๐‘ฃ๐‘’๐‘Ÿ ๐‘๐‘™๐‘’๐‘ฃ๐‘’๐‘Ÿ NOUN cana-733 92 33 0.6 0.6 NUM cana-733 92 34 0.6 0.6 NUM cana-733 92 35 0.3 0.3 NUM cana-733 92 36 0.3 0.3 NUM cana-733 92 37 0.5 0.5 NUM cana-733 92 38 then then ADV cana-733 92 39 a a DET cana-733 92 40 fs fs PROPN cana-733 92 41 - - PUNCT cana-733 92 42 w w NOUN cana-733 92 43 - - PUNCT cana-733 92 44 algebra algebra NOUN cana-733 92 45 over over ADP cana-733 92 46 โ„ณ โ„ณ PROPN cana-733 92 47 is be AUX cana-733 92 48 ( ( PUNCT cana-733 92 49 ๏ฟฝ ๏ฟฝ PROPN cana-733 92 50 ฬŒ ฬŒ NUM cana-733 92 51 ๏ฟฝ ๏ฟฝ PROPN cana-733 92 52 , , PUNCT cana-733 92 53 ๐ผ ๐ผ PROPN cana-733 92 54 ) ) PUNCT cana-733 92 55 . . PUNCT cana-733 93 1 if if SCONJ cana-733 93 2 ( ( PUNCT cana-733 93 3 ๏ฟฝ ๏ฟฝ PROPN cana-733 93 4 ฬŒ ฬŒ NUM cana-733 93 5 ๏ฟฝ ๏ฟฝ PROPN cana-733 93 6 , , PUNCT cana-733 93 7 ๐’ฅ ๐’ฅ PROPN cana-733 93 8 ) ) PUNCT cana-733 93 9 be be AUX cana-733 93 10 a a DET cana-733 93 11 fs fs PROPN cana-733 93 12 - - PUNCT cana-733 93 13 w w NOUN cana-733 93 14 - - PUNCT cana-733 93 15 algebra algebra NOUN cana-733 93 16 over over ADP cana-733 93 17 โ„ณ โ„ณ PROPN cana-733 93 18 , , PUNCT cana-733 93 19 then then ADV cana-733 93 20 the the DET cana-733 93 21 fuzzy fuzzy ADJ cana-733 93 22 sets set NOUN cana-733 93 23 in in ADP cana-733 93 24 โ„ณ โ„ณ PROPN cana-733 93 25 ๏ฟฝ ๏ฟฝ PROPN cana-733 93 26 ฬŒ ฬŒ NUM cana-733 93 27 ๏ฟฝ ๏ฟฝ NOUN cana-733 93 28 [modest [modest X cana-733 93 29 ] ] X cana-733 93 30 , , PUNCT cana-733 93 31 ๏ฟฝ ๏ฟฝ PROPN cana-733 93 32 ฬŒ ฬŒ NUM cana-733 93 33 ๏ฟฝ ๏ฟฝ PROPN cana-733 93 34 [clever [clever X cana-733 93 35 ] ] PUNCT cana-733 93 36 and and CCONJ cana-733 93 37 ๏ฟฝ ๏ฟฝ PROPN cana-733 93 38 ฬŒ ฬŒ NUM cana-733 93 39 ๏ฟฝ ๏ฟฝ NOUN cana-733 93 40 [gentle [gentle NOUN cana-733 93 41 ] ] X cana-733 93 42 . . PUNCT cana-733 94 1 here here ADV cana-733 94 2 is be AUX cana-733 94 3 how how SCONJ cana-733 94 4 we we PRON cana-733 94 5 define define VERB cana-733 94 6 them they PRON cana-733 94 7 : : PUNCT cana-733 94 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 94 9 ฬŒ ฬŒ NUM cana-733 94 10 ๏ฟฝ ๏ฟฝ PROPN cana-733 94 11 ๐‘๐‘–๐‘›๐‘˜ ๐‘๐‘–๐‘›๐‘˜ PROPN cana-733 94 12 ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ ๐‘”๐‘Ÿ๐‘Ž๐‘ฆ PROPN cana-733 94 13 ๐‘Ÿ๐‘’๐‘‘ ๐‘Ÿ๐‘’๐‘‘ PROPN cana-733 94 14 ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ ๐‘œ๐‘™๐‘–๐‘ฃ๐‘’ PROPN cana-733 94 15 ๐‘ก๐‘Ž๐‘› ๐‘ก๐‘Ž๐‘› NOUN cana-733 94 16 ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก ๐‘š๐‘œ๐‘‘๐‘’๐‘ ๐‘ก VERB cana-733 94 17 0.7 0.7 NUM cana-733 94 18 0.6 0.6 NUM cana-733 94 19 0.4 0.4 NUM cana-733 94 20 0.2 0.2 NUM cana-733 94 21 0.2 0.2 NUM cana-733 94 22 ๐‘๐‘™๐‘’๐‘ฃ๐‘’๐‘Ÿ ๐‘๐‘™๐‘’๐‘ฃ๐‘’๐‘Ÿ ADP cana-733 94 23 0.6 0.6 NUM cana-733 94 24 0.6 0.6 NUM cana-733 94 25 0.4 0.4 NUM cana-733 94 26 0.4 0.4 NUM cana-733 94 27 0.6 0.6 NUM cana-733 94 28 ๐‘”๐‘’๐‘›๐‘ก๐‘™๐‘’ ๐‘”๐‘’๐‘›๐‘ก๐‘™๐‘’ NOUN cana-733 94 29 0.8 0.8 NUM cana-733 94 30 0.5 0.5 NUM cana-733 94 31 0.3 0.3 NUM cana-733 94 32 0.5 0.5 NUM cana-733 94 33 0.3 0.3 NUM cana-733 94 34 communications communication NOUN cana-733 94 35 on on ADP cana-733 94 36 applied apply VERB cana-733 94 37 nonlinear nonlinear ADJ cana-733 94 38 analysis analysis NOUN cana-733 94 39 issn issn NOUN cana-733 94 40 : : PUNCT cana-733 94 41 1074 1074 NUM cana-733 94 42 - - PUNCT cana-733 94 43 133x 133x NUM cana-733 94 44 vol vol NOUN cana-733 94 45 31 31 NUM cana-733 94 46 no no NOUN cana-733 94 47 . . PUNCT cana-733 95 1 3s 3s NUM cana-733 95 2 ( ( PUNCT cana-733 95 3 2024 2024 NUM cana-733 95 4 ) ) PUNCT cana-733 95 5 88 88 NUM cana-733 95 6 https://internationalpubls.com https://internationalpubls.com X cana-733 95 7 hence hence ADV cana-733 95 8 , , PUNCT cana-733 95 9 a a DET cana-733 95 10 fs fs PROPN cana-733 95 11 - - PUNCT cana-733 95 12 w w NOUN cana-733 95 13 - - PUNCT cana-733 95 14 algebra algebra NOUN cana-733 95 15 over over ADP cana-733 95 16 โ„ณ โ„ณ PROPN cana-733 95 17 is be AUX cana-733 95 18 ( ( PUNCT cana-733 95 19 ๏ฟฝ ๏ฟฝ PROPN cana-733 95 20 ฬŒ ฬŒ NUM cana-733 95 21 ๏ฟฝ ๏ฟฝ PROPN cana-733 95 22 , , PUNCT cana-733 95 23 ๐’ฅ ๐’ฅ PROPN cana-733 95 24 ) ) PUNCT cana-733 95 25 . . PUNCT cana-733 96 1 however however ADV cana-733 96 2 , , PUNCT cana-733 96 3 the the DET cana-733 96 4 union union NOUN cana-733 96 5 ( ( PUNCT cana-733 96 6 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 7 ฬŒ ฬŒ NUM cana-733 96 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 9 , , PUNCT cana-733 96 10 ๐ผ ๐ผ PROPN cana-733 96 11 ) ) PUNCT cana-733 96 12 โˆช โˆช NOUN cana-733 96 13 ( ( PUNCT cana-733 96 14 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 15 ฬŒ ฬŒ NUM cana-733 96 16 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 17 , , PUNCT cana-733 96 18 ๐’ฅ ๐’ฅ PROPN cana-733 96 19 ) ) PUNCT cana-733 96 20 is be AUX cana-733 96 21 not not PART cana-733 96 22 a a DET cana-733 96 23 fs fs VERB cana-733 96 24 - - PUNCT cana-733 96 25 w w NOUN cana-733 96 26 - - PUNCT cana-733 96 27 algebra algebra NOUN cana-733 96 28 over over ADP cana-733 96 29 โ„ณ. โ„ณ. PROPN cana-733 96 30 ( ( PUNCT cana-733 96 31 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 32 ฬŒ ฬŒ NUM cana-733 96 33 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 34 [modest [modest X cana-733 96 35 ] ] X cana-733 96 36 โˆช โˆช ADP cana-733 96 37 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 38 ฬŒ ฬŒ NUM cana-733 96 39 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 40 [modest])(olive [modest])(olive X cana-733 96 41 โŸ โŸ X cana-733 96 42 red red NOUN cana-733 96 43 ) ) PUNCT cana-733 96 44 = = PRON cana-733 96 45 ( ( PUNCT cana-733 96 46 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 47 ฬŒ ฬŒ NUM cana-733 96 48 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 49 [modest [modest X cana-733 96 50 ] ] X cana-733 96 51 โˆช โˆช ADP cana-733 96 52 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 53 ฬŒ ฬŒ NUM cana-733 96 54 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 55 [modest])(tan [modest])(tan NOUN cana-733 96 56 ) ) PUNCT cana-733 96 57 = = SYM cana-733 96 58 max{ max{ ADJ cana-733 96 59 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 60 ฬŒ ฬŒ NUM cana-733 96 61 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 62 modest](tan modest](tan NOUN cana-733 96 63 ) ) PUNCT cana-733 96 64 , , PUNCT cana-733 96 65 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 66 ฬŒ ฬŒ NUM cana-733 96 67 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 68 [modest](tan)}=0.2 [modest](tan)}=0.2 NOUN cana-733 96 69 and and CCONJ cana-733 96 70 min{( min{( PROPN cana-733 96 71 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 72 ฬŒ ฬŒ NUM cana-733 96 73 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 74 [modest [modest X cana-733 96 75 ] ] X cana-733 96 76 โˆช โˆช ADP cana-733 96 77 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 78 ฬŒ ฬŒ NUM cana-733 96 79 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 80 [modest])(olive [modest])(olive NOUN cana-733 96 81 ) ) PUNCT cana-733 96 82 , , PUNCT cana-733 96 83 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 84 ฬŒ ฬŒ NUM cana-733 96 85 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 86 [modest [modest X cana-733 96 87 ] ] X cana-733 96 88 โˆช โˆช ADP cana-733 96 89 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 90 ฬŒ ฬŒ NUM cana-733 96 91 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 92 [modest])(red [modest])(re VERB cana-733 96 93 ) ) PUNCT cana-733 96 94 } } PUNCT cana-733 96 95 = = SYM cana-733 96 96 min{max{ min{max{ PROPN cana-733 96 97 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 98 ฬŒ ฬŒ NUM cana-733 96 99 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 100 [modest [modest X cana-733 96 101 ] ] X cana-733 96 102 ( ( PUNCT cana-733 96 103 olive olive NOUN cana-733 96 104 ) ) PUNCT cana-733 96 105 , , PUNCT cana-733 96 106 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 107 ฬŒ ฬŒ NUM cana-733 96 108 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 109 [modest])(olive [modest])(olive NOUN cana-733 96 110 ) ) PUNCT cana-733 96 111 } } PUNCT cana-733 96 112 , , PUNCT cana-733 96 113 max{ max{ PROPN cana-733 96 114 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 115 ฬŒ ฬŒ NUM cana-733 96 116 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 117 [modest [modest X cana-733 96 118 ] ] X cana-733 96 119 ( ( PUNCT cana-733 96 120 red red PROPN cana-733 96 121 ) ) PUNCT cana-733 96 122 , , PUNCT cana-733 96 123 ๏ฟฝ ๏ฟฝ PROPN cana-733 96 124 ฬŒ ฬŒ NUM cana-733 96 125 ๏ฟฝ ๏ฟฝ NOUN cana-733 96 126 [modest](red [modest](re VERB cana-733 96 127 ) ) PUNCT cana-733 96 128 } } PUNCT cana-733 96 129 } } PUNCT cana-733 96 130 = = SYM cana-733 96 131 min min NOUN cana-733 96 132 { { PUNCT cana-733 96 133 max{0.4 max{0.4 PROPN cana-733 96 134 , , PUNCT cana-733 96 135 0.2 0.2 NUM cana-733 96 136 } } PUNCT cana-733 96 137 , , PUNCT cana-733 96 138 max{0.2 max{0.2 PROPN cana-733 96 139 , , PUNCT cana-733 96 140 0.4 0.4 NUM cana-733 96 141 } } PUNCT cana-733 96 142 } } PUNCT cana-733 96 143 = = PUNCT cana-733 96 144 0.4 0.4 NUM cana-733 96 145 . . PUNCT cana-733 97 1 definition definition NOUN cana-733 97 2 3.14 3.14 NUM cana-733 97 3 . . PUNCT cana-733 98 1 a a DET cana-733 98 2 fs fs NOUN cana-733 98 3 - - PUNCT cana-733 98 4 set set ADJ cana-733 98 5 ( ( PUNCT cana-733 98 6 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 7 ฬŒ ฬŒ NUM cana-733 98 8 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 9 , , PUNCT cana-733 98 10 ๐ผ ๐ผ PROPN cana-733 98 11 ) ) PUNCT cana-733 98 12 over over ADP cana-733 98 13 a a DET cana-733 98 14 w w NOUN cana-733 98 15 - - PUNCT cana-733 98 16 algebra algebra ADJ cana-733 98 17 โ„ณ. โ„ณ. PROPN cana-733 98 18 ( ( PUNCT cana-733 98 19 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 20 ฬŒ ฬŒ NUM cana-733 98 21 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 22 , , PUNCT cana-733 98 23 ๐ผ ๐ผ PROPN cana-733 98 24 ) ) PUNCT cana-733 98 25 is be AUX cana-733 98 26 a a DET cana-733 98 27 fs fs NOUN cana-733 98 28 - - PUNCT cana-733 98 29 ideal ideal NOUN cana-733 98 30 of of ADP cana-733 98 31 โ„ณ โ„ณ PROPN cana-733 98 32 based base VERB cana-733 98 33 on on ADP cana-733 98 34 a a DET cana-733 98 35 parameter parameter NOUN cana-733 98 36 u u NOUN cana-733 98 37 , , PUNCT cana-733 98 38 if if SCONJ cana-733 98 39 there there PRON cana-733 98 40 exists exist VERB cana-733 98 41 a a DET cana-733 98 42 parameter parameter NOUN cana-733 98 43 u u NOUN cana-733 98 44 โˆˆ โˆˆ PROPN cana-733 98 45 ๐ผ ๐ผ ADP cana-733 98 46 such such ADJ cana-733 98 47 that that DET cana-733 98 48 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 49 ฬŒ ฬŒ NUM cana-733 98 50 ๏ฟฝ ๏ฟฝ NOUN cana-733 98 51 [u [u X cana-733 98 52 ] ] X cana-733 98 53 is be AUX cana-733 98 54 a a DET cana-733 98 55 fuzzy fuzzy ADJ cana-733 98 56 ideal ideal NOUN cana-733 98 57 of of ADP cana-733 98 58 โ„ณ. โ„ณ. PROPN cana-733 98 59 we we PRON cana-733 98 60 say say VERB cana-733 98 61 that that SCONJ cana-733 98 62 ( ( PUNCT cana-733 98 63 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 64 ฬŒ ฬŒ NUM cana-733 98 65 ๏ฟฝ ๏ฟฝ PROPN cana-733 98 66 , , PUNCT cana-733 98 67 ๐ผ ๐ผ PROPN cana-733 98 68 ) ) PUNCT cana-733 98 69 is be AUX cana-733 98 70 a a DET cana-733 98 71 fs fs X cana-733 98 72 ideal ideal NOUN cana-733 98 73 of of ADP cana-733 98 74 โ„ณ โ„ณ PROPN cana-733 98 75 if if SCONJ cana-733 98 76 and and CCONJ cana-733 98 77 only only ADV cana-733 98 78 if if SCONJ cana-733 98 79 it it PRON cana-733 98 80 is be AUX cana-733 98 81 based base VERB cana-733 98 82 on on ADP cana-733 98 83 all all DET cana-733 98 84 parameters parameter NOUN cana-733 98 85 . . PUNCT cana-733 99 1 example example NOUN cana-733 100 1 3.15 3.15 NUM cana-733 100 2 . . PUNCT cana-733 101 1 let let VERB cana-733 101 2 โ„ณ โ„ณ PROPN cana-733 101 3 = = SYM cana-733 101 4 { { PUNCT cana-733 101 5 guava guava NOUN cana-733 101 6 , , PUNCT cana-733 101 7 mango mango NOUN cana-733 101 8 , , PUNCT cana-733 101 9 beetroot beetroot NOUN cana-733 101 10 , , PUNCT cana-733 101 11 plum plum NOUN cana-733 101 12 , , PUNCT cana-733 101 13 turnip turnip NOUN cana-733 101 14 } } PUNCT cana-733 101 15 be be AUX cana-733 101 16 a a DET cana-733 101 17 universe universe NOUN cana-733 101 18 , , PUNCT cana-733 101 19 and and CCONJ cana-733 101 20 look look VERB cana-733 101 21 at at ADP cana-733 101 22 a a DET cana-733 101 23 soft soft ADJ cana-733 101 24 machine machine NOUN cana-733 101 25 that that PRON cana-733 101 26 produces produce VERB cana-733 101 27 the the DET cana-733 101 28 items item NOUN cana-733 101 29 listed list VERB cana-733 101 30 below below ADV cana-733 101 31 . . PUNCT cana-733 102 1 guava guava PROPN cana-733 102 2 โ‹” โ‹” PROPN cana-733 102 3 ฯฑ ฯฑ PROPN cana-733 102 4 = = X cana-733 102 5 guava guava NOUN cana-733 102 6 for for ADP cana-733 102 7 all all PRON cana-733 102 8 ฯฑ ฯฑ PROPN cana-733 102 9 โˆˆ โˆˆ PROPN cana-733 102 10 โ„ณ โ„ณ PROPN cana-733 102 11 , , PUNCT cana-733 102 12 mango mango NOUN cana-733 102 13 โ‹” โ‹” PROPN cana-733 102 14 ฯ‚ ฯ‚ PROPN cana-733 102 15 = = PUNCT cana-733 102 16 { { PUNCT cana-733 102 17 guava guava NOUN cana-733 102 18 โˆถ โˆถ NOUN cana-733 102 19 ฯ‚ ฯ‚ PROPN cana-733 102 20 โˆˆ โˆˆ PROPN cana-733 102 21 { { PUNCT cana-733 102 22 mango mango NOUN cana-733 102 23 , , PUNCT cana-733 102 24 plum plum NOUN cana-733 102 25 , , PUNCT cana-733 102 26 turnip turnip NOUN cana-733 102 27 } } PUNCT cana-733 102 28 banana banana NOUN cana-733 102 29 โˆถ โˆถ NOUN cana-733 102 30 ฯ‚ ฯ‚ X cana-733 102 31 โˆˆ โˆˆ PROPN cana-733 102 32 { { PUNCT cana-733 102 33 guava guava NOUN cana-733 102 34 , , PUNCT cana-733 102 35 beetroot beetroot NOUN cana-733 102 36 } } PUNCT cana-733 102 37 } } PUNCT cana-733 102 38 carrot carrot NOUN cana-733 102 39 โ‹” โ‹” NOUN cana-733 102 40 z z NOUN cana-733 102 41 = = PRON cana-733 102 42 { { PUNCT cana-733 102 43 beetroot beetroot NOUN cana-733 102 44 โˆถ โˆถ PROPN cana-733 102 45 z z X cana-733 102 46 โˆˆ โˆˆ PROPN cana-733 102 47 { { PUNCT cana-733 102 48 guava guava NOUN cana-733 102 49 , , PUNCT cana-733 102 50 mango mango NOUN cana-733 102 51 , , PUNCT cana-733 102 52 turnip turnip NOUN cana-733 102 53 } } PUNCT cana-733 102 54 guava guava NOUN cana-733 102 55 โˆถ โˆถ PROPN cana-733 102 56 z z PROPN cana-733 102 57 โˆˆ โˆˆ PROPN cana-733 102 58 { { PUNCT cana-733 102 59 beetroot beetroot NOUN cana-733 102 60 , , PUNCT cana-733 102 61 plum plum NOUN cana-733 102 62 } } PUNCT cana-733 102 63 } } PUNCT cana-733 103 1 plum plum NOUN cana-733 103 2 โ‹” โ‹” VERB cana-733 103 3 u u NOUN cana-733 103 4 = = PUNCT cana-733 103 5 { { PUNCT cana-733 103 6 plum plum NOUN cana-733 103 7 โˆถ โˆถ NOUN cana-733 103 8 u u X cana-733 103 9 = = PROPN cana-733 103 10 guava guava NOUN cana-733 103 11 , , PUNCT cana-733 103 12 mango mango PROPN cana-733 103 13 โˆถ โˆถ PROPN cana-733 103 14 u u X cana-733 103 15 = = NOUN cana-733 103 16 beetroot beetroot NOUN cana-733 103 17 , , PUNCT cana-733 103 18 guava guava NOUN cana-733 103 19 โˆถ โˆถ PROPN cana-733 103 20 u u X cana-733 103 21 = = NOUN cana-733 103 22 plum plum NOUN cana-733 103 23 , , PUNCT cana-733 103 24 beetroot beetroot NOUN cana-733 103 25 : : PUNCT cana-733 103 26 u u PROPN cana-733 103 27 โˆˆ โˆˆ PROPN cana-733 103 28 { { PUNCT cana-733 103 29 mango mango NOUN cana-733 103 30 , , PUNCT cana-733 103 31 turnip turnip NOUN cana-733 103 32 } } PUNCT cana-733 103 33 } } PUNCT cana-733 103 34 turnip turnip NOUN cana-733 103 35 โ‹” โ‹” VERB cana-733 103 36 v v NOUN cana-733 103 37 = = PUNCT cana-733 103 38 { { PUNCT cana-733 103 39 guava guava NOUN cana-733 103 40 โˆถ โˆถ NOUN cana-733 103 41 v v X cana-733 103 42 = = SYM cana-733 103 43 turnip turnip NOUN cana-733 103 44 , , PUNCT cana-733 103 45 turnip turnip NOUN cana-733 103 46 โˆถ โˆถ NOUN cana-733 103 47 v v ADP cana-733 103 48 โˆˆ โˆˆ PROPN cana-733 103 49 { { PUNCT cana-733 103 50 guava guava NOUN cana-733 103 51 , , PUNCT cana-733 103 52 beetroot beetroot NOUN cana-733 103 53 } } PUNCT cana-733 103 54 mango mango NOUN cana-733 103 55 โˆถ โˆถ NOUN cana-733 103 56 v v ADP cana-733 103 57 โˆˆ โˆˆ PROPN cana-733 103 58 { { PUNCT cana-733 103 59 mango mango NOUN cana-733 103 60 , , PUNCT cana-733 103 61 plum plum NOUN cana-733 103 62 } } PUNCT cana-733 103 63 } } PUNCT cana-733 103 64 then then ADV cana-733 103 65 ( ( PUNCT cana-733 103 66 โ„ณ โ„ณ NOUN cana-733 103 67 , , PUNCT cana-733 103 68 โ‹” โ‹” PROPN cana-733 103 69 , , PUNCT cana-733 103 70 guava guava NOUN cana-733 103 71 ) ) PUNCT cana-733 103 72 is be AUX cana-733 103 73 a a DET cana-733 103 74 w w NOUN cana-733 103 75 - - PUNCT cana-733 103 76 algebra algebra NOUN cana-733 103 77 . . PUNCT cana-733 104 1 define define VERB cana-733 104 2 ๐’ฆ ๐’ฆ PROPN cana-733 104 3 = = PUNCT cana-733 104 4 { { PUNCT cana-733 104 5 puss puss NOUN cana-733 104 6 , , PUNCT cana-733 104 7 goat goat PROPN cana-733 104 8 , , PUNCT cana-733 104 9 yak yak NOUN cana-733 104 10 , , PUNCT cana-733 104 11 hen hen NOUN cana-733 104 12 , , PUNCT cana-733 104 13 sheep sheep NOUN cana-733 104 14 , , PUNCT cana-733 104 15 rabbit rabbit NOUN cana-733 104 16 } } PUNCT cana-733 104 17 . . PUNCT cana-733 105 1 let let AUX cana-733 105 2 ( ( PUNCT cana-733 105 3 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 4 ฬŒ ฬŒ NUM cana-733 105 5 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 6 ,๐’ฆ ,๐’ฆ PUNCT cana-733 105 7 ) ) PUNCT cana-733 105 8 be be AUX cana-733 105 9 a a DET cana-733 105 10 fs fs NOUN cana-733 105 11 - - PUNCT cana-733 105 12 set set NOUN cana-733 105 13 over over ADP cana-733 105 14 โ„ณ. โ„ณ. PROPN cana-733 105 15 then then ADV cana-733 105 16 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 17 ฬŒ ฬŒ NUM cana-733 105 18 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 19 [puss [puss NOUN cana-733 105 20 ] ] X cana-733 105 21 , , PUNCT cana-733 105 22 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 23 ฬŒ ฬŒ NUM cana-733 105 24 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 25 [goat [goat X cana-733 105 26 ] ] X cana-733 105 27 , , PUNCT cana-733 105 28 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 29 ฬŒ ฬŒ NUM cana-733 105 30 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 31 [yak [yak X cana-733 105 32 ] ] X cana-733 105 33 , , PUNCT cana-733 105 34 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 35 ฬŒ ฬŒ NUM cana-733 105 36 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 37 [hen [hen NOUN cana-733 105 38 ] ] X cana-733 105 39 , , PUNCT cana-733 105 40 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 41 ฬŒ ฬŒ NUM cana-733 105 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 43 [sheep [sheep X cana-733 105 44 ] ] X cana-733 105 45 & & CCONJ cana-733 105 46 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 47 ฬŒ ฬŒ NUM cana-733 105 48 ๏ฟฝ ๏ฟฝ NOUN cana-733 105 49 [rabbit [rabbit X cana-733 105 50 ] ] X cana-733 105 51 are be AUX cana-733 105 52 fuzzy fuzzy ADJ cana-733 105 53 sets set NOUN cana-733 105 54 in in ADP cana-733 105 55 โ„ณ. โ„ณ. PROPN cana-733 105 56 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 57 ฬŒ ฬŒ NUM cana-733 105 58 ๏ฟฝ ๏ฟฝ PROPN cana-733 105 59 ๐‘”๐‘ข๐‘Ž๐‘ฃ๐‘Ž ๐‘”๐‘ข๐‘Ž๐‘ฃ๐‘Ž PROPN cana-733 106 1 ๐‘š๐‘Ž๐‘›๐‘”๐‘œ ๐‘š๐‘Ž๐‘›๐‘”๐‘œ PROPN cana-733 106 2 ๐‘๐‘’๐‘’๐‘ก๐‘Ÿ๐‘œ๐‘œ๐‘ก ๐‘๐‘’๐‘’๐‘ก๐‘Ÿ๐‘œ๐‘œ๐‘ก PROPN cana-733 106 3 ๐‘๐‘™๐‘ข๐‘š ๐‘๐‘™๐‘ข๐‘š PROPN cana-733 106 4 ๐‘ก๐‘ข๐‘Ÿ๐‘›๐‘–๐‘ ๐‘ก๐‘ข๐‘Ÿ๐‘›๐‘–๐‘ VERB cana-733 106 5 ๐‘๐‘ข๐‘ ๐‘  ๐‘๐‘ข๐‘ ๐‘  PROPN cana-733 106 6 0.6 0.6 NUM cana-733 106 7 0.4 0.4 NUM cana-733 106 8 0.4 0.4 NUM cana-733 106 9 0.4 0.4 NUM cana-733 106 10 0.4 0.4 NUM cana-733 106 11 ๐‘”๐‘œ๐‘Ž๐‘ก ๐‘”๐‘œ๐‘Ž๐‘ก NOUN cana-733 106 12 0.7 0.7 NUM cana-733 106 13 0.5 0.5 NUM cana-733 106 14 0.7 0.7 NUM cana-733 106 15 0.5 0.5 NUM cana-733 106 16 0.5 0.5 NUM cana-733 106 17 ๐‘ฆ๐‘Ž๐‘˜ ๐‘ฆ๐‘Ž๐‘˜ NOUN cana-733 106 18 0.8 0.8 NUM cana-733 106 19 0.8 0.8 NUM cana-733 106 20 0.3 0.3 NUM cana-733 106 21 0.3 0.3 NUM cana-733 106 22 0.8 0.8 NUM cana-733 106 23 โ„Ž๐‘’๐‘› โ„Ž๐‘’๐‘› NOUN cana-733 106 24 0.4 0.4 NUM cana-733 106 25 0.2 0.2 NUM cana-733 106 26 0.4 0.4 NUM cana-733 106 27 0.2 0.2 NUM cana-733 106 28 0.2 0.2 NUM cana-733 106 29 ๐‘ โ„Ž๐‘’๐‘’๐‘ ๐‘ โ„Ž๐‘’๐‘’๐‘ NOUN cana-733 106 30 0.5 0.5 NUM cana-733 106 31 0.5 0.5 NUM cana-733 106 32 0.9 0.9 NUM cana-733 106 33 0.7 0.7 NUM cana-733 106 34 0.4 0.4 NUM cana-733 106 35 ๐‘Ÿ๐‘Ž๐‘๐‘๐‘–๐‘ก ๐‘Ÿ๐‘Ž๐‘๐‘๐‘–๐‘ก NOUN cana-733 106 36 0.6 0.6 NUM cana-733 106 37 0.5 0.5 NUM cana-733 106 38 0.2 0.2 NUM cana-733 106 39 0.2 0.2 NUM cana-733 106 40 0.5 0.5 NUM cana-733 106 41 communications communication NOUN cana-733 106 42 on on ADP cana-733 106 43 applied apply VERB cana-733 106 44 nonlinear nonlinear ADJ cana-733 106 45 analysis analysis NOUN cana-733 106 46 issn issn NOUN cana-733 106 47 : : PUNCT cana-733 106 48 1074 1074 NUM cana-733 106 49 - - PUNCT cana-733 106 50 133x 133x NUM cana-733 106 51 vol vol NOUN cana-733 106 52 31 31 NUM cana-733 106 53 no no NOUN cana-733 106 54 . . PUNCT cana-733 107 1 3s 3s NUM cana-733 107 2 ( ( PUNCT cana-733 107 3 2024 2024 NUM cana-733 107 4 ) ) PUNCT cana-733 107 5 89 89 NUM cana-733 107 6 https://internationalpubls.com https://internationalpubls.com X cana-733 107 7 a a DET cana-733 107 8 fs fs NOUN cana-733 107 9 - - PUNCT cana-733 107 10 ideal ideal NOUN cana-733 107 11 that that PRON cana-733 107 12 is be AUX cana-733 107 13 based base VERB cana-733 107 14 on on ADP cana-733 107 15 the the DET cana-733 107 16 parameters parameter NOUN cana-733 107 17 โ€œ " PUNCT cana-733 107 18 puss puss NOUN cana-733 107 19 โ€ " PUNCT cana-733 107 20 , , PUNCT cana-733 107 21 โ€œ " PUNCT cana-733 107 22 goat goat PROPN cana-733 107 23 โ€ " PUNCT cana-733 107 24 , , PUNCT cana-733 107 25 โ€œ " PUNCT cana-733 107 26 yak yak NOUN cana-733 107 27 โ€ " PUNCT cana-733 107 28 , , PUNCT cana-733 107 29 โ€œ " PUNCT cana-733 107 30 hen hen NOUN cana-733 107 31 โ€ " PUNCT cana-733 107 32 and and CCONJ cana-733 107 33 โ€œ " PUNCT cana-733 107 34 rabbit rabbit NOUN cana-733 107 35 โ€ " PUNCT cana-733 107 36 , , PUNCT cana-733 107 37 then then ADV cana-733 107 38 ( ( PUNCT cana-733 107 39 ๏ฟฝ ๏ฟฝ NOUN cana-733 107 40 ฬŒ ฬŒ NUM cana-733 107 41 ๏ฟฝ ๏ฟฝ NOUN cana-733 107 42 ,๐’ฆ ,๐’ฆ PUNCT cana-733 107 43 ) ) PUNCT cana-733 107 44 . . PUNCT cana-733 108 1 however however ADV cana-733 108 2 , , PUNCT cana-733 108 3 based base VERB cana-733 108 4 on on ADP cana-733 108 5 the the DET cana-733 108 6 parameters parameter NOUN cana-733 108 7 โ€œ " PUNCT cana-733 108 8 sheep sheep NOUN cana-733 108 9 โ€ " PUNCT cana-733 108 10 , , PUNCT cana-733 108 11 ( ( PUNCT cana-733 108 12 ๏ฟฝ ๏ฟฝ PROPN cana-733 108 13 ฬŒ ฬŒ NUM cana-733 108 14 ๏ฟฝ ๏ฟฝ NOUN cana-733 108 15 ,๐’ฆ ,๐’ฆ PUNCT cana-733 108 16 ) ) PUNCT cana-733 108 17 is be AUX cana-733 108 18 not not PART cana-733 108 19 a a DET cana-733 108 20 fs fs NOUN cana-733 108 21 - - PUNCT cana-733 108 22 ideal ideal NOUN cana-733 108 23 of of ADP cana-733 108 24 โ„ณ โ„ณ PROPN cana-733 108 25 , , PUNCT cana-733 108 26 as as ADP cana-733 108 27 ๏ฟฝ ๏ฟฝ PROPN cana-733 108 28 ฬŒ ฬŒ NUM cana-733 108 29 ๏ฟฝ ๏ฟฝ NOUN cana-733 108 30 [sheep [sheep X cana-733 108 31 ] ] X cana-733 108 32 ( ( PUNCT cana-733 108 33 turnip turnip NOUN cana-733 108 34 ) ) PUNCT cana-733 108 35 = = PUNCT cana-733 108 36 0.4 0.4 NUM cana-733 108 37 < < SYM cana-733 108 38 0.5 0.5 NUM cana-733 108 39 = = SYM cana-733 108 40 min min PROPN cana-733 108 41 { { PUNCT cana-733 108 42 ๏ฟฝ ๏ฟฝ PROPN cana-733 108 43 ฬŒ ฬŒ NUM cana-733 108 44 ๏ฟฝ ๏ฟฝ NOUN cana-733 108 45 [sheep [sheep X cana-733 108 46 ] ] X cana-733 108 47 ] ] X cana-733 108 48 ( ( PUNCT cana-733 108 49 turnip turnip NOUN cana-733 108 50 โ‹” โ‹” PART cana-733 108 51 plum plum NOUN cana-733 108 52 ) ) PUNCT cana-733 108 53 , , PUNCT cana-733 108 54 ๏ฟฝ ๏ฟฝ PROPN cana-733 108 55 ฬŒ ฬŒ NUM cana-733 108 56 ๏ฟฝ ๏ฟฝ PROPN cana-733 108 57 [sheep [sheep X cana-733 108 58 ] ] X cana-733 108 59 ( ( PUNCT cana-733 108 60 plum plum NOUN cana-733 108 61 ) ) PUNCT cana-733 108 62 } } PUNCT cana-733 108 63 . . PUNCT cana-733 109 1 we we PRON cana-733 109 2 know know VERB cana-733 109 3 for for ADP cana-733 109 4 the the DET cana-733 109 5 most most ADJ cana-733 109 6 part part NOUN cana-733 109 7 , , PUNCT cana-733 109 8 that that PRON cana-733 109 9 sheeps sheep NOUN cana-733 109 10 prefer prefer VERB cana-733 109 11 beetroot beetroot NOUN cana-733 109 12 . . PUNCT cana-733 110 1 based base VERB cana-733 110 2 on on ADP cana-733 110 3 the the DET cana-733 110 4 parameter parameter NOUN cana-733 110 5 โ€œ " PUNCT cana-733 110 6 sheep sheep NOUN cana-733 110 7 โ€ " PUNCT cana-733 110 8 , , PUNCT cana-733 110 9 we we PRON cana-733 110 10 may may AUX cana-733 110 11 determine determine VERB cana-733 110 12 that that SCONJ cana-733 110 13 ( ( PUNCT cana-733 110 14 ๏ฟฝ ๏ฟฝ PROPN cana-733 110 15 ฬŒ ฬŒ NUM cana-733 110 16 ๏ฟฝ ๏ฟฝ NOUN cana-733 110 17 ,๐’ฆ ,๐’ฆ PUNCT cana-733 110 18 ) ) PUNCT cana-733 110 19 in in ADP cana-733 110 20 the the DET cana-733 110 21 case case NOUN cana-733 110 22 above above ADV cana-733 110 23 is be AUX cana-733 110 24 not not PART cana-733 110 25 a a DET cana-733 110 26 fs fs NOUN cana-733 110 27 - - PUNCT cana-733 110 28 ideal ideal NOUN cana-733 110 29 of of ADP cana-733 110 30 โ„ณ. โ„ณ. PROPN cana-733 110 31 this this PRON cana-733 110 32 implies imply VERB cana-733 110 33 that that SCONJ cana-733 110 34 ( ( PUNCT cana-733 110 35 ๏ฟฝ ๏ฟฝ PROPN cana-733 110 36 ฬŒ ฬŒ NUM cana-733 110 37 ๏ฟฝ ๏ฟฝ NOUN cana-733 110 38 ,๐’ฆ ,๐’ฆ PUNCT cana-733 110 39 ) ) PUNCT cana-733 110 40 can can AUX cana-733 110 41 not not PART cana-733 110 42 be be AUX cana-733 110 43 a a DET cana-733 110 44 fuzzy fuzzy ADJ cana-733 110 45 ideal ideal NOUN cana-733 110 46 of of ADP cana-733 110 47 โ„ณ โ„ณ PROPN cana-733 110 48 , , PUNCT cana-733 110 49 just just ADV cana-733 110 50 as as SCONJ cana-733 110 51 sheep sheep NOUN cana-733 110 52 prefers prefer VERB cana-733 110 53 a a DET cana-733 110 54 beetroot beetroot NOUN cana-733 110 55 over over ADP cana-733 110 56 another another PRON cana-733 110 57 . . PUNCT cana-733 111 1 4 4 X cana-733 111 2 . . X cana-733 111 3 conclusion conclusion NOUN cana-733 111 4 in in ADP cana-733 111 5 this this DET cana-733 111 6 paper paper NOUN cana-733 111 7 , , PUNCT cana-733 111 8 we we PRON cana-733 111 9 combine combine VERB cana-733 111 10 the the DET cana-733 111 11 notion notion NOUN cana-733 111 12 of of ADP cana-733 111 13 fs f NOUN cana-733 111 14 - - PUNCT cana-733 111 15 sets set NOUN cana-733 111 16 with with ADP cana-733 111 17 the the DET cana-733 111 18 theory theory NOUN cana-733 111 19 of of ADP cana-733 111 20 w w NOUN cana-733 111 21 - - PUNCT cana-733 111 22 algebras algebra NOUN cana-733 111 23 . . PUNCT cana-733 112 1 fs f NOUN cana-733 112 2 - - PUNCT cana-733 112 3 ideals ideal NOUN cana-733 112 4 and and CCONJ cana-733 112 5 fsw fsw PROPN cana-733 112 6 - - PUNCT cana-733 112 7 algebras algebras PROPN cana-733 112 8 were be AUX cana-733 112 9 introduced introduce VERB cana-733 112 10 , , PUNCT cana-733 112 11 and and CCONJ cana-733 112 12 then then ADV cana-733 112 13 some some PRON cana-733 112 14 of of ADP cana-733 112 15 their their PRON cana-733 112 16 associated associated ADJ cana-733 112 17 features feature NOUN cana-733 112 18 were be AUX cana-733 112 19 investigated investigate VERB cana-733 112 20 . . PUNCT cana-733 113 1 we we PRON cana-733 113 2 shall shall AUX cana-733 113 3 investigate investigate VERB cana-733 113 4 the the DET cana-733 113 5 applicability applicability NOUN cana-733 113 6 of of ADP cana-733 113 7 fs f NOUN cana-733 113 8 - - PUNCT cana-733 113 9 sets set NOUN cana-733 113 10 to to ADP cana-733 113 11 different different ADJ cana-733 113 12 w w ADJ cana-733 113 13 - - ADJ cana-733 113 14 algebraic algebraic ADJ cana-733 113 15 ideals ideal NOUN cana-733 113 16 on on ADP cana-733 113 17 the the DET cana-733 113 18 basis basis NOUN cana-733 113 19 of of ADP cana-733 113 20 these these DET cana-733 113 21 results result NOUN cana-733 113 22 . . PUNCT cana-733 114 1 references reference NOUN cana-733 114 2 [ [ X cana-733 114 3 1 1 NUM cana-733 114 4 ] ] X cana-733 114 5 ali ali PROPN cana-733 114 6 , , PUNCT cana-733 114 7 m.i m.i PROPN cana-733 114 8 . . PROPN cana-733 114 9 , , PUNCT cana-733 114 10 feng feng PROPN cana-733 114 11 , , PUNCT cana-733 114 12 f. f. PROPN cana-733 114 13 , , PUNCT cana-733 114 14 liu liu PROPN cana-733 114 15 , , PUNCT cana-733 114 16 x. x. PROPN cana-733 114 17 , , PUNCT cana-733 114 18 min min PROPN cana-733 114 19 , , PUNCT cana-733 114 20 w.k w.k PROPN cana-733 114 21 . . PROPN cana-733 114 22 , , PUNCT cana-733 114 23 shabir shabir PROPN cana-733 114 24 , , PUNCT cana-733 114 25 m. m. NOUN cana-733 114 26 , , PUNCT cana-733 114 27 on on ADP cana-733 114 28 some some DET cana-733 114 29 new new ADJ cana-733 114 30 operations operation NOUN cana-733 114 31 in in ADP cana-733 114 32 soft soft ADJ cana-733 114 33 set set NOUN cana-733 114 34 theory theory NOUN cana-733 114 35 , , PUNCT cana-733 114 36 comput comput NOUN cana-733 114 37 . . PUNCT cana-733 115 1 math math NOUN cana-733 115 2 . . PUNCT cana-733 116 1 appl appl PROPN cana-733 116 2 . . PROPN cana-733 117 1 57 57 NUM cana-733 117 2 , , PUNCT cana-733 117 3 1547 1547 NUM cana-733 117 4 - - SYM cana-733 117 5 1553 1553 NUM cana-733 117 6 , , PUNCT cana-733 117 7 2009 2009 NUM cana-733 117 8 . . PUNCT cana-733 118 1 [ [ X cana-733 118 2 2 2 NUM cana-733 118 3 ] ] X cana-733 118 4 ceterchi ceterchi ADJ cana-733 118 5 rodica rodica PROPN cana-733 118 6 , , PUNCT cana-733 118 7 the the DET cana-733 118 8 lattice lattice NOUN cana-733 118 9 structure structure NOUN cana-733 118 10 of of ADP cana-733 118 11 pseudo pseudo NOUN cana-733 118 12 - - ADJ cana-733 118 13 wajsberg wajsberg ADJ cana-733 118 14 algebras algebra NOUN cana-733 118 15 , , PUNCT cana-733 118 16 journal journal NOUN cana-733 118 17 of of ADP cana-733 118 18 universal universal ADJ cana-733 118 19 computer computer NOUN cana-733 118 20 science science NOUN cana-733 118 21 , , PUNCT cana-733 118 22 6 6 NUM cana-733 118 23 , , PUNCT cana-733 118 24 22 22 NUM cana-733 118 25 , , PUNCT cana-733 118 26 2000 2000 NUM cana-733 118 27 . . PUNCT cana-733 119 1 [ [ X cana-733 119 2 3 3 X cana-733 119 3 ] ] X cana-733 119 4 ceterchi ceterchi ADJ cana-733 119 5 rodica rodica ADJ cana-733 119 6 , , PUNCT cana-733 119 7 pseudo pseudo NOUN cana-733 119 8 - - ADJ cana-733 119 9 wajsberg wajsberg ADJ cana-733 119 10 algebras algebra NOUN cana-733 119 11 , , PUNCT cana-733 119 12 multi multi ADJ cana-733 119 13 - - ADJ cana-733 119 14 valued value VERB cana-733 119 15 logic logic NOUN cana-733 119 16 , , PUNCT cana-733 119 17 6 6 NUM cana-733 119 18 , , PUNCT cana-733 119 19 67 67 NUM cana-733 119 20 , , PUNCT cana-733 119 21 2001 2001 NUM cana-733 119 22 . . PUNCT cana-733 120 1 [ [ X cana-733 120 2 4 4 NUM cana-733 120 3 ] ] X cana-733 120 4 chen chen PROPN cana-733 120 5 , , PUNCT cana-733 120 6 d. d. PROPN cana-733 120 7 , , PUNCT cana-733 120 8 tsang tsang PROPN cana-733 120 9 , , PUNCT cana-733 120 10 e.c.c e.c.c PROPN cana-733 120 11 . . PROPN cana-733 120 12 , , PUNCT cana-733 120 13 yeung yeung PROPN cana-733 120 14 , , PUNCT cana-733 120 15 d.s d.s PROPN cana-733 120 16 . . PROPN cana-733 120 17 , , PUNCT cana-733 120 18 wang wang PROPN cana-733 120 19 , , PUNCT cana-733 120 20 x. x. PROPN cana-733 120 21 , , PUNCT cana-733 120 22 the the DET cana-733 120 23 parametrization parametrization NOUN cana-733 120 24 reduction reduction NOUN cana-733 120 25 of of ADP cana-733 120 26 soft soft ADJ cana-733 120 27 sets set NOUN cana-733 120 28 and and CCONJ cana-733 120 29 its its PRON cana-733 120 30 applications application NOUN cana-733 120 31 , , PUNCT cana-733 120 32 comput comput NOUN cana-733 120 33 . . PUNCT cana-733 121 1 math math NOUN cana-733 121 2 . . PUNCT cana-733 122 1 appl appl PROPN cana-733 122 2 . . PROPN cana-733 123 1 49 49 NUM cana-733 123 2 , , PUNCT cana-733 123 3 757 757 PROPN cana-733 123 4 - - SYM cana-733 123 5 763 763 NUM cana-733 123 6 , , PUNCT cana-733 123 7 2005 2005 NUM cana-733 123 8 . . PUNCT cana-733 124 1 [ [ X cana-733 124 2 5 5 NUM cana-733 124 3 ] ] SYM cana-733 124 4 font font NOUN cana-733 124 5 , , PUNCT cana-733 124 6 j. j. PROPN cana-733 124 7 m. m. PROPN cana-733 124 8 , , PUNCT cana-733 124 9 rodriguez rodriguez PROPN cana-733 124 10 , , PUNCT cana-733 124 11 a. a. PROPN cana-733 124 12 j. j. PROPN cana-733 124 13 , , PUNCT cana-733 124 14 and and CCONJ cana-733 124 15 torrens torren NOUN cana-733 124 16 , , PUNCT cana-733 124 17 a. a. NOUN cana-733 124 18 , , PUNCT cana-733 124 19 wajsberg wajsberg PROPN cana-733 124 20 algebras algebra NOUN cana-733 124 21 , , PUNCT cana-733 124 22 stochastica stochastica PROPN cana-733 124 23 , , PUNCT cana-733 124 24 8 8 NUM cana-733 124 25 , , PUNCT cana-733 124 26 5 5 NUM cana-733 124 27 , , PUNCT cana-733 124 28 1984 1984 NUM cana-733 124 29 . . PUNCT cana-733 125 1 [ [ X cana-733 125 2 6 6 NUM cana-733 125 3 ] ] X cana-733 125 4 ibrahim ibrahim PROPN cana-733 125 5 , , PUNCT cana-733 125 6 a. a. NOUN cana-733 125 7 , , PUNCT cana-733 125 8 and and CCONJ cana-733 125 9 indhumathi indhumathi NOUN cana-733 125 10 , , PUNCT cana-733 125 11 m. m. NOUN cana-733 125 12 , , PUNCT cana-733 125 13 pwi pwi NOUN cana-733 125 14 - - PUNCT cana-733 125 15 ideals ideal NOUN cana-733 125 16 of of ADP cana-733 125 17 lattice lattice NOUN cana-733 125 18 pseudo pseudo NOUN cana-733 125 19 - - ADJ cana-733 125 20 wajsberg wajsberg ADJ cana-733 125 21 algebras algebra NOUN cana-733 125 22 , , PUNCT cana-733 125 23 advances advance NOUN cana-733 125 24 in in ADP cana-733 125 25 theoretical theoretical ADJ cana-733 125 26 and and CCONJ cana-733 125 27 applied applied ADJ cana-733 125 28 mathematics mathematic NOUN cana-733 125 29 , , PUNCT cana-733 125 30 13 13 NUM cana-733 125 31 , , PUNCT cana-733 125 32 1 1 NUM cana-733 125 33 , , PUNCT cana-733 125 34 2018 2018 NUM cana-733 125 35 . . PUNCT cana-733 126 1 [ [ X cana-733 126 2 7 7 X cana-733 126 3 ] ] X cana-733 126 4 ibrahim ibrahim PROPN cana-733 126 5 , , PUNCT cana-733 126 6 a. a. NOUN cana-733 126 7 , , PUNCT cana-733 126 8 and and CCONJ cana-733 126 9 indhumathi indhumathi NOUN cana-733 126 10 , , PUNCT cana-733 126 11 m. m. NOUN cana-733 126 12 , , PUNCT cana-733 126 13 classes class NOUN cana-733 126 14 of of ADP cana-733 126 15 p p NOUN cana-733 126 16 - - PUNCT cana-733 126 17 ideals ideal NOUN cana-733 126 18 of of ADP cana-733 126 19 lattice lattice NOUN cana-733 126 20 pseudo pseudo NOUN cana-733 126 21 - - ADJ cana-733 126 22 wajsberg wajsberg ADJ cana-733 126 23 algebras algebra NOUN cana-733 126 24 , , PUNCT cana-733 126 25 international international ADJ cana-733 126 26 journal journal NOUN cana-733 126 27 of of ADP cana-733 126 28 research research NOUN cana-733 126 29 in in ADP cana-733 126 30 advent advent ADJ cana-733 126 31 technology technology NOUN cana-733 126 32 , , PUNCT cana-733 126 33 7 7 NUM cana-733 126 34 , , PUNCT cana-733 126 35 172 172 NUM cana-733 126 36 , , PUNCT cana-733 126 37 2019 2019 NUM cana-733 126 38 . . PUNCT cana-733 127 1 [ [ X cana-733 127 2 8 8 NUM cana-733 127 3 ] ] X cana-733 127 4 ibrahim ibrahim PROPN cana-733 127 5 , , PUNCT cana-733 127 6 a. a. NOUN cana-733 127 7 , , PUNCT cana-733 127 8 and and CCONJ cana-733 127 9 indhumathi indhumathi NOUN cana-733 127 10 , , PUNCT cana-733 127 11 m. m. NOUN cana-733 127 12 , , PUNCT cana-733 127 13 various various ADJ cana-733 127 14 types type NOUN cana-733 127 15 of of ADP cana-733 127 16 pwi pwi NOUN cana-733 127 17 - - PUNCT cana-733 127 18 ideals ideal NOUN cana-733 127 19 of of ADP cana-733 127 20 a a DET cana-733 127 21 lattice lattice ADJ cana-733 127 22 psะตuิo psะตuิo PROPN cana-733 127 23 - - PUNCT cana-733 127 24 wajsberg wajsberg PROPN cana-733 127 25 algebras algebra NOUN cana-733 127 26 , , PUNCT cana-733 127 27 advances advance NOUN cana-733 127 28 in in ADP cana-733 127 29 mathematics mathematic NOUN cana-733 127 30 , , PUNCT cana-733 127 31 3 3 NUM cana-733 127 32 , , PUNCT cana-733 127 33 285 285 NUM cana-733 127 34 , , PUNCT cana-733 127 35 2019 2019 NUM cana-733 127 36 . . PUNCT cana-733 128 1 [ [ X cana-733 128 2 9 9 NUM cana-733 128 3 ] ] X cana-733 128 4 ibrahim ibrahim PROPN cana-733 128 5 , , PUNCT cana-733 128 6 a. a. NOUN cana-733 128 7 , , PUNCT cana-733 128 8 and and CCONJ cana-733 128 9 indhumathi indhumathi NOUN cana-733 128 10 , , PUNCT cana-733 128 11 m. m. NOUN cana-733 128 12 , , PUNCT cana-733 128 13 on on ADP cana-733 128 14 fuzzy fuzzy ADJ cana-733 128 15 extended extend VERB cana-733 128 16 pwi pwi NOUN cana-733 128 17 - - PUNCT cana-733 128 18 ideals ideal NOUN cana-733 128 19 of of ADP cana-733 128 20 lattice lattice NOUN cana-733 128 21 pseudo pseudo NOUN cana-733 128 22 - - ADJ cana-733 128 23 wajsberg wajsberg ADJ cana-733 128 24 algebras algebra NOUN cana-733 128 25 , , PUNCT cana-733 128 26 international international ADJ cana-733 128 27 journal journal NOUN cana-733 128 28 of of ADP cana-733 128 29 advanced advanced ADJ cana-733 128 30 science science NOUN cana-733 128 31 and and CCONJ cana-733 128 32 technology technology NOUN cana-733 128 33 , , PUNCT cana-733 128 34 29 29 NUM cana-733 128 35 , , PUNCT cana-733 128 36 1163 1163 NUM cana-733 128 37 , , PUNCT cana-733 128 38 2020 2020 NUM cana-733 128 39 . . PUNCT cana-733 129 1 [ [ X cana-733 129 2 10 10 NUM cana-733 129 3 ] ] X cana-733 129 4 ibrahim ibrahim PROPN cana-733 129 5 , , PUNCT cana-733 129 6 a. a. NOUN cana-733 129 7 , , PUNCT cana-733 129 8 and and CCONJ cana-733 129 9 indhumathi indhumathi NOUN cana-733 129 10 , , PUNCT cana-733 129 11 m. m. NOUN cana-733 129 12 , , PUNCT cana-733 129 13 on on ADP cana-733 129 14 anti anti ADJ cana-733 129 15 - - ADJ cana-733 129 16 fuzzy fuzzy ADJ cana-733 129 17 epwi epwi NOUN cana-733 129 18 - - PUNCT cana-733 129 19 ideals ideal NOUN cana-733 129 20 of of ADP cana-733 129 21 lattice lattice NOUN cana-733 129 22 pseudo pseudo NOUN cana-733 129 23 w w NOUN cana-733 129 24 - - PUNCT cana-733 129 25 algebras algebra NOUN cana-733 129 26 , , PUNCT cana-733 129 27 malaya malaya PROPN cana-733 129 28 journal journal PROPN cana-733 129 29 of of ADP cana-733 129 30 matematik matematik PROPN cana-733 129 31 , , PUNCT cana-733 129 32 8 8 NUM cana-733 129 33 , , PUNCT cana-733 129 34 1587 1587 NUM cana-733 129 35 , , PUNCT cana-733 129 36 2020 2020 NUM cana-733 129 37 . . PUNCT cana-733 130 1 [ [ X cana-733 130 2 11 11 NUM cana-733 130 3 ] ] X cana-733 130 4 maji maji PROPN cana-733 130 5 , , PUNCT cana-733 130 6 p.k p.k PROPN cana-733 130 7 . . PROPN cana-733 130 8 , , PUNCT cana-733 130 9 roy roy PROPN cana-733 130 10 , , PUNCT cana-733 130 11 a.r a.r PROPN cana-733 130 12 . . PROPN cana-733 130 13 , , PUNCT cana-733 130 14 biswas biswas PROPN cana-733 130 15 , , PUNCT cana-733 130 16 r r NOUN cana-733 130 17 , , PUNCT cana-733 130 18 fuzzy fuzzy ADJ cana-733 130 19 soft soft ADJ cana-733 130 20 sets set NOUN cana-733 130 21 , , PUNCT cana-733 130 22 j. j. PROPN cana-733 130 23 fuzzy fuzzy PROPN cana-733 130 24 math math PROPN cana-733 130 25 . . PUNCT cana-733 130 26 9 9 NUM cana-733 130 27 , , PUNCT cana-733 130 28 589 589 NUM cana-733 130 29 - - SYM cana-733 130 30 602 602 NUM cana-733 130 31 , , PUNCT cana-733 130 32 2001 2001 NUM cana-733 130 33 . . PUNCT cana-733 131 1 [ [ X cana-733 131 2 12 12 NUM cana-733 131 3 ] ] X cana-733 131 4 maji maji PROPN cana-733 131 5 , , PUNCT cana-733 131 6 p.k p.k PROPN cana-733 131 7 . . PROPN cana-733 131 8 , , PUNCT cana-733 131 9 roy roy PROPN cana-733 131 10 , , PUNCT cana-733 131 11 a.r a.r PROPN cana-733 131 12 . . PROPN cana-733 131 13 , , PUNCT cana-733 131 14 biswas biswas PROPN cana-733 131 15 , , PUNCT cana-733 131 16 r r NOUN cana-733 131 17 , , PUNCT cana-733 131 18 an an DET cana-733 131 19 application application NOUN cana-733 131 20 of of ADP cana-733 131 21 soft soft ADJ cana-733 131 22 sets set NOUN cana-733 131 23 in in ADP cana-733 131 24 a a DET cana-733 131 25 decision decision NOUN cana-733 131 26 making making NOUN cana-733 131 27 problem problem NOUN cana-733 131 28 , , PUNCT cana-733 131 29 comput comput NOUN cana-733 131 30 . . PUNCT cana-733 132 1 maths maths PROPN cana-733 132 2 . . PUNCT cana-733 133 1 appl appl PROPN cana-733 133 2 . . PROPN cana-733 134 1 44 44 NUM cana-733 134 2 , , PUNCT cana-733 134 3 1077 1077 NUM cana-733 134 4 - - SYM cana-733 134 5 1083 1083 NUM cana-733 134 6 , , PUNCT cana-733 134 7 2002 2002 NUM cana-733 134 8 . . PUNCT cana-733 135 1 [ [ X cana-733 135 2 13 13 NUM cana-733 135 3 ] ] X cana-733 135 4 maji maji PROPN cana-733 135 5 , , PUNCT cana-733 135 6 p.k p.k PROPN cana-733 135 7 . . PROPN cana-733 135 8 , , PUNCT cana-733 135 9 roy roy PROPN cana-733 135 10 , , PUNCT cana-733 135 11 a.r a.r PROPN cana-733 135 12 . . PROPN cana-733 135 13 , , PUNCT cana-733 135 14 biswas biswas PROPN cana-733 135 15 , , PUNCT cana-733 135 16 r r NOUN cana-733 135 17 , , PUNCT cana-733 135 18 soft soft ADJ cana-733 135 19 set set NOUN cana-733 135 20 theory theory NOUN cana-733 135 21 , , PUNCT cana-733 135 22 comput comput NOUN cana-733 135 23 . . PUNCT cana-733 136 1 math math NOUN cana-733 136 2 . . PUNCT cana-733 137 1 appl.45 appl.45 PROPN cana-733 137 2 , , PUNCT cana-733 137 3 555 555 NUM cana-733 137 4 - - SYM cana-733 137 5 562 562 NUM cana-733 137 6 , , PUNCT cana-733 137 7 2003 2003 NUM cana-733 137 8 . . PUNCT cana-733 138 1 [ [ X cana-733 138 2 14 14 NUM cana-733 138 3 ] ] X cana-733 138 4 molodtsov molodtsov PROPN cana-733 138 5 , , PUNCT cana-733 138 6 d. d. PROPN cana-733 138 7 , , PUNCT cana-733 138 8 soft soft ADJ cana-733 138 9 set set NOUN cana-733 138 10 theory theory NOUN cana-733 138 11 - - PUNCT cana-733 138 12 first first ADJ cana-733 138 13 results result NOUN cana-733 138 14 , , PUNCT cana-733 138 15 comput.math comput.math NOUN cana-733 138 16 . . PUNCT cana-733 138 17 appl appl PROPN cana-733 138 18 . . PUNCT cana-733 139 1 37 37 NUM cana-733 139 2 , , PUNCT cana-733 139 3 19 19 NUM cana-733 139 4 - - SYM cana-733 139 5 31,1999 31,1999 NUM cana-733 139 6 . . PUNCT cana-733 140 1 [ [ X cana-733 140 2 15 15 NUM cana-733 140 3 ] ] X cana-733 140 4 wajsberg wajsberg PROPN cana-733 140 5 , , PUNCT cana-733 140 6 m. m. NOUN cana-733 140 7 , , PUNCT cana-733 140 8 beitrage beitrage NOUN cana-733 140 9 zum zum NOUN cana-733 140 10 metaaussagenkalkul metaaussagenkalkul NOUN cana-733 140 11 i i PROPN cana-733 140 12 , , PUNCT cana-733 140 13 monatshefte monatshefte PROPN cana-733 140 14 fur fur NOUN cana-733 140 15 mathematik mathematik PROPN cana-733 140 16 , , PUNCT cana-733 140 17 42 42 NUM cana-733 140 18 , , PUNCT cana-733 140 19 221 221 NUM cana-733 140 20 , , PUNCT cana-733 140 21 1935 1935 NUM cana-733 140 22 . . PUNCT cana-733 141 1 [ [ X cana-733 141 2 16 16 NUM cana-733 141 3 ] ] X cana-733 141 4 young young ADJ cana-733 141 5 bae bae PROPN cana-733 141 6 jun jun PROPN cana-733 141 7 , , PUNCT cana-733 141 8 kyoung kyoung PROPN cana-733 141 9 ja ja PROPN cana-733 141 10 lee lee PROPN cana-733 141 11 , , PUNCT cana-733 141 12 chul chul PROPN cana-733 141 13 hwan hwan PROPN cana-733 141 14 park park PROPN cana-733 141 15 . . PUNCT cana-733 141 16 , , PUNCT cana-733 141 17 fuzzy fuzzy ADJ cana-733 141 18 softset softset NOUN cana-733 141 19 theory theory NOUN cana-733 141 20 applied apply VERB cana-733 141 21 to to PART cana-733 141 22 bck bck VERB cana-733 141 23 / / SYM cana-733 141 24 bci bci NOUN cana-733 141 25 - - PUNCT cana-733 141 26 algebras algebra NOUN cana-733 141 27 , , PUNCT cana-733 141 28 computers computer NOUN cana-733 141 29 and and CCONJ cana-733 141 30 mathematics mathematic NOUN cana-733 141 31 with with ADP cana-733 141 32 applications application NOUN cana-733 141 33 , , PUNCT cana-733 141 34 59 59 NUM cana-733 141 35 , , PUNCT cana-733 141 36 3180 3180 NUM cana-733 141 37 - - SYM cana-733 141 38 3192 3192 NUM cana-733 141 39 , , PUNCT cana-733 141 40 2010 2010 NUM cana-733 141 41 . . PUNCT cana-733 142 1 [ [ X cana-733 142 2 17 17 NUM cana-733 142 3 ] ] X cana-733 142 4 yousif yousif PROPN cana-733 142 5 , , PUNCT cana-733 142 6 y.y y.y PROPN cana-733 142 7 . . PROPN cana-733 142 8 , , PUNCT cana-733 142 9 hussain hussain PROPN cana-733 142 10 , , PUNCT cana-733 142 11 m. m. NOUN cana-733 142 12 a. a. PROPN cana-733 142 13 , , PUNCT cana-733 142 14 hussain hussain PROPN cana-733 142 15 , , PUNCT cana-733 142 16 l.a l.a PROPN cana-733 142 17 . . PROPN cana-733 142 18 , , PUNCT cana-733 142 19 fibrewise fibrewise NOUN cana-733 142 20 pairwise pairwise NOUN cana-733 142 21 soft soft ADJ cana-733 142 22 separation separation NOUN cana-733 142 23 axioms axiom NOUN cana-733 142 24 , , PUNCT cana-733 142 25 journal journal NOUN cana-733 142 26 of of ADP cana-733 142 27 physics physics PROPN cana-733 142 28 : : PUNCT cana-733 142 29 conference conference NOUN cana-733 142 30 series series NOUN cana-733 142 31 , , PUNCT cana-733 142 32 2019 2019 NUM cana-733 142 33 . . PUNCT