id sid tid token lemma pos cana-591 1 1 communications communication NOUN cana-591 1 2 on on ADP cana-591 1 3 applied apply VERB cana-591 1 4 nonlinear nonlinear ADJ cana-591 1 5 analysis analysis NOUN cana-591 1 6 issn issn NOUN cana-591 1 7 : : PUNCT cana-591 1 8 1074 1074 NUM cana-591 1 9 - - PUNCT cana-591 1 10 133x 133x NUM cana-591 1 11 vol vol NOUN cana-591 1 12 31 31 NUM cana-591 1 13 no no NOUN cana-591 1 14 . . PUNCT cana-591 2 1 2s 2s NUM cana-591 2 2 ( ( PUNCT cana-591 2 3 2024 2024 NUM cana-591 2 4 ) ) PUNCT cana-591 2 5 32 32 NUM cana-591 2 6 https://internationalpubls.com https://internationalpubls.com X cana-591 2 7 rough rough ADJ cana-591 2 8 set set VERB cana-591 2 9 analysis analysis NOUN cana-591 2 10 for for ADP cana-591 2 11 categorizing categorize VERB cana-591 2 12 motorcycles motorcycle NOUN cana-591 2 13 based base VERB cana-591 2 14 on on ADP cana-591 2 15 100 100 NUM cana-591 2 16 cubic cubic ADJ cana-591 2 17 centimeters centimeter NOUN cana-591 2 18 ( ( PUNCT cana-591 2 19 cc cc NOUN cana-591 2 20 ) ) PUNCT cana-591 2 21 engine engine NOUN cana-591 2 22 displacements displacement NOUN cana-591 2 23 1r 1r NUM cana-591 2 24 . . PUNCT cana-591 3 1 venmani venmani NOUN cana-591 3 2 , , PUNCT cana-591 3 3 2,*k 2,*k NUM cana-591 3 4 . . PUNCT cana-591 4 1 rajendran rajendran PROPN cana-591 4 2 1research 1research NUM cana-591 4 3 scholar scholar NOUN cana-591 4 4 , , PUNCT cana-591 4 5 vels vels PROPN cana-591 4 6 institute institute PROPN cana-591 4 7 of of ADP cana-591 4 8 science science PROPN cana-591 4 9 technology technology NOUN cana-591 4 10 and and CCONJ cana-591 4 11 advanced advanced ADJ cana-591 4 12 studies study NOUN cana-591 4 13 , , PUNCT cana-591 4 14 chennai chennai PROPN cana-591 4 15 , , PUNCT cana-591 4 16 tamil tamil PROPN cana-591 4 17 nadu nadu PROPN cana-591 4 18 , , PUNCT cana-591 4 19 india india PROPN cana-591 4 20 . . PUNCT cana-591 5 1 2associate 2associate NUM cana-591 5 2 professor professor NOUN cana-591 5 3 , , PUNCT cana-591 5 4 vels vels PROPN cana-591 5 5 institute institute PROPN cana-591 5 6 of of ADP cana-591 5 7 science science PROPN cana-591 5 8 technology technology NOUN cana-591 5 9 and and CCONJ cana-591 5 10 advanced advanced ADJ cana-591 5 11 studies study NOUN cana-591 5 12 , , PUNCT cana-591 5 13 chennai chennai PROPN cana-591 5 14 , , PUNCT cana-591 5 15 tamil tamil PROPN cana-591 5 16 nadu nadu PROPN cana-591 5 17 , , PUNCT cana-591 5 18 india india PROPN cana-591 5 19 1 1 NUM cana-591 5 20 email email NOUN cana-591 5 21 i i PROPN cana-591 5 22 d d NOUN cana-591 5 23 : : PUNCT cana-591 5 24 rvenmani@yahoo.co.in rvenmani@yahoo.co.in NOUN cana-591 5 25 2 2 NUM cana-591 5 26 corresponding correspond VERB cana-591 5 27 author author NOUN cana-591 5 28 : : PUNCT cana-591 5 29 gkrajendra59@gmail.com gkrajendra59@gmail.com X cana-591 5 30 article article NOUN cana-591 5 31 history history NOUN cana-591 5 32 : : PUNCT cana-591 5 33 received receive VERB cana-591 5 34 : : PUNCT cana-591 5 35 01 01 NUM cana-591 5 36 - - PUNCT cana-591 5 37 03 03 NUM cana-591 5 38 - - PUNCT cana-591 5 39 2024 2024 NUM cana-591 5 40 revised revise VERB cana-591 5 41 : : PUNCT cana-591 5 42 19 19 NUM cana-591 5 43 - - PUNCT cana-591 5 44 04 04 NUM cana-591 5 45 - - PUNCT cana-591 5 46 2024 2024 NUM cana-591 5 47 accepted accept VERB cana-591 5 48 : : PUNCT cana-591 5 49 15 15 NUM cana-591 5 50 - - SYM cana-591 5 51 05 05 NUM cana-591 5 52 - - PUNCT cana-591 5 53 2024 2024 NUM cana-591 5 54 abstract abstract NOUN cana-591 5 55 : : PUNCT cana-591 5 56 rough rough ADJ cana-591 5 57 set set NOUN cana-591 5 58 theory theory NOUN cana-591 5 59 ( ( PUNCT cana-591 5 60 rst rst PROPN cana-591 5 61 ) ) PUNCT cana-591 5 62 is be AUX cana-591 5 63 a a DET cana-591 5 64 mathematical mathematical ADJ cana-591 5 65 approach approach NOUN cana-591 5 66 used use VERB cana-591 5 67 for for ADP cana-591 5 68 dealing deal VERB cana-591 5 69 with with ADP cana-591 5 70 uncertainty uncertainty NOUN cana-591 5 71 and and CCONJ cana-591 5 72 vagueness vagueness NOUN cana-591 5 73 in in ADP cana-591 5 74 decision decision NOUN cana-591 5 75 - - PUNCT cana-591 5 76 making make VERB cana-591 5 77 and and CCONJ cana-591 5 78 data datum NOUN cana-591 5 79 analysis analysis NOUN cana-591 5 80 . . PUNCT cana-591 6 1 it it PRON cana-591 6 2 provides provide VERB cana-591 6 3 a a DET cana-591 6 4 framework framework NOUN cana-591 6 5 for for ADP cana-591 6 6 classifying classify VERB cana-591 6 7 objects object NOUN cana-591 6 8 into into ADP cana-591 6 9 different different ADJ cana-591 6 10 equivalence equivalence NOUN cana-591 6 11 classes class NOUN cana-591 6 12 based base VERB cana-591 6 13 on on ADP cana-591 6 14 their their PRON cana-591 6 15 attributes attribute NOUN cana-591 6 16 or or CCONJ cana-591 6 17 characteristics characteristic NOUN cana-591 6 18 . . PUNCT cana-591 7 1 in in ADP cana-591 7 2 rst rst PROPN cana-591 7 3 , , PUNCT cana-591 7 4 the the DET cana-591 7 5 concept concept NOUN cana-591 7 6 of of ADP cana-591 7 7 different different ADJ cana-591 7 8 𝑐𝑐 𝑐𝑐 NOUN cana-591 7 9 bikes bike NOUN cana-591 7 10 can can AUX cana-591 7 11 be be AUX cana-591 7 12 analyzed analyze VERB cana-591 7 13 based base VERB cana-591 7 14 on on ADP cana-591 7 15 their their PRON cana-591 7 16 attributes attribute NOUN cana-591 7 17 or or CCONJ cana-591 7 18 characteristics characteristic NOUN cana-591 7 19 . . PUNCT cana-591 8 1 each each DET cana-591 8 2 bike bike NOUN cana-591 8 3 can can AUX cana-591 8 4 be be AUX cana-591 8 5 represented represent VERB cana-591 8 6 as as ADP cana-591 8 7 an an DET cana-591 8 8 object object NOUN cana-591 8 9 with with ADP cana-591 8 10 a a DET cana-591 8 11 set set NOUN cana-591 8 12 of of ADP cana-591 8 13 attributes attribute NOUN cana-591 8 14 such such ADJ cana-591 8 15 as as ADP cana-591 8 16 engine engine NOUN cana-591 8 17 displacement displacement NOUN cana-591 8 18 , , PUNCT cana-591 8 19 weight weight NOUN cana-591 8 20 , , PUNCT cana-591 8 21 top top ADJ cana-591 8 22 speed speed NOUN cana-591 8 23 , , PUNCT cana-591 8 24 fuel fuel NOUN cana-591 8 25 efficiency efficiency NOUN cana-591 8 26 and and CCONJ cana-591 8 27 price price NOUN cana-591 8 28 . . PUNCT cana-591 9 1 another another DET cana-591 9 2 class class NOUN cana-591 9 3 may may AUX cana-591 9 4 consist consist VERB cana-591 9 5 of of ADP cana-591 9 6 bikes bike NOUN cana-591 9 7 with with ADP cana-591 9 8 lower low ADJ cana-591 9 9 engine engine NOUN cana-591 9 10 displacement displacement NOUN cana-591 9 11 , , PUNCT cana-591 9 12 lighter light ADJ cana-591 9 13 weight weight NOUN cana-591 9 14 , , PUNCT cana-591 9 15 and and CCONJ cana-591 9 16 better well ADJ cana-591 9 17 fuel fuel NOUN cana-591 9 18 efficiency efficiency NOUN cana-591 9 19 , , PUNCT cana-591 9 20 which which PRON cana-591 9 21 could could AUX cana-591 9 22 be be AUX cana-591 9 23 more more ADV cana-591 9 24 suitable suitable ADJ cana-591 9 25 for for ADP cana-591 9 26 daily daily ADJ cana-591 9 27 commuting commuting NOUN cana-591 9 28 . . PUNCT cana-591 10 1 by by ADP cana-591 10 2 applying apply VERB cana-591 10 3 rst rst PROPN cana-591 10 4 , , PUNCT cana-591 10 5 we we PRON cana-591 10 6 can can AUX cana-591 10 7 analyze analyze VERB cana-591 10 8 the the DET cana-591 10 9 relationship relationship NOUN cana-591 10 10 between between ADP cana-591 10 11 these these DET cana-591 10 12 attributes attribute NOUN cana-591 10 13 and and CCONJ cana-591 10 14 determine determine VERB cana-591 10 15 the the DET cana-591 10 16 essential essential ADJ cana-591 10 17 and and CCONJ cana-591 10 18 non non ADJ cana-591 10 19 - - ADJ cana-591 10 20 essential essential ADJ cana-591 10 21 features feature NOUN cana-591 10 22 of of ADP cana-591 10 23 100 100 NUM cana-591 10 24 𝐢𝐢 𝐢𝐢 NOUN cana-591 10 25 bikes bike NOUN cana-591 10 26 . . PUNCT cana-591 11 1 this this DET cana-591 11 2 analysis analysis NOUN cana-591 11 3 can can AUX cana-591 11 4 help help VERB cana-591 11 5 in in ADP cana-591 11 6 decision decision NOUN cana-591 11 7 making making NOUN cana-591 11 8 processes process NOUN cana-591 11 9 , , PUNCT cana-591 11 10 such such ADJ cana-591 11 11 as as ADP cana-591 11 12 choosing choose VERB cana-591 11 13 the the DET cana-591 11 14 right right ADJ cana-591 11 15 bike bike NOUN cana-591 11 16 based base VERB cana-591 11 17 on on ADP cana-591 11 18 specific specific ADJ cana-591 11 19 requirements requirement NOUN cana-591 11 20 or or CCONJ cana-591 11 21 preferences preference NOUN cana-591 11 22 . . PUNCT cana-591 12 1 it it PRON cana-591 12 2 's be AUX cana-591 12 3 important important ADJ cana-591 12 4 to to PART cana-591 12 5 note note VERB cana-591 12 6 that that SCONJ cana-591 12 7 the the DET cana-591 12 8 application application NOUN cana-591 12 9 of of ADP cana-591 12 10 rst rst PROPN cana-591 12 11 to100 to100 PROPN cana-591 12 12 𝑐𝑐 𝑐𝑐 NOUN cana-591 12 13 bikes bike NOUN cana-591 12 14 is be AUX cana-591 12 15 just just ADV cana-591 12 16 one one NUM cana-591 12 17 example example NOUN cana-591 12 18 of of ADP cana-591 12 19 how how SCONJ cana-591 12 20 this this DET cana-591 12 21 mathematical mathematical ADJ cana-591 12 22 approach approach NOUN cana-591 12 23 can can AUX cana-591 12 24 be be AUX cana-591 12 25 used use VERB cana-591 12 26 in in ADP cana-591 12 27 decisionmaking decisionmake VERB cana-591 12 28 and and CCONJ cana-591 12 29 data datum NOUN cana-591 12 30 analysis analysis NOUN cana-591 12 31 . . PUNCT cana-591 13 1 the the DET cana-591 13 2 specific specific ADJ cana-591 13 3 attributes attribute NOUN cana-591 13 4 and and CCONJ cana-591 13 5 classes class NOUN cana-591 13 6 may may AUX cana-591 13 7 vary vary VERB cana-591 13 8 depending depend VERB cana-591 13 9 on on ADP cana-591 13 10 the the DET cana-591 13 11 context context NOUN cana-591 13 12 and and CCONJ cana-591 13 13 purpure purpure NOUN cana-591 13 14 of of ADP cana-591 13 15 the the DET cana-591 13 16 analysis analysis NOUN cana-591 13 17 . . PUNCT cana-591 14 1 .keywords .keyword NOUN cana-591 14 2 : : PUNCT cana-591 14 3 rough rough ADJ cana-591 14 4 set set NOUN cana-591 14 5 , , PUNCT cana-591 14 6 motorbike motorbike NOUN cana-591 14 7 , , PUNCT cana-591 14 8 energy energy NOUN cana-591 14 9 , , PUNCT cana-591 14 10 decision decision NOUN cana-591 14 11 - - PUNCT cana-591 14 12 making making NOUN cana-591 14 13 , , PUNCT cana-591 14 14 reduct reduct PROPN cana-591 14 15 1 1 NUM cana-591 14 16 . . PUNCT cana-591 15 1 introduction introduction NOUN cana-591 15 2 in in ADP cana-591 15 3 decision decision NOUN cana-591 15 4 - - PUNCT cana-591 15 5 making make VERB cana-591 15 6 and and CCONJ cana-591 15 7 data datum NOUN cana-591 15 8 analysis analysis NOUN cana-591 15 9 , , PUNCT cana-591 15 10 rough rough ADJ cana-591 15 11 set set NOUN cana-591 15 12 theory theory NOUN cana-591 15 13 provides provide VERB cana-591 15 14 a a DET cana-591 15 15 mathematical mathematical ADJ cana-591 15 16 framework framework NOUN cana-591 15 17 for for ADP cana-591 15 18 handling handle VERB cana-591 15 19 ambiguity ambiguity NOUN cana-591 15 20 and and CCONJ cana-591 15 21 uncertainty uncertainty NOUN cana-591 15 22 . . PUNCT cana-591 16 1 pawlak pawlak PROPN cana-591 16 2 first first ADV cana-591 16 3 presented present VERB cana-591 16 4 it it PRON cana-591 16 5 as as ADP cana-591 16 6 a a DET cana-591 16 7 method method NOUN cana-591 16 8 of of ADP cana-591 16 9 handling handle VERB cana-591 16 10 imprecise imprecise NOUN cana-591 16 11 and and CCONJ cana-591 16 12 imperfect imperfect ADJ cana-591 16 13 data datum NOUN cana-591 16 14 in in ADP cana-591 16 15 the the DET cana-591 16 16 early early ADJ cana-591 16 17 1980s 1980 NOUN cana-591 16 18 [ [ X cana-591 16 19 1 1 NUM cana-591 16 20 ] ] PUNCT cana-591 16 21 . . PUNCT cana-591 17 1 the the DET cana-591 17 2 concept concept NOUN cana-591 17 3 of of ADP cana-591 17 4 approximations approximation NOUN cana-591 17 5 is be AUX cana-591 17 6 the the DET cana-591 17 7 foundation foundation NOUN cana-591 17 8 of of ADP cana-591 17 9 rough rough ADJ cana-591 17 10 set set NOUN cana-591 17 11 theory theory NOUN cana-591 17 12 . . PUNCT cana-591 18 1 separating separate VERB cana-591 18 2 the the DET cana-591 18 3 data datum NOUN cana-591 18 4 into into ADP cana-591 18 5 lower low ADJ cana-591 18 6 and and CCONJ cana-591 18 7 upper upper ADJ cana-591 18 8 approximations approximation NOUN cana-591 18 9 offers offer VERB cana-591 18 10 a a DET cana-591 18 11 formal formal ADJ cana-591 18 12 technique technique NOUN cana-591 18 13 for for ADP cana-591 18 14 its its PRON cana-591 18 15 analysis analysis NOUN cana-591 18 16 and and CCONJ cana-591 18 17 classification classification NOUN cana-591 18 18 . . PUNCT cana-591 19 1 the the DET cana-591 19 2 lower low ADJ cana-591 19 3 approximation approximation NOUN cana-591 19 4 represents represent VERB cana-591 19 5 the the DET cana-591 19 6 set set NOUN cana-591 19 7 of of ADP cana-591 19 8 things thing NOUN cana-591 19 9 that that PRON cana-591 19 10 unquestionably unquestionably ADV cana-591 19 11 belong belong VERB cana-591 19 12 to to ADP cana-591 19 13 one one NUM cana-591 19 14 idea idea NOUN cana-591 19 15 , , PUNCT cana-591 19 16 while while SCONJ cana-591 19 17 the the DET cana-591 19 18 higher high ADJ cana-591 19 19 approximation approximation NOUN cana-591 19 20 represents represent VERB cana-591 19 21 the the DET cana-591 19 22 set set NOUN cana-591 19 23 of of ADP cana-591 19 24 potential potential ADJ cana-591 19 25 concepts concept NOUN cana-591 19 26 . . PUNCT cana-591 20 1 the the DET cana-591 20 2 lower low ADJ cana-591 20 3 and and CCONJ cana-591 20 4 higher high ADJ cana-591 20 5 approximation approximation NOUN cana-591 20 6 operators operator NOUN cana-591 20 7 in in ADP cana-591 20 8 pawlak pawlak ADJ cana-591 20 9 rough rough ADJ cana-591 20 10 set set NOUN cana-591 20 11 theory theory NOUN cana-591 20 12 [ [ X cana-591 20 13 2 2 NUM cana-591 20 14 ] ] PUNCT cana-591 20 15 are be AUX cana-591 20 16 based base VERB cana-591 20 17 on on ADP cana-591 20 18 equivalence equivalence NOUN cana-591 20 19 relations relation NOUN cana-591 20 20 . . PUNCT cana-591 21 1 the the DET cana-591 21 2 need need NOUN cana-591 21 3 for for ADP cana-591 21 4 an an DET cana-591 21 5 equivalence equivalence NOUN cana-591 21 6 relation relation NOUN cana-591 21 7 in in ADP cana-591 21 8 pawlak pawlak ADJ cana-591 21 9 rough rough ADJ cana-591 21 10 set set NOUN cana-591 21 11 models model NOUN cana-591 21 12 , , PUNCT cana-591 21 13 however however ADV cana-591 21 14 , , PUNCT cana-591 21 15 appears appear VERB cana-591 21 16 to to PART cana-591 21 17 be be AUX cana-591 21 18 a a DET cana-591 21 19 highly highly ADV cana-591 21 20 rigorous rigorous ADJ cana-591 21 21 requirement requirement NOUN cana-591 21 22 that that PRON cana-591 21 23 can can AUX cana-591 21 24 constrain constrain VERB cana-591 21 25 the the DET cana-591 21 26 applicability applicability NOUN cana-591 21 27 of of ADP cana-591 21 28 the the DET cana-591 21 29 rough rough ADJ cana-591 21 30 set set NOUN cana-591 21 31 models model NOUN cana-591 21 32 . . PUNCT cana-591 22 1 based base VERB cana-591 22 2 on on ADP cana-591 22 3 the the DET cana-591 22 4 comparable comparable ADJ cana-591 22 5 classes class NOUN cana-591 22 6 produced produce VERB cana-591 22 7 by by ADP cana-591 22 8 the the DET cana-591 22 9 attribute attribute NOUN cana-591 22 10 values value NOUN cana-591 22 11 , , PUNCT cana-591 22 12 rough rough ADJ cana-591 22 13 set set NOUN cana-591 22 14 theory theory NOUN cana-591 22 15 divides divide VERB cana-591 22 16 into into ADP cana-591 22 17 three three NUM cana-591 22 18 regions region NOUN cana-591 22 19 : : PUNCT cana-591 22 20 boundary boundary ADJ cana-591 22 21 , , PUNCT cana-591 22 22 lower low ADJ cana-591 22 23 approximation approximation NOUN cana-591 22 24 , , PUNCT cana-591 22 25 and and CCONJ cana-591 22 26 upper upper ADJ cana-591 22 27 approximation approximation NOUN cana-591 22 28 . . PUNCT cana-591 23 1 according accord VERB cana-591 23 2 to to ADP cana-591 23 3 the the DET cana-591 23 4 data datum NOUN cana-591 23 5 gathered gather VERB cana-591 23 6 , , PUNCT cana-591 23 7 the the DET cana-591 23 8 upper upper ADJ cana-591 23 9 approximation approximation NOUN cana-591 23 10 comprises comprise VERB cana-591 23 11 all all DET cana-591 23 12 the the DET cana-591 23 13 things thing NOUN cana-591 23 14 that that PRON cana-591 23 15 can can AUX cana-591 23 16 be be AUX cana-591 23 17 classified classify VERB cana-591 23 18 presumably presumably ADV cana-591 23 19 , , PUNCT cana-591 23 20 while while SCONJ cana-591 23 21 the the DET cana-591 23 22 lower low ADJ cana-591 23 23 approximation approximation NOUN cana-591 23 24 contains contain VERB cana-591 23 25 all all DET cana-591 23 26 the the DET cana-591 23 27 objects object NOUN cana-591 23 28 that that PRON cana-591 23 29 are be AUX cana-591 23 30 classified classify VERB cana-591 23 31 with with ADP cana-591 23 32 certainty certainty PROPN cana-591 23 33 . . PUNCT cana-591 24 1 the the DET cana-591 24 2 boundary boundary NOUN cana-591 24 3 is be AUX cana-591 24 4 the the DET cana-591 24 5 difference difference NOUN cana-591 24 6 between between ADP cana-591 24 7 the the DET cana-591 24 8 upper upper ADJ cana-591 24 9 and and CCONJ cana-591 24 10 lower low ADJ cana-591 24 11 approximations approximation NOUN cana-591 24 12 [ [ X cana-591 24 13 3 3 NUM cana-591 24 14 ] ] PUNCT cana-591 24 15 . . PUNCT cana-591 25 1 communications communication NOUN cana-591 25 2 on on ADP cana-591 25 3 applied apply VERB cana-591 25 4 nonlinear nonlinear ADJ cana-591 25 5 analysis analysis NOUN cana-591 25 6 issn issn NOUN cana-591 25 7 : : PUNCT cana-591 25 8 1074 1074 NUM cana-591 25 9 - - PUNCT cana-591 25 10 133x 133x NUM cana-591 25 11 vol vol NOUN cana-591 25 12 31 31 NUM cana-591 25 13 no no NOUN cana-591 25 14 . . PUNCT cana-591 26 1 2s 2s NUM cana-591 26 2 ( ( PUNCT cana-591 26 3 2024 2024 NUM cana-591 26 4 ) ) PUNCT cana-591 26 5 33 33 NUM cana-591 26 6 https://internationalpubls.com https://internationalpubls.com X cana-591 26 7 from from ADP cana-591 26 8 the the DET cana-591 26 9 perspective perspective NOUN cana-591 26 10 of of ADP cana-591 26 11 decision decision NOUN cana-591 26 12 - - PUNCT cana-591 26 13 making making NOUN cana-591 26 14 , , PUNCT cana-591 26 15 an an DET cana-591 26 16 attained attain VERB cana-591 26 17 rule rule NOUN cana-591 26 18 results result NOUN cana-591 26 19 in in ADP cana-591 26 20 an an DET cana-591 26 21 optimistic optimistic ADJ cana-591 26 22 decision decision NOUN cana-591 26 23 . . PUNCT cana-591 27 1 in in ADP cana-591 27 2 multigranulation multigranulation NOUN cana-591 27 3 rough rough ADJ cana-591 27 4 set set NOUN cana-591 27 5 theory theory NOUN cana-591 27 6 , , PUNCT cana-591 27 7 this this DET cana-591 27 8 model model NOUN cana-591 27 9 is be AUX cana-591 27 10 known know VERB cana-591 27 11 as as ADP cana-591 27 12 the the DET cana-591 27 13 optimistic optimistic ADJ cana-591 27 14 rough rough ADJ cana-591 27 15 set set NOUN cana-591 27 16 model model NOUN cana-591 27 17 . . PUNCT cana-591 28 1 additionally additionally ADV cana-591 28 2 , , PUNCT cana-591 28 3 qian qian PROPN cana-591 28 4 [ [ X cana-591 28 5 4,5 4,5 NUM cana-591 28 6 ] ] PUNCT cana-591 28 7 defines define VERB cana-591 28 8 another another DET cana-591 28 9 model model NOUN cana-591 28 10 known know VERB cana-591 28 11 as as ADP cana-591 28 12 the the DET cana-591 28 13 pessimistic pessimistic ADJ cana-591 28 14 multi multi ADJ cana-591 28 15 - - ADJ cana-591 28 16 granulation granulation ADJ cana-591 28 17 rough rough ADJ cana-591 28 18 set set NOUN cana-591 28 19 model model NOUN cana-591 28 20 . . PUNCT cana-591 29 1 equivalence equivalence NOUN cana-591 29 2 relations relation NOUN cana-591 29 3 are be AUX cana-591 29 4 expanded expand VERB cana-591 29 5 to to ADP cana-591 29 6 comparable comparable ADJ cana-591 29 7 relations relation NOUN cana-591 29 8 or or CCONJ cana-591 29 9 generic generic ADJ cana-591 29 10 binary binary ADJ cana-591 29 11 relations relation NOUN cana-591 29 12 in in ADP cana-591 29 13 the the DET cana-591 29 14 extension extension NOUN cana-591 29 15 of of ADP cana-591 29 16 the the DET cana-591 29 17 classical classical ADJ cana-591 29 18 rough rough ADJ cana-591 29 19 set set NOUN cana-591 29 20 model model NOUN cana-591 29 21 to to ADP cana-591 29 22 the the DET cana-591 29 23 generalized generalized ADJ cana-591 29 24 rough rough ADJ cana-591 29 25 set set NOUN cana-591 29 26 model model NOUN cana-591 29 27 [ [ X cana-591 29 28 6 6 NUM cana-591 29 29 ] ] PUNCT cana-591 29 30 . . PUNCT cana-591 30 1 data datum NOUN cana-591 30 2 distribution distribution NOUN cana-591 30 3 - - PUNCT cana-591 30 4 based base VERB cana-591 30 5 rough rough ADJ cana-591 30 6 set set NOUN cana-591 30 7 models model NOUN cana-591 30 8 , , PUNCT cana-591 30 9 including include VERB cana-591 30 10 the the DET cana-591 30 11 decision decision NOUN cana-591 30 12 - - PUNCT cana-591 30 13 theoretic theoretic NOUN cana-591 30 14 , , PUNCT cana-591 30 15 the the DET cana-591 30 16 probabilistic probabilistic NOUN cana-591 30 17 , , PUNCT cana-591 30 18 the the DET cana-591 30 19 cloud cloud ADJ cana-591 30 20 rough rough ADJ cana-591 30 21 set set NOUN cana-591 30 22 model model NOUN cana-591 30 23 , , PUNCT cana-591 30 24 etc etc X cana-591 31 1 [ [ X cana-591 31 2 7 7 NUM cana-591 31 3 - - SYM cana-591 31 4 9 9 NUM cana-591 31 5 ] ] PUNCT cana-591 31 6 . . PUNCT cana-591 32 1 it it PRON cana-591 32 2 is be AUX cana-591 32 3 essential essential ADJ cana-591 32 4 to to PART cana-591 32 5 have have VERB cana-591 32 6 a a DET cana-591 32 7 technique technique NOUN cana-591 32 8 for for ADP cana-591 32 9 making make VERB cana-591 32 10 decisions decision NOUN cana-591 32 11 that that PRON cana-591 32 12 will will AUX cana-591 32 13 help help VERB cana-591 32 14 in in ADP cana-591 32 15 identifying identify VERB cana-591 32 16 and and CCONJ cana-591 32 17 choosing choose VERB cana-591 32 18 the the DET cana-591 32 19 best good ADJ cana-591 32 20 motorized motorize VERB cana-591 32 21 vehicles vehicle NOUN cana-591 32 22 . . PUNCT cana-591 33 1 there there PRON cana-591 33 2 are be VERB cana-591 33 3 a a DET cana-591 33 4 number number NOUN cana-591 33 5 of of ADP cana-591 33 6 approaches approach NOUN cana-591 33 7 for for ADP cana-591 33 8 creating create VERB cana-591 33 9 a a DET cana-591 33 10 decision decision NOUN cana-591 33 11 support support NOUN cana-591 33 12 system system NOUN cana-591 33 13 ( ( PUNCT cana-591 33 14 dss dss NOUN cana-591 33 15 ) ) PUNCT cana-591 33 16 , , PUNCT cana-591 33 17 and and CCONJ cana-591 33 18 one one NUM cana-591 33 19 method method NOUN cana-591 33 20 that that PRON cana-591 33 21 may may AUX cana-591 33 22 be be AUX cana-591 33 23 utilized utilize VERB cana-591 33 24 for for ADP cana-591 33 25 decision decision NOUN cana-591 33 26 making make VERB cana-591 33 27 systems system NOUN cana-591 33 28 is be AUX cana-591 33 29 wp wp PROPN cana-591 33 30 ( ( PUNCT cana-591 33 31 weighted weight VERB cana-591 33 32 product product NOUN cana-591 33 33 ) ) PUNCT cana-591 34 1 [ [ X cana-591 34 2 10 10 NUM cana-591 34 3 ] ] PUNCT cana-591 34 4 . . PUNCT cana-591 35 1 although although SCONJ cana-591 35 2 bikes bike NOUN cana-591 35 3 with with ADP cana-591 35 4 small small ADJ cana-591 35 5 engines engine NOUN cana-591 35 6 spend spend VERB cana-591 35 7 less less ADJ cana-591 35 8 fuel fuel NOUN cana-591 35 9 ( ( PUNCT cana-591 35 10 per per ADP cana-591 35 11 person person NOUN cana-591 35 12 - - PUNCT cana-591 35 13 kilometer kilometer NOUN cana-591 35 14 ) ) PUNCT cana-591 35 15 than than ADP cana-591 35 16 cars car NOUN cana-591 35 17 , , PUNCT cana-591 35 18 the the DET cana-591 35 19 situation situation NOUN cana-591 35 20 may may AUX cana-591 35 21 be be AUX cana-591 35 22 the the DET cana-591 35 23 opposite opposite NOUN cana-591 35 24 for for ADP cana-591 35 25 motorcycles motorcycle NOUN cana-591 35 26 with with ADP cana-591 35 27 larger large ADJ cana-591 35 28 engines engine NOUN cana-591 35 29 that that PRON cana-591 35 30 are be AUX cana-591 35 31 more more ADV cana-591 35 32 potent potent ADJ cana-591 35 33 . . PUNCT cana-591 36 1 additionally additionally ADV cana-591 36 2 , , PUNCT cana-591 36 3 if if SCONJ cana-591 36 4 short short ADJ cana-591 36 5 non non ADJ cana-591 36 6 - - ADJ cana-591 36 7 motorized motorized ADJ cana-591 36 8 journeys journey NOUN cana-591 36 9 are be AUX cana-591 36 10 replaced replace VERB cana-591 36 11 with with ADP cana-591 36 12 longer long ADJ cana-591 36 13 motorbike motorbike NOUN cana-591 36 14 excursions excursion NOUN cana-591 36 15 , , PUNCT cana-591 36 16 the the DET cana-591 36 17 overall overall ADJ cana-591 36 18 energy energy NOUN cana-591 36 19 efficiency efficiency NOUN cana-591 36 20 of of ADP cana-591 36 21 the the DET cana-591 36 22 transportation transportation NOUN cana-591 36 23 system system NOUN cana-591 36 24 declines decline VERB cana-591 36 25 . . PUNCT cana-591 37 1 pfaffenbichler pfaffenbichler NOUN cana-591 37 2 and and CCONJ cana-591 37 3 circella circella NOUN cana-591 38 1 [ [ X cana-591 38 2 11 11 NUM cana-591 38 3 ] ] PUNCT cana-591 38 4 analyzed analyze VERB cana-591 38 5 the the DET cana-591 38 6 conditions condition NOUN cana-591 38 7 under under ADP cana-591 38 8 which which PRON cana-591 38 9 motorbikes motorbike NOUN cana-591 38 10 can can AUX cana-591 38 11 significantly significantly ADV cana-591 38 12 contribute contribute VERB cana-591 38 13 to to ADP cana-591 38 14 the the DET cana-591 38 15 development development NOUN cana-591 38 16 of of ADP cana-591 38 17 an an DET cana-591 38 18 energy energy NOUN cana-591 38 19 - - PUNCT cana-591 38 20 efficient efficient ADJ cana-591 38 21 and and CCONJ cana-591 38 22 sustainable sustainable ADJ cana-591 38 23 transportation transportation NOUN cana-591 38 24 system system NOUN cana-591 38 25 . . PUNCT cana-591 39 1 butalia butalia PROPN cana-591 39 2 et et PROPN cana-591 39 3 al al PROPN cana-591 39 4 . . PUNCT cana-591 40 1 [ [ X cana-591 40 2 12 12 NUM cana-591 40 3 ] ] PUNCT cana-591 40 4 revealed reveal VERB cana-591 40 5 that that SCONJ cana-591 40 6 two two NUM cana-591 40 7 innovative innovative ADJ cana-591 40 8 methods method NOUN cana-591 40 9 are be AUX cana-591 40 10 implemented implement VERB cana-591 40 11 in in ADP cana-591 40 12 java java PROPN cana-591 40 13 1.5 1.5 NUM cana-591 40 14 to to PART cana-591 40 15 determine determine VERB cana-591 40 16 , , PUNCT cana-591 40 17 in in ADP cana-591 40 18 light light NOUN cana-591 40 19 of of ADP cana-591 40 20 the the DET cana-591 40 21 relative relative ADJ cana-591 40 22 attribute attribute NOUN cana-591 40 23 dependency dependency NOUN cana-591 40 24 , , PUNCT cana-591 40 25 the the DET cana-591 40 26 best good ADJ cana-591 40 27 reductions reduction NOUN cana-591 40 28 of of ADP cana-591 40 29 condition condition NOUN cana-591 40 30 attributes attribute VERB cana-591 40 31 . . PUNCT cana-591 41 1 the the DET cana-591 41 2 first first ADJ cana-591 41 3 algorithm algorithm NOUN cana-591 41 4 provides provide VERB cana-591 41 5 a a DET cana-591 41 6 simple simple ADJ cana-591 41 7 reduct reduct NOUN cana-591 41 8 , , PUNCT cana-591 41 9 while while SCONJ cana-591 41 10 the the DET cana-591 41 11 second second ADJ cana-591 41 12 one one NOUN cana-591 41 13 provides provide VERB cana-591 41 14 a a DET cana-591 41 15 reduct reduct NOUN cana-591 41 16 with with ADP cana-591 41 17 minimum minimum ADJ cana-591 41 18 attributes attribute NOUN cana-591 41 19 . . PUNCT cana-591 42 1 in in ADP cana-591 42 2 order order NOUN cana-591 42 3 to to PART cana-591 42 4 create create VERB cana-591 42 5 the the DET cana-591 42 6 core core NOUN cana-591 42 7 of of ADP cana-591 42 8 the the DET cana-591 42 9 attribute attribute NOUN cana-591 42 10 set set VERB cana-591 42 11 or or CCONJ cana-591 42 12 the the DET cana-591 42 13 effective effective ADJ cana-591 42 14 reduct reduct PROPN cana-591 42 15 set set PROPN cana-591 42 16 , , PUNCT cana-591 42 17 unnecessary unnecessary ADJ cana-591 42 18 attributes attribute NOUN cana-591 42 19 are be AUX cana-591 42 20 removed remove VERB cana-591 42 21 using use VERB cana-591 42 22 vashist vashist NOUN cana-591 42 23 's 's PART cana-591 42 24 [ [ X cana-591 42 25 13 13 NUM cana-591 42 26 ] ] PUNCT cana-591 42 27 suggested suggest VERB cana-591 42 28 algorithm algorithm NOUN cana-591 42 29 . . PUNCT cana-591 43 1 the the DET cana-591 43 2 space space NOUN cana-591 43 3 complexity complexity NOUN cana-591 43 4 and and CCONJ cana-591 43 5 computed compute VERB cana-591 43 6 time time NOUN cana-591 43 7 of of ADP cana-591 43 8 the the DET cana-591 43 9 suggested suggest VERB cana-591 43 10 approach approach NOUN cana-591 43 11 is be AUX cana-591 43 12 compared compare VERB cana-591 43 13 to to ADP cana-591 43 14 that that PRON cana-591 43 15 of of ADP cana-591 43 16 other other ADJ cana-591 43 17 known know VERB cana-591 43 18 algorithms algorithm NOUN cana-591 43 19 . . PUNCT cana-591 44 1 it it PRON cana-591 44 2 is be AUX cana-591 44 3 proven prove VERB cana-591 44 4 that that SCONJ cana-591 44 5 the the DET cana-591 44 6 suggested suggest VERB cana-591 44 7 method method NOUN cana-591 44 8 reduces reduce VERB cana-591 44 9 computation computation NOUN cana-591 44 10 time time NOUN cana-591 44 11 and and CCONJ cana-591 44 12 space space NOUN cana-591 44 13 without without ADP cana-591 44 14 sacrificing sacrifice VERB cana-591 44 15 the the DET cana-591 44 16 efficacy efficacy NOUN cana-591 44 17 and and CCONJ cana-591 44 18 quality quality NOUN cana-591 44 19 of of ADP cana-591 44 20 the the DET cana-591 44 21 output output NOUN cana-591 44 22 . . PUNCT cana-591 45 1 wu wu PROPN cana-591 45 2 and and CCONJ cana-591 45 3 mi mi PROPN cana-591 46 1 [ [ X cana-591 46 2 14 14 NUM cana-591 46 3 ] ] PUNCT cana-591 46 4 investigated investigate VERB cana-591 46 5 rough rough ADJ cana-591 46 6 sets set NOUN cana-591 46 7 ' ' PART cana-591 46 8 mathematical mathematical ADJ cana-591 46 9 structure structure NOUN cana-591 46 10 in in ADP cana-591 46 11 infinite infinite ADJ cana-591 46 12 universes universe NOUN cana-591 46 13 of of ADP cana-591 46 14 discourse discourse NOUN cana-591 46 15 . . PUNCT cana-591 47 1 nowadays nowadays ADV cana-591 47 2 , , PUNCT cana-591 47 3 there there PRON cana-591 47 4 are be VERB cana-591 47 5 many many ADJ cana-591 47 6 various various ADJ cana-591 47 7 types type NOUN cana-591 47 8 of of ADP cana-591 47 9 motorcycles motorcycle NOUN cana-591 47 10 , , PUNCT cana-591 47 11 including include VERB cana-591 47 12 mopeds moped NOUN cana-591 47 13 with with ADP cana-591 47 14 a a DET cana-591 47 15 50 50 NUM cana-591 47 16 cubic cubic ADJ cana-591 47 17 centimeter centimeter NOUN cana-591 47 18 engine engine NOUN cana-591 47 19 , , PUNCT cana-591 47 20 scooters scooter NOUN cana-591 47 21 with with ADP cana-591 47 22 engines engine NOUN cana-591 47 23 between between ADP cana-591 47 24 50 50 NUM cana-591 47 25 and and CCONJ cana-591 47 26 250 250 NUM cana-591 47 27 cubic cubic ADJ cana-591 47 28 centimeters centimeter NOUN cana-591 47 29 , , PUNCT cana-591 47 30 and and CCONJ cana-591 47 31 motorbikes motorbike NOUN cana-591 47 32 with with ADP cana-591 47 33 engines engine NOUN cana-591 47 34 up up ADP cana-591 47 35 to to PART cana-591 47 36 1,000 1,000 NUM cana-591 47 37 centimeters centimeter NOUN cana-591 47 38 and and CCONJ cana-591 47 39 even even ADV cana-591 47 40 more more ADJ cana-591 47 41 . . PUNCT cana-591 48 1 based base VERB cana-591 48 2 on on ADP cana-591 48 3 these these DET cana-591 48 4 characteristics characteristic NOUN cana-591 48 5 , , PUNCT cana-591 48 6 we we PRON cana-591 48 7 may may AUX cana-591 48 8 divide divide VERB cana-591 48 9 bikes bike NOUN cana-591 48 10 into into ADP cana-591 48 11 various various ADJ cana-591 48 12 equivalence equivalence NOUN cana-591 48 13 classes class NOUN cana-591 48 14 in in ADP cana-591 48 15 this this DET cana-591 48 16 study study NOUN cana-591 48 17 using use VERB cana-591 48 18 rst rst PRON cana-591 48 19 . . PUNCT cana-591 49 1 also also ADV cana-591 49 2 , , PUNCT cana-591 49 3 we we PRON cana-591 49 4 discover discover VERB cana-591 49 5 the the DET cana-591 49 6 important important ADJ cana-591 49 7 and and CCONJ cana-591 49 8 optional optional ADJ cana-591 49 9 aspects aspect NOUN cana-591 49 10 of of ADP cana-591 49 11 various various ADJ cana-591 49 12 cc cc NOUN cana-591 49 13 motorbikes motorbike NOUN cana-591 49 14 by by ADP cana-591 49 15 using use VERB cana-591 49 16 rst rst PROPN cana-591 49 17 and and CCONJ cana-591 49 18 examining examine VERB cana-591 49 19 the the DET cana-591 49 20 relationship relationship NOUN cana-591 49 21 between between ADP cana-591 49 22 these these DET cana-591 49 23 attributes attribute NOUN cana-591 49 24 . . PUNCT cana-591 50 1 the the DET cana-591 50 2 results result NOUN cana-591 50 3 of of ADP cana-591 50 4 this this DET cana-591 50 5 research research NOUN cana-591 50 6 can can AUX cana-591 50 7 be be AUX cana-591 50 8 useful useful ADJ cana-591 50 9 for for ADP cana-591 50 10 making make VERB cana-591 50 11 decisions decision NOUN cana-591 50 12 , , PUNCT cana-591 50 13 such such ADJ cana-591 50 14 as as ADP cana-591 50 15 selecting select VERB cana-591 50 16 the the DET cana-591 50 17 best good ADJ cana-591 50 18 bike bike NOUN cana-591 50 19 for for ADP cana-591 50 20 a a DET cana-591 50 21 particular particular ADJ cana-591 50 22 set set NOUN cana-591 50 23 of of ADP cana-591 50 24 requirements requirement NOUN cana-591 50 25 or or CCONJ cana-591 50 26 desires desire NOUN cana-591 50 27 . . PUNCT cana-591 51 1 let let VERB cana-591 51 2 's us PRON cana-591 51 3 consider consider VERB cana-591 51 4 that that SCONJ cana-591 51 5 we we PRON cana-591 51 6 have have VERB cana-591 51 7 a a DET cana-591 51 8 list list NOUN cana-591 51 9 of of ADP cana-591 51 10 bikes bike NOUN cana-591 51 11 with with ADP cana-591 51 12 the the DET cana-591 51 13 following follow VERB cana-591 51 14 attributes attribute NOUN cana-591 51 15 : : PUNCT cana-591 52 1 1 1 X cana-591 52 2 . . X cana-591 52 3 brand brand NOUN cana-591 52 4 ( ( PUNCT cana-591 52 5 b b NOUN cana-591 52 6 ): ): PUNCT cana-591 52 7 the the DET cana-591 52 8 brand brand NOUN cana-591 52 9 of of ADP cana-591 52 10 the the DET cana-591 52 11 bike bike NOUN cana-591 52 12 ( ( PUNCT cana-591 52 13 e.g. e.g. ADV cana-591 52 14 , , PUNCT cana-591 52 15 honda honda PROPN cana-591 52 16 , , PUNCT cana-591 52 17 yamaha yamaha PROPN cana-591 52 18 , , PUNCT cana-591 52 19 suzuki suzuki PROPN cana-591 52 20 , , PUNCT cana-591 52 21 etc etc X cana-591 52 22 . . X cana-591 52 23 ) ) PUNCT cana-591 53 1 as as ADP cana-591 53 2 ( ( PUNCT cana-591 53 3 π‘₯1 π‘₯1 NOUN cana-591 53 4 , , PUNCT cana-591 53 5 π‘₯2 π‘₯2 NOUN cana-591 53 6 , , PUNCT cana-591 53 7 π‘₯3 π‘₯3 NOUN cana-591 53 8 , , PUNCT cana-591 53 9 π‘₯4 π‘₯4 NOUN cana-591 53 10 … … PUNCT cana-591 53 11 ) ) PUNCT cana-591 53 12 2 2 NUM cana-591 53 13 . . X cana-591 53 14 engine engine NOUN cana-591 53 15 displacement displacement NOUN cana-591 53 16 ( ( PUNCT cana-591 53 17 e e NOUN cana-591 53 18 ): ): PUNCT cana-591 53 19 the the DET cana-591 53 20 engine engine NOUN cana-591 53 21 displacement displacement NOUN cana-591 53 22 in in ADP cana-591 53 23 cubic cubic ADJ cana-591 53 24 centimeters centimeter NOUN cana-591 53 25 ( ( PUNCT cana-591 53 26 e.g. e.g. ADV cana-591 53 27 , , PUNCT cana-591 53 28 100 100 NUM cana-591 53 29 cc cc NOUN cana-591 53 30 , , PUNCT cana-591 53 31 150 150 NUM cana-591 53 32 cc cc NOUN cana-591 53 33 , , PUNCT cana-591 53 34 etc etc X cana-591 53 35 . . X cana-591 53 36 ) ) PUNCT cana-591 53 37 . . PUNCT cana-591 54 1 3 3 X cana-591 54 2 . . X cana-591 54 3 fuel fuel NOUN cana-591 54 4 efficiency efficiency NOUN cana-591 54 5 ( ( PUNCT cana-591 54 6 f f X cana-591 54 7 ): ): PUNCT cana-591 54 8 the the DET cana-591 54 9 fuel fuel NOUN cana-591 54 10 efficiency efficiency NOUN cana-591 54 11 of of ADP cana-591 54 12 the the DET cana-591 54 13 bike bike NOUN cana-591 54 14 in in ADP cana-591 54 15 kilometers kilometer NOUN cana-591 54 16 per per ADP cana-591 54 17 litre litre NOUN cana-591 54 18 ( ( PUNCT cana-591 54 19 e.g. e.g. ADV cana-591 54 20 , , PUNCT cana-591 54 21 40 40 NUM cana-591 54 22 km km NOUN cana-591 54 23 / / SYM cana-591 54 24 l l NOUN cana-591 54 25 , , PUNCT cana-591 54 26 50 50 NUM cana-591 54 27 km km NOUN cana-591 54 28 / / SYM cana-591 54 29 l l NOUN cana-591 54 30 , , PUNCT cana-591 54 31 etc etc X cana-591 54 32 . . X cana-591 54 33 ) ) PUNCT cana-591 54 34 . . PUNCT cana-591 55 1 4 4 X cana-591 55 2 . . X cana-591 55 3 price price NOUN cana-591 55 4 ( ( PUNCT cana-591 55 5 p p X cana-591 55 6 ): ): PUNCT cana-591 55 7 the the DET cana-591 55 8 price price NOUN cana-591 55 9 of of ADP cana-591 55 10 the the DET cana-591 55 11 bike bike NOUN cana-591 55 12 in in ADP cana-591 55 13 a a DET cana-591 55 14 certain certain ADJ cana-591 55 15 currency currency NOUN cana-591 55 16 ( ( PUNCT cana-591 55 17 e.g. e.g. ADV cana-591 55 18 , , PUNCT cana-591 55 19 usd usd NOUN cana-591 55 20 , , PUNCT cana-591 55 21 inr inr PROPN cana-591 55 22 , , PUNCT cana-591 55 23 etc etc X cana-591 55 24 . . X cana-591 55 25 ) ) PUNCT cana-591 55 26 . . PUNCT cana-591 56 1 5 5 X cana-591 56 2 . . X cana-591 56 3 style style NOUN cana-591 56 4 ( ( PUNCT cana-591 56 5 s s X cana-591 56 6 ): ): PUNCT cana-591 56 7 the the DET cana-591 56 8 style style NOUN cana-591 56 9 of of ADP cana-591 56 10 the the DET cana-591 56 11 bike bike NOUN cana-591 56 12 ( ( PUNCT cana-591 56 13 e.g. e.g. ADV cana-591 56 14 , , PUNCT cana-591 56 15 commuter commuter NOUN cana-591 56 16 , , PUNCT cana-591 56 17 sport sport NOUN cana-591 56 18 , , PUNCT cana-591 56 19 cruiser cruiser NOUN cana-591 56 20 , , PUNCT cana-591 56 21 etc etc X cana-591 56 22 . . X cana-591 56 23 ) ) PUNCT cana-591 56 24 . . PUNCT cana-591 57 1 communications communication NOUN cana-591 57 2 on on ADP cana-591 57 3 applied apply VERB cana-591 57 4 nonlinear nonlinear ADJ cana-591 57 5 analysis analysis NOUN cana-591 57 6 issn issn NOUN cana-591 57 7 : : PUNCT cana-591 57 8 1074 1074 NUM cana-591 57 9 - - PUNCT cana-591 57 10 133x 133x NUM cana-591 57 11 vol vol NOUN cana-591 57 12 31 31 NUM cana-591 57 13 no no NOUN cana-591 57 14 . . PUNCT cana-591 58 1 2s 2s NUM cana-591 58 2 ( ( PUNCT cana-591 58 3 2024 2024 NUM cana-591 58 4 ) ) PUNCT cana-591 58 5 34 34 NUM cana-591 59 1 https://internationalpubls.com https://internationalpubls.com X cana-591 59 2 2 2 NUM cana-591 59 3 . . X cana-591 59 4 rough rough ADJ cana-591 59 5 set set NOUN cana-591 59 6 analysis analysis NOUN cana-591 59 7 now now ADV cana-591 59 8 , , PUNCT cana-591 59 9 let let VERB cana-591 59 10 's us PRON cana-591 59 11 apply apply VERB cana-591 59 12 a a DET cana-591 59 13 simplified simplified ADJ cana-591 59 14 rough rough ADJ cana-591 59 15 set set NOUN cana-591 59 16 analysis analysis NOUN cana-591 59 17 with with ADP cana-591 59 18 seven seven NUM cana-591 59 19 types type NOUN cana-591 59 20 of of ADP cana-591 59 21 analysis analysis NOUN cana-591 59 22 : : PUNCT cana-591 59 23 2.1 2.1 NUM cana-591 59 24 lower low ADJ cana-591 59 25 approximation approximation NOUN cana-591 59 26 ( ( PUNCT cana-591 59 27 certain certain ADJ cana-591 59 28 knowledge knowledge NOUN cana-591 59 29 ) ) PUNCT cana-591 59 30 identify identify VERB cana-591 59 31 the the DET cana-591 59 32 bikes bike NOUN cana-591 59 33 that that PRON cana-591 59 34 definitely definitely ADV cana-591 59 35 belong belong VERB cana-591 59 36 to to ADP cana-591 59 37 the the DET cana-591 59 38 100 100 NUM cana-591 59 39 cc cc NOUN cana-591 59 40 category category NOUN cana-591 59 41 based base VERB cana-591 59 42 on on ADP cana-591 59 43 their their PRON cana-591 59 44 engine engine NOUN cana-591 59 45 displacement displacement NOUN cana-591 59 46 of of ADP cana-591 59 47 a a DET cana-591 59 48 set set NOUN cana-591 59 49 𝑋 𝑋 NOUN cana-591 59 50 with with ADP cana-591 59 51 respect respect NOUN cana-591 59 52 to to ADP cana-591 59 53 𝑆. 𝑆. NOUN cana-591 59 54 the the DET cana-591 59 55 lower low ADJ cana-591 59 56 approximation approximation NOUN cana-591 59 57 is be AUX cana-591 59 58 represented represent VERB cana-591 59 59 by by ADP cana-591 59 60 π‘†βˆ—(π‘₯ π‘†βˆ—(π‘₯ PROPN cana-591 59 61 ) ) PUNCT cana-591 59 62 . . PUNCT cana-591 60 1 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 60 2 ) ) PUNCT cana-591 60 3 = = PRON cana-591 60 4 { { PUNCT cana-591 60 5 π‘₯ π‘₯ NOUN cana-591 60 6 : : PUNCT cana-591 60 7 𝑆(π‘₯ 𝑆(π‘₯ NUM cana-591 60 8 ) ) PUNCT cana-591 60 9 βŠ† βŠ† NUM cana-591 60 10 𝑋 𝑋 PROPN cana-591 60 11 } } PUNCT cana-591 60 12 . . PUNCT cana-591 60 13 2.2 2.2 NUM cana-591 60 14 upper upper ADJ cana-591 60 15 approximation approximation NOUN cana-591 60 16 ( ( PUNCT cana-591 60 17 potential potential ADJ cana-591 60 18 knowledge knowledge NOUN cana-591 60 19 ) ) PUNCT cana-591 60 20 identify identify VERB cana-591 60 21 the the DET cana-591 60 22 bikes bike NOUN cana-591 60 23 that that PRON cana-591 60 24 potentially potentially ADV cana-591 60 25 belong belong VERB cana-591 60 26 to to ADP cana-591 60 27 the the DET cana-591 60 28 100 100 NUM cana-591 60 29 cc cc NOUN cana-591 60 30 category category NOUN cana-591 60 31 based base VERB cana-591 60 32 on on ADP cana-591 60 33 their their PRON cana-591 60 34 engine engine NOUN cana-591 60 35 displacement displacement NOUN cana-591 60 36 𝑋 𝑋 NOUN cana-591 60 37 with with ADP cana-591 60 38 respect respect NOUN cana-591 60 39 to to ADP cana-591 60 40 𝑆. 𝑆. PROPN cana-591 60 41 the the DET cana-591 60 42 upper upper ADJ cana-591 60 43 approximation approximation NOUN cana-591 60 44 is be AUX cana-591 60 45 referred refer VERB cana-591 60 46 by by ADP cana-591 60 47 π‘†βˆ—(π‘₯ π‘†βˆ—(π‘₯ PROPN cana-591 60 48 ) ) PUNCT cana-591 60 49 . . PUNCT cana-591 61 1 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 61 2 ) ) PUNCT cana-591 61 3 = = PRON cana-591 61 4 { { PUNCT cana-591 61 5 π‘₯ π‘₯ NOUN cana-591 61 6 : : PUNCT cana-591 61 7 𝑆(π‘₯ 𝑆(π‘₯ NUM cana-591 61 8 ) ) PUNCT cana-591 61 9 βŠ† βŠ† NUM cana-591 61 10 𝑋 𝑋 PROPN cana-591 61 11 } } PUNCT cana-591 61 12 . . PUNCT cana-591 62 1 2.3 2.3 NUM cana-591 62 2 negative negative ADJ cana-591 62 3 region region NOUN cana-591 62 4 ( ( PUNCT cana-591 62 5 contradiction contradiction NOUN cana-591 62 6 ) ) PUNCT cana-591 62 7 identify identify VERB cana-591 62 8 attributes attribute NOUN cana-591 62 9 of of ADP cana-591 62 10 the the DET cana-591 62 11 set set NOUN cana-591 62 12 of of ADP cana-591 62 13 objects object NOUN cana-591 62 14 that that PRON cana-591 62 15 are be AUX cana-591 62 16 contradictory contradictory ADJ cana-591 62 17 to to ADP cana-591 62 18 the the DET cana-591 62 19 100 100 NUM cana-591 62 20 cc cc NOUN cana-591 62 21 category category NOUN cana-591 62 22 of of ADP cana-591 62 23 the the DET cana-591 62 24 set set NOUN cana-591 62 25 𝑋. 𝑋. PROPN cana-591 62 26 π‘ˆ π‘ˆ PROPN cana-591 62 27 βˆ’ βˆ’ PROPN cana-591 62 28 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 62 29 ) ) PUNCT cana-591 62 30 2.4 2.4 NUM cana-591 62 31 boundary boundary ADJ cana-591 62 32 region region NOUN cana-591 62 33 ( ( PUNCT cana-591 62 34 uncertainty uncertainty NOUN cana-591 62 35 ) ) PUNCT cana-591 62 36 identify identify VERB cana-591 62 37 attributes attribute NOUN cana-591 62 38 that that PRON cana-591 62 39 are be AUX cana-591 62 40 ambiguous ambiguous ADJ cana-591 62 41 and and CCONJ cana-591 62 42 contribute contribute VERB cana-591 62 43 to to ADP cana-591 62 44 the the DET cana-591 62 45 uncertainty uncertainty NOUN cana-591 62 46 of of ADP cana-591 62 47 bike bike NOUN cana-591 62 48 categorisation categorisation NOUN cana-591 62 49 of of ADP cana-591 62 50 a a DET cana-591 62 51 set set NOUN cana-591 62 52 𝑋 𝑋 NOUN cana-591 62 53 with with ADP cana-591 62 54 respect respect NOUN cana-591 62 55 to to ADP cana-591 62 56 𝑆 𝑆 PROPN cana-591 62 57 and and CCONJ cana-591 62 58 is be AUX cana-591 62 59 denoted denote VERB cana-591 62 60 by by ADP cana-591 62 61 𝑆𝑁𝑆(𝑋 𝑆𝑁𝑆(𝑋 PROPN cana-591 62 62 ) ) PUNCT cana-591 62 63 . . PUNCT cana-591 63 1 𝑆𝑁𝑆(𝑋 𝑆𝑁𝑆(𝑋 NOUN cana-591 63 2 ) ) PUNCT cana-591 63 3 = = PUNCT cana-591 64 1 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 64 2 ) ) PUNCT cana-591 64 3 βˆ’ βˆ’ PROPN cana-591 64 4 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 64 5 ) ) PUNCT cana-591 64 6 . . PUNCT cana-591 65 1 2.5 2.5 NUM cana-591 65 2 indiscernibility indiscernibility NOUN cana-591 65 3 relation relation NOUN cana-591 65 4 ( ( PUNCT cana-591 65 5 equivalence equivalence NOUN cana-591 65 6 ) ) PUNCT cana-591 65 7 identify identify VERB cana-591 65 8 bikes bike NOUN cana-591 65 9 that that PRON cana-591 65 10 are be AUX cana-591 65 11 indiscernible indiscernible ADJ cana-591 65 12 ( ( PUNCT cana-591 65 13 indistinguishable indistinguishable ADJ cana-591 65 14 ) ) PUNCT cana-591 65 15 based base VERB cana-591 65 16 on on ADP cana-591 65 17 the the DET cana-591 65 18 selected select VERB cana-591 65 19 attributes attribute NOUN cana-591 65 20 . . PUNCT cana-591 66 1 let let VERB cana-591 66 2 𝑅 𝑅 PROPN cana-591 66 3 = = SYM cana-591 66 4 ( ( PUNCT cana-591 66 5 𝐴 𝐴 PROPN cana-591 66 6 , , PUNCT cana-591 66 7 𝐡 𝐡 PROPN cana-591 66 8 ) ) PUNCT cana-591 66 9 be be VERB cana-591 66 10 an an DET cana-591 66 11 information information NOUN cana-591 66 12 system system NOUN cana-591 66 13 , , PUNCT cana-591 66 14 and and CCONJ cana-591 66 15 𝑋 𝑋 PROPN cana-591 66 16 βŠ† βŠ† PROPN cana-591 66 17 𝐴. 𝐴. PROPN cana-591 66 18 a a DET cana-591 66 19 binary binary ADJ cana-591 66 20 relation relation NOUN cana-591 66 21 𝐼𝑁𝐷𝑅(𝑋 𝐼𝑁𝐷𝑅(𝑋 NOUN cana-591 66 22 ) ) PUNCT cana-591 66 23 defined define VERB cana-591 66 24 in in ADP cana-591 66 25 the the DET cana-591 66 26 following following ADJ cana-591 66 27 way way NOUN cana-591 66 28 𝐼𝑁𝐷𝑅⁑(𝑋 𝐼𝑁𝐷𝑅⁑(𝑋 NUM cana-591 66 29 ) ) PUNCT cana-591 66 30 = = PRON cana-591 66 31 { { PUNCT cana-591 66 32 ( ( PUNCT cana-591 66 33 π‘₯1 π‘₯1 NOUN cana-591 66 34 , , PUNCT cana-591 66 35 π‘₯2 π‘₯2 NOUN cana-591 66 36 ) ) PUNCT cana-591 66 37 ∈ ∈ PROPN cana-591 66 38 𝐴2 𝐴2 PROPN cana-591 66 39 ∣ ∣ PROPN cana-591 66 40 βˆ€π‘Žπ‘‹ βˆ€π‘Žπ‘‹ PROPN cana-591 66 41 , , PUNCT cana-591 66 42 π‘Ž(π‘₯1 π‘Ž(π‘₯1 NOUN cana-591 66 43 ) ) PUNCT cana-591 66 44 = = SYM cana-591 66 45 π‘Ž(π‘₯2 π‘Ž(π‘₯2 X cana-591 66 46 ) ) PUNCT cana-591 66 47 } } PUNCT cana-591 66 48 is be AUX cana-591 66 49 called call VERB cana-591 66 50 a a DET cana-591 66 51 𝑋-indiscernibility 𝑋-indiscernibility PROPN cana-591 66 52 relation relation NOUN cana-591 66 53 [ [ X cana-591 66 54 π‘₯]𝑅. π‘₯]𝑅. X cana-591 66 55 if if SCONJ cana-591 66 56 ( ( PUNCT cana-591 66 57 π‘₯1 π‘₯1 NOUN cana-591 66 58 , , PUNCT cana-591 66 59 π‘₯2 π‘₯2 NOUN cana-591 66 60 ) ) PUNCT cana-591 66 61 ∈ ∈ PROPN cana-591 66 62 𝐼𝑁𝐷𝑅(𝑋 𝐼𝑁𝐷𝑅(𝑋 NOUN cana-591 66 63 ) ) PUNCT cana-591 66 64 , , PUNCT cana-591 66 65 then then ADV cana-591 66 66 π‘₯1 π‘₯1 NOUN cana-591 66 67 and and CCONJ cana-591 66 68 π‘₯2 π‘₯2 NOUN cana-591 66 69 are be AUX cana-591 66 70 indiscernible indiscernible ADJ cana-591 66 71 ( ( PUNCT cana-591 66 72 or or CCONJ cana-591 66 73 indistinguishable indistinguishable ADJ cana-591 66 74 ) ) PUNCT cana-591 66 75 by by ADP cana-591 66 76 attributes attribute NOUN cana-591 66 77 from from ADP cana-591 66 78 𝑋. 𝑋. PROPN cana-591 66 79 2.6 2.6 NUM cana-591 66 80 reduct reduct PROPN cana-591 66 81 ( ( PUNCT cana-591 66 82 minimal minimal ADJ cana-591 66 83 set set NOUN cana-591 66 84 of of ADP cana-591 66 85 attributes attribute NOUN cana-591 66 86 ) ) PUNCT cana-591 66 87 identify identify VERB cana-591 66 88 the the DET cana-591 66 89 smallest small ADJ cana-591 66 90 set set NOUN cana-591 66 91 of of ADP cana-591 66 92 attributes attribute NOUN cana-591 66 93 that that PRON cana-591 66 94 are be AUX cana-591 66 95 sufficient sufficient ADJ cana-591 66 96 to to PART cana-591 66 97 determine determine VERB cana-591 66 98 the the DET cana-591 66 99 category category NOUN cana-591 66 100 of of ADP cana-591 66 101 a a DET cana-591 66 102 bike bike NOUN cana-591 66 103 . . PUNCT cana-591 67 1 using use VERB cana-591 67 2 these these DET cana-591 67 3 analyses analysis NOUN cana-591 67 4 , , PUNCT cana-591 67 5 you you PRON cana-591 67 6 would would AUX cana-591 67 7 analyze analyze VERB cana-591 67 8 the the DET cana-591 67 9 attributes attribute NOUN cana-591 67 10 of of ADP cana-591 67 11 the the DET cana-591 67 12 bikes bike NOUN cana-591 67 13 in in ADP cana-591 67 14 your your PRON cana-591 67 15 list list NOUN cana-591 67 16 and and CCONJ cana-591 67 17 determine determine VERB cana-591 67 18 their their PRON cana-591 67 19 relationships relationship NOUN cana-591 67 20 to to ADP cana-591 67 21 the the DET cana-591 67 22 100 100 NUM cana-591 67 23 cc cc NOUN cana-591 67 24 category category NOUN cana-591 67 25 in in ADP cana-591 67 26 table table NOUN cana-591 67 27 1 1 NUM cana-591 67 28 . . PUNCT cana-591 68 1 this this DET cana-591 68 2 analysis analysis NOUN cana-591 68 3 would would AUX cana-591 68 4 provide provide VERB cana-591 68 5 insights insight NOUN cana-591 68 6 into into ADP cana-591 68 7 the the DET cana-591 68 8 characteristics characteristic NOUN cana-591 68 9 of of ADP cana-591 68 10 bikes bike NOUN cana-591 68 11 that that PRON cana-591 68 12 belong belong VERB cana-591 68 13 to to ADP cana-591 68 14 the the DET cana-591 68 15 100 100 NUM cana-591 68 16 cc cc NOUN cana-591 68 17 category category NOUN cana-591 68 18 and and CCONJ cana-591 68 19 help help VERB cana-591 68 20 in in ADP cana-591 68 21 classifying classify VERB cana-591 68 22 them they PRON cana-591 68 23 based base VERB cana-591 68 24 on on ADP cana-591 68 25 these these DET cana-591 68 26 attributes attribute NOUN cana-591 68 27 . . PUNCT cana-591 69 1 communications communication NOUN cana-591 69 2 on on ADP cana-591 69 3 applied apply VERB cana-591 69 4 nonlinear nonlinear ADJ cana-591 69 5 analysis analysis NOUN cana-591 69 6 issn issn NOUN cana-591 69 7 : : PUNCT cana-591 69 8 1074 1074 NUM cana-591 69 9 - - PUNCT cana-591 69 10 133x 133x NUM cana-591 69 11 vol vol NOUN cana-591 69 12 31 31 NUM cana-591 69 13 no no NOUN cana-591 69 14 . . PUNCT cana-591 70 1 2s 2s NUM cana-591 70 2 ( ( PUNCT cana-591 70 3 2024 2024 NUM cana-591 70 4 ) ) PUNCT cana-591 70 5 35 35 NUM cana-591 70 6 https://internationalpubls.com https://internationalpubls.com X cana-591 70 7 please please INTJ cana-591 70 8 note note VERB cana-591 70 9 that that SCONJ cana-591 70 10 this this DET cana-591 70 11 example example NOUN cana-591 70 12 is be AUX cana-591 70 13 a a DET cana-591 70 14 simplified simplified ADJ cana-591 70 15 illustration illustration NOUN cana-591 70 16 and and CCONJ cana-591 70 17 may may AUX cana-591 70 18 not not PART cana-591 70 19 reflect reflect VERB cana-591 70 20 the the DET cana-591 70 21 full full ADJ cana-591 70 22 complexity complexity NOUN cana-591 70 23 of of ADP cana-591 70 24 applying apply VERB cana-591 70 25 rough rough ADJ cana-591 70 26 set set NOUN cana-591 70 27 theory theory NOUN cana-591 70 28 to to ADP cana-591 70 29 real real ADJ cana-591 70 30 - - PUNCT cana-591 70 31 world world NOUN cana-591 70 32 data datum NOUN cana-591 70 33 . . PUNCT cana-591 71 1 in in ADP cana-591 71 2 practice practice NOUN cana-591 71 3 , , PUNCT cana-591 71 4 rough rough ADJ cana-591 71 5 set set NOUN cana-591 71 6 analysis analysis NOUN cana-591 71 7 involves involve VERB cana-591 71 8 more more ADV cana-591 71 9 rigorous rigorous ADJ cana-591 71 10 mathematical mathematical ADJ cana-591 71 11 concepts concept NOUN cana-591 71 12 and and CCONJ cana-591 71 13 techniques technique NOUN cana-591 71 14 . . PUNCT cana-591 72 1 table table NOUN cana-591 72 2 1 1 NUM cana-591 72 3 . . PUNCT cana-591 73 1 analysis analysis NOUN cana-591 73 2 of of ADP cana-591 73 3 engine engine NOUN cana-591 73 4 , , PUNCT cana-591 73 5 power power NOUN cana-591 73 6 , , PUNCT cana-591 73 7 torque torque NOUN cana-591 73 8 and and CCONJ cana-591 73 9 mileage mileage NOUN cana-591 73 10 in in ADP cana-591 73 11 100cc 100cc PROPN cana-591 73 12 bikes bike NOUN cana-591 73 13 bike bike NOUN cana-591 73 14 ( ( PUNCT cana-591 73 15 100 100 NUM cana-591 73 16 cc cc NOUN cana-591 73 17 ) ) PUNCT cana-591 73 18 engine engine NOUN cana-591 73 19 ( ( PUNCT cana-591 73 20 cc cc NOUN cana-591 73 21 ) ) PUNCT cana-591 73 22 power power NOUN cana-591 73 23 torque torque NOUN cana-591 73 24 mileage mileage NOUN cana-591 73 25 decision decision NOUN cana-591 73 26 attributes attribute VERB cana-591 73 27 π‘₯1 π‘₯1 NOUN cana-591 73 28 97.2 97.2 NUM cana-591 73 29 8.02 8.02 NUM cana-591 73 30 8.05 8.05 NUM cana-591 73 31 70 70 NUM cana-591 73 32 good good ADJ cana-591 73 33 π‘₯2 π‘₯2 NOUN cana-591 73 34 97 97 NUM cana-591 73 35 8.02 8.02 NUM cana-591 73 36 8.05 8.05 NUM cana-591 73 37 70 70 NUM cana-591 73 38 good good ADJ cana-591 73 39 π‘₯3 π‘₯3 NOUN cana-591 73 40 97.2 97.2 NUM cana-591 73 41 8.02 8.02 NUM cana-591 73 42 8.05 8.05 NUM cana-591 73 43 70 70 NUM cana-591 73 44 good good ADJ cana-591 73 45 π‘₯4 π‘₯4 NOUN cana-591 73 46 97.2 97.2 NUM cana-591 73 47 8.02 8.02 NUM cana-591 73 48 8.05 8.05 NUM cana-591 73 49 70 70 NUM cana-591 73 50 good good ADJ cana-591 73 51 π‘₯5 π‘₯5 PROPN cana-591 73 52 102 102 NUM cana-591 73 53 7.9 7.9 NUM cana-591 73 54 8.3 8.3 NUM cana-591 73 55 70 70 NUM cana-591 73 56 good good ADJ cana-591 73 57 π‘₯6 π‘₯6 PROPN cana-591 73 58 109.7 109.7 NUM cana-591 73 59 8.29 8.29 NUM cana-591 73 60 8.7 8.7 NUM cana-591 73 61 70 70 NUM cana-591 73 62 good good ADJ cana-591 73 63 π‘₯7 π‘₯7 VERB cana-591 73 64 109.51 109.51 NUM cana-591 73 65 8.79 8.79 NUM cana-591 73 66 9.3 9.3 NUM cana-591 73 67 65 65 NUM cana-591 73 68 good good ADJ cana-591 73 69 π‘₯8 π‘₯8 NOUN cana-591 73 70 109.51 109.51 NUM cana-591 73 71 8.79 8.79 NUM cana-591 73 72 9.3 9.3 NUM cana-591 73 73 60 60 NUM cana-591 73 74 bad bad ADJ cana-591 73 75 π‘₯9 π‘₯9 NOUN cana-591 73 76 109.7 109.7 NUM cana-591 73 77 8.19 8.19 NUM cana-591 73 78 8.7 8.7 NUM cana-591 73 79 83.09 83.09 NUM cana-591 73 80 good good ADJ cana-591 73 81 π‘₯10 π‘₯10 NOUN cana-591 73 82 109.7 109.7 NUM cana-591 73 83 8.19 8.19 NUM cana-591 73 84 8.7 8.7 NUM cana-591 73 85 73.68 73.68 NUM cana-591 73 86 good good ADJ cana-591 73 87 π‘₯11 π‘₯11 ADV cana-591 73 88 113.2 113.2 NUM cana-591 73 89 9.15 9.15 NUM cana-591 73 90 9.79 9.79 NUM cana-591 73 91 0 0 NUM cana-591 73 92 bad bad ADJ cana-591 73 93 π‘₯12 π‘₯12 VERB cana-591 73 94 113.2 113.2 NUM cana-591 73 95 9.15 9.15 NUM cana-591 73 96 9.89 9.89 NUM cana-591 73 97 0 0 NUM cana-591 73 98 bad bad ADJ cana-591 73 99 𝐴 𝐴 NOUN cana-591 73 100 = = SYM cana-591 73 101 { { PUNCT cana-591 73 102 π‘₯1 π‘₯1 NOUN cana-591 73 103 , , PUNCT cana-591 73 104 π‘₯2 π‘₯2 NOUN cana-591 73 105 , , PUNCT cana-591 73 106 π‘₯3 π‘₯3 NOUN cana-591 73 107 , , PUNCT cana-591 73 108 π‘₯4 π‘₯4 NOUN cana-591 73 109 , , PUNCT cana-591 73 110 … … PUNCT cana-591 73 111 , , PUNCT cana-591 73 112 π‘₯12 π‘₯12 VERB cana-591 73 113 } } PUNCT cana-591 73 114 𝐡 𝐡 NOUN cana-591 73 115 = = NOUN cana-591 73 116 { { PUNCT cana-591 73 117 engine engine NOUN cana-591 73 118 , , PUNCT cana-591 73 119 power power NOUN cana-591 73 120 , , PUNCT cana-591 73 121 torque torque NOUN cana-591 73 122 , , PUNCT cana-591 73 123 mileage}⁑ mileage}⁑ NOUN cana-591 73 124 𝑋engine 𝑋engine NOUN cana-591 73 125 = = PUNCT cana-591 73 126 { { PUNCT cana-591 73 127 97.2 97.2 NUM cana-591 73 128 , , PUNCT cana-591 73 129 97 97 NUM cana-591 73 130 , , PUNCT cana-591 73 131 102 102 NUM cana-591 73 132 , , PUNCT cana-591 73 133 109.7 109.7 NUM cana-591 73 134 , , PUNCT cana-591 73 135 109.51,113.2 109.51,113.2 NUM cana-591 73 136 } } PUNCT cana-591 73 137 𝑋power 𝑋power PROPN cana-591 73 138 = = PUNCT cana-591 73 139 { { PUNCT cana-591 73 140 8.02 8.02 NUM cana-591 73 141 , , PUNCT cana-591 73 142 7.9 7.9 NUM cana-591 73 143 , , PUNCT cana-591 73 144 8.29 8.29 NUM cana-591 73 145 , , PUNCT cana-591 73 146 8.79 8.79 NUM cana-591 73 147 , , PUNCT cana-591 73 148 8.19 8.19 NUM cana-591 73 149 , , PUNCT cana-591 73 150 9.15 9.15 NUM cana-591 73 151 } } PUNCT cana-591 73 152 𝑋torque 𝑋torque PROPN cana-591 73 153 = = PUNCT cana-591 73 154 { { PUNCT cana-591 73 155 8.05 8.05 NUM cana-591 73 156 , , PUNCT cana-591 73 157 8.3 8.3 NUM cana-591 73 158 , , PUNCT cana-591 73 159 8.7 8.7 NUM cana-591 73 160 , , PUNCT cana-591 73 161 9.3 9.3 NUM cana-591 73 162 , , PUNCT cana-591 73 163 9.79 9.79 NUM cana-591 73 164 , , PUNCT cana-591 73 165 9.89 9.89 NUM cana-591 73 166 } } PUNCT cana-591 73 167 𝑋mileage 𝑋mileage PROPN cana-591 73 168 = = PUNCT cana-591 73 169 { { PUNCT cana-591 73 170 60 60 NUM cana-591 73 171 , , PUNCT cana-591 73 172 65 65 NUM cana-591 73 173 , , PUNCT cana-591 73 174 70 70 NUM cana-591 73 175 , , PUNCT cana-591 73 176 73.68 73.68 NUM cana-591 73 177 , , PUNCT cana-591 73 178 83.09 83.09 NUM cana-591 73 179 } } PUNCT cana-591 73 180 𝑋decision 𝑋decision NOUN cana-591 73 181 = = SYM cana-591 73 182 { { PUNCT cana-591 73 183 good good ADJ cana-591 73 184 , , PUNCT cana-591 73 185 bad bad ADJ cana-591 73 186 } } PUNCT cana-591 73 187 consider consider VERB cana-591 73 188 𝑃 𝑃 NOUN cana-591 73 189 = = SYM cana-591 73 190 { { PUNCT cana-591 73 191 engine engine NOUN cana-591 73 192 } } PUNCT cana-591 73 193 𝑃 𝑃 NOUN cana-591 73 194 = = PUNCT cana-591 73 195 elementary⁑sets elementary⁑set NOUN cana-591 74 1 [ [ X cana-591 74 2 π‘₯1]𝑃 π‘₯1]𝑃 X cana-591 74 3 = = SYM cana-591 75 1 [ [ X cana-591 75 2 π‘₯3]𝑃 π‘₯3]𝑃 X cana-591 75 3 = = SYM cana-591 76 1 [ [ X cana-591 76 2 π‘₯4]𝑃 π‘₯4]𝑃 X cana-591 76 3 = = SYM cana-591 76 4 { { PUNCT cana-591 76 5 π‘₯1 π‘₯1 NOUN cana-591 76 6 , , PUNCT cana-591 76 7 π‘₯3 π‘₯3 NOUN cana-591 76 8 , , PUNCT cana-591 76 9 π‘₯4 π‘₯4 NOUN cana-591 76 10 } } PUNCT cana-591 77 1 [ [ X cana-591 77 2 π‘₯2]𝑃 π‘₯2]𝑃 NOUN cana-591 77 3 = = SYM cana-591 77 4 { { PUNCT cana-591 77 5 π‘₯2 π‘₯2 NOUN cana-591 77 6 } } PUNCT cana-591 77 7 [ [ X cana-591 77 8 π‘₯5]𝑃 π‘₯5]𝑃 NUM cana-591 77 9 = = SYM cana-591 77 10 { { PUNCT cana-591 77 11 π‘₯5 π‘₯5 ADV cana-591 77 12 } } PUNCT cana-591 78 1 [ [ X cana-591 78 2 π‘₯6]𝑃 π‘₯6]𝑃 X cana-591 78 3 = = SYM cana-591 79 1 [ [ X cana-591 79 2 π‘₯9]𝑃 π‘₯9]𝑃 X cana-591 79 3 = = SYM cana-591 80 1 [ [ X cana-591 80 2 π‘₯10]𝑃 π‘₯10]𝑃 NOUN cana-591 80 3 = = SYM cana-591 80 4 { { PUNCT cana-591 80 5 π‘₯6 π‘₯6 PROPN cana-591 80 6 , , PUNCT cana-591 80 7 π‘₯9 π‘₯9 PROPN cana-591 80 8 , , PUNCT cana-591 80 9 π‘₯10 π‘₯10 NOUN cana-591 80 10 } } PUNCT cana-591 80 11 [ [ X cana-591 80 12 π‘₯11]𝑃 π‘₯11]𝑃 X cana-591 80 13 = = PUNCT cana-591 81 1 [ [ X cana-591 81 2 π‘₯12]𝑃 π‘₯12]𝑃 X cana-591 81 3 = = X cana-591 81 4 { { PUNCT cana-591 81 5 π‘₯11 π‘₯11 ADV cana-591 81 6 , , PUNCT cana-591 81 7 π‘₯12 π‘₯12 VERB cana-591 81 8 } } PUNCT cana-591 81 9 communications communication NOUN cana-591 81 10 on on ADP cana-591 81 11 applied apply VERB cana-591 81 12 nonlinear nonlinear ADJ cana-591 81 13 analysis analysis NOUN cana-591 81 14 issn issn NOUN cana-591 81 15 : : PUNCT cana-591 81 16 1074 1074 NUM cana-591 81 17 - - PUNCT cana-591 81 18 133x 133x NUM cana-591 81 19 vol vol NOUN cana-591 81 20 31 31 NUM cana-591 81 21 no no NOUN cana-591 81 22 . . PUNCT cana-591 82 1 2s 2s NUM cana-591 82 2 ( ( PUNCT cana-591 82 3 2024 2024 NUM cana-591 82 4 ) ) PUNCT cana-591 82 5 36 36 NUM cana-591 82 6 https://internationalpubls.com https://internationalpubls.com X cana-591 82 7 the the DET cana-591 82 8 equivalence equivalence NOUN cana-591 82 9 classes class NOUN cana-591 82 10 are be AUX cana-591 82 11 𝑋1 𝑋1 NOUN cana-591 82 12 = = SYM cana-591 82 13 { { PUNCT cana-591 82 14 π‘₯1 π‘₯1 NOUN cana-591 82 15 , , PUNCT cana-591 82 16 π‘₯3 π‘₯3 NOUN cana-591 82 17 , , PUNCT cana-591 82 18 π‘₯4 π‘₯4 ADJ cana-591 82 19 } } PUNCT cana-591 82 20 𝑋2 𝑋2 VERB cana-591 82 21 = = PUNCT cana-591 82 22 { { PUNCT cana-591 82 23 π‘₯2 π‘₯2 NOUN cana-591 82 24 } } PUNCT cana-591 82 25 𝑋3 𝑋3 NOUN cana-591 82 26 = = PUNCT cana-591 82 27 { { PUNCT cana-591 82 28 π‘₯5 π‘₯5 ADV cana-591 82 29 } } PUNCT cana-591 82 30 𝑋4 𝑋4 NOUN cana-591 82 31 = = SYM cana-591 82 32 { { PUNCT cana-591 82 33 π‘₯6 π‘₯6 PROPN cana-591 82 34 , , PUNCT cana-591 82 35 π‘₯9 π‘₯9 PROPN cana-591 82 36 , , PUNCT cana-591 82 37 π‘₯10 π‘₯10 NOUN cana-591 82 38 } } PUNCT cana-591 82 39 𝑋5 𝑋5 NOUN cana-591 82 40 = = SYM cana-591 82 41 { { PUNCT cana-591 82 42 π‘₯11 π‘₯11 ADV cana-591 82 43 , , PUNCT cana-591 82 44 π‘₯12 π‘₯12 VERB cana-591 82 45 } } PUNCT cana-591 82 46 ind(engine ind(engine NOUN cana-591 82 47 ) ) PUNCT cana-591 82 48 = = SYM cana-591 82 49 { { PUNCT cana-591 82 50 𝑋1 𝑋1 PROPN cana-591 82 51 , , PUNCT cana-591 82 52 𝑋2 𝑋2 VERB cana-591 82 53 , , PUNCT cana-591 82 54 𝑋3 𝑋3 NOUN cana-591 82 55 , , PUNCT cana-591 82 56 𝑋4 𝑋4 VERB cana-591 82 57 , , PUNCT cana-591 82 58 𝑋5 𝑋5 NOUN cana-591 82 59 } } PUNCT cana-591 82 60 = = SYM cana-591 82 61 { { PUNCT cana-591 82 62 { { PUNCT cana-591 82 63 π‘₯1 π‘₯1 NOUN cana-591 82 64 , , PUNCT cana-591 82 65 π‘₯3 π‘₯3 NOUN cana-591 82 66 , , PUNCT cana-591 82 67 π‘₯4 π‘₯4 PROPN cana-591 82 68 } } PUNCT cana-591 82 69 , , PUNCT cana-591 82 70 { { PUNCT cana-591 82 71 π‘₯2 π‘₯2 NOUN cana-591 82 72 } } PUNCT cana-591 82 73 , , PUNCT cana-591 82 74 { { PUNCT cana-591 82 75 π‘₯5 π‘₯5 ADV cana-591 82 76 } } PUNCT cana-591 82 77 , , PUNCT cana-591 82 78 { { PUNCT cana-591 82 79 π‘₯6 π‘₯6 PROPN cana-591 82 80 , , PUNCT cana-591 82 81 π‘₯9 π‘₯9 PROPN cana-591 82 82 , , PUNCT cana-591 82 83 π‘₯10 π‘₯10 NOUN cana-591 82 84 } } PUNCT cana-591 82 85 , , PUNCT cana-591 82 86 { { PUNCT cana-591 82 87 π‘₯11 π‘₯11 ADV cana-591 82 88 , , PUNCT cana-591 82 89 π‘₯12 π‘₯12 VERB cana-591 82 90 } } PUNCT cana-591 82 91 } } PUNCT cana-591 82 92 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 82 93 ) ) PUNCT cana-591 82 94 = = PRON cana-591 82 95 { { PUNCT cana-591 82 96 π‘₯2 π‘₯2 NOUN cana-591 82 97 } } PUNCT cana-591 82 98 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 82 99 ) ) PUNCT cana-591 82 100 = = PRON cana-591 82 101 { { PUNCT cana-591 82 102 π‘₯7 π‘₯7 VERB cana-591 82 103 , , PUNCT cana-591 82 104 π‘₯8 π‘₯8 ADJ cana-591 82 105 } } PUNCT cana-591 82 106 𝑆𝑁𝑆(𝑋 𝑆𝑁𝑆(𝑋 NOUN cana-591 82 107 ) ) PUNCT cana-591 82 108 = = PUNCT cana-591 83 1 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 83 2 ) ) PUNCT cana-591 83 3 βˆ’ βˆ’ PROPN cana-591 83 4 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 83 5 ) ) PUNCT cana-591 83 6 = = PRON cana-591 83 7 { { PUNCT cana-591 83 8 π‘₯7 π‘₯7 VERB cana-591 83 9 , , PUNCT cana-591 83 10 π‘₯8 π‘₯8 NOUN cana-591 83 11 } } PUNCT cana-591 83 12 π‘ˆ π‘ˆ NOUN cana-591 83 13 βˆ’ βˆ’ NOUN cana-591 83 14 π‘†βˆ—(𝑋 π‘†βˆ—(𝑋 ADV cana-591 83 15 ) ) PUNCT cana-591 83 16 = = PRON cana-591 83 17 { { PUNCT cana-591 83 18 π‘₯1 π‘₯1 NOUN cana-591 83 19 , , PUNCT cana-591 83 20 π‘₯3 π‘₯3 NOUN cana-591 83 21 , , PUNCT cana-591 83 22 π‘₯4 π‘₯4 NOUN cana-591 83 23 , , PUNCT cana-591 83 24 π‘₯5 π‘₯5 PROPN cana-591 83 25 , , PUNCT cana-591 83 26 π‘₯6 π‘₯6 PROPN cana-591 83 27 , , PUNCT cana-591 83 28 π‘₯9 π‘₯9 PROPN cana-591 83 29 , , PUNCT cana-591 83 30 π‘₯10 π‘₯10 NOUN cana-591 83 31 , , PUNCT cana-591 83 32 π‘₯11 π‘₯11 ADV cana-591 83 33 , , PUNCT cana-591 83 34 π‘₯12 π‘₯12 VERB cana-591 83 35 } } PUNCT cana-591 83 36 this this DET cana-591 83 37 scatter scatter NOUN cana-591 83 38 plot plot NOUN cana-591 83 39 visually visually ADV cana-591 83 40 represents represent VERB cana-591 83 41 the the DET cana-591 83 42 bikes bike NOUN cana-591 83 43 ' ' PART cana-591 83 44 data datum NOUN cana-591 83 45 points point NOUN cana-591 83 46 in in ADP cana-591 83 47 the the DET cana-591 83 48 " " PUNCT cana-591 83 49 engine engine NOUN cana-591 83 50 ( ( PUNCT cana-591 83 51 cc cc NOUN cana-591 83 52 ) ) PUNCT cana-591 83 53 " " PUNCT cana-591 83 54 vs. vs. ADP cana-591 83 55 " " PUNCT cana-591 83 56 power power NOUN cana-591 83 57 " " PUNCT cana-591 83 58 space space NOUN cana-591 83 59 . . PUNCT cana-591 84 1 the the DET cana-591 84 2 placement placement NOUN cana-591 84 3 of of ADP cana-591 84 4 the the DET cana-591 84 5 data data NOUN cana-591 84 6 points point NOUN cana-591 84 7 can can AUX cana-591 84 8 give give VERB cana-591 84 9 you you PRON cana-591 84 10 an an DET cana-591 84 11 idea idea NOUN cana-591 84 12 of of ADP cana-591 84 13 how how SCONJ cana-591 84 14 the the DET cana-591 84 15 bikes bike NOUN cana-591 84 16 are be AUX cana-591 84 17 distributed distribute VERB cana-591 84 18 in in ADP cana-591 84 19 this this DET cana-591 84 20 attribute attribute NOUN cana-591 84 21 space space NOUN cana-591 84 22 . . PUNCT cana-591 85 1 this this DET cana-591 85 2 concept concept NOUN cana-591 85 3 can can AUX cana-591 85 4 be be AUX cana-591 85 5 extended extend VERB cana-591 85 6 to to ADP cana-591 85 7 additional additional ADJ cana-591 85 8 attributes attribute NOUN cana-591 85 9 or or CCONJ cana-591 85 10 even even ADV cana-591 85 11 use use VERB cana-591 85 12 advanced advanced ADJ cana-591 85 13 visualization visualization NOUN cana-591 85 14 techniques technique NOUN cana-591 85 15 to to PART cana-591 85 16 represent represent VERB cana-591 85 17 decision decision NOUN cana-591 85 18 boundaries boundary NOUN cana-591 85 19 , , PUNCT cana-591 85 20 discernibility discernibility NOUN cana-591 85 21 , , PUNCT cana-591 85 22 core core NOUN cana-591 85 23 , , PUNCT cana-591 85 24 and and CCONJ cana-591 85 25 reducts reduct NOUN cana-591 85 26 . . PUNCT cana-591 86 1 however however ADV cana-591 86 2 , , PUNCT cana-591 86 3 visualizing visualize VERB cana-591 86 4 rough rough ADJ cana-591 86 5 set set NOUN cana-591 86 6 theory theory NOUN cana-591 86 7 concepts concept NOUN cana-591 86 8 comprehensively comprehensively ADV cana-591 86 9 requires require VERB cana-591 86 10 advanced advanced ADJ cana-591 86 11 data datum NOUN cana-591 86 12 visualization visualization NOUN cana-591 86 13 techniques technique NOUN cana-591 86 14 and and CCONJ cana-591 86 15 tools tool NOUN cana-591 86 16 . . PUNCT cana-591 87 1 rough rough ADJ cana-591 87 2 set set NOUN cana-591 87 3 theory theory NOUN cana-591 87 4 involves involve VERB cana-591 87 5 mathematical mathematical ADJ cana-591 87 6 concepts concept NOUN cana-591 87 7 and and CCONJ cana-591 87 8 notations notation NOUN cana-591 87 9 that that PRON cana-591 87 10 can can AUX cana-591 87 11 be be AUX cana-591 87 12 challenging challenge VERB cana-591 87 13 to to PART cana-591 87 14 represent represent VERB cana-591 87 15 in in ADP cana-591 87 16 a a DET cana-591 87 17 single single ADJ cana-591 87 18 diagram diagram NOUN cana-591 87 19 . . PUNCT cana-591 88 1 however however ADV cana-591 88 2 , , PUNCT cana-591 88 3 we we PRON cana-591 88 4 can can AUX cana-591 88 5 provide provide VERB cana-591 88 6 you you PRON cana-591 88 7 with with ADP cana-591 88 8 a a DET cana-591 88 9 simplified simplified ADJ cana-591 88 10 algorithm algorithm NOUN cana-591 88 11 1 1 NUM cana-591 88 12 that that PRON cana-591 88 13 illustrates illustrate VERB cana-591 88 14 the the DET cana-591 88 15 basic basic ADJ cana-591 88 16 idea idea NOUN cana-591 88 17 of of ADP cana-591 88 18 rough rough ADJ cana-591 88 19 set set NOUN cana-591 88 20 theory theory NOUN cana-591 88 21 and and CCONJ cana-591 88 22 its its PRON cana-591 88 23 components component NOUN cana-591 88 24 : : PUNCT cana-591 88 25 universe universe NOUN cana-591 88 26 of of ADP cana-591 88 27 discourse discourse NOUN cana-591 88 28 , , PUNCT cana-591 88 29 attributes attribute VERB cana-591 88 30 , , PUNCT cana-591 88 31 and and CCONJ cana-591 88 32 approximations approximation NOUN cana-591 88 33 . . PUNCT cana-591 89 1 algorithm algorithm NOUN cana-591 89 2 1 1 NUM cana-591 89 3 ( ( PUNCT cana-591 89 4 python python PROPN cana-591 89 5 ) ) PUNCT cana-591 89 6 step1 step1 PROPN cana-591 89 7 : : PUNCT cana-591 89 8 find find VERB cana-591 89 9 the the DET cana-591 89 10 decision decision NOUN cana-591 89 11 attribute attribute NOUN cana-591 89 12 . . PUNCT cana-591 90 1 step step NOUN cana-591 90 2 2 2 NUM cana-591 90 3 : : PUNCT cana-591 90 4 create create VERB cana-591 90 5 the the DET cana-591 90 6 concept concept NOUN cana-591 90 7 class class NOUN cana-591 90 8 based base VERB cana-591 90 9 on on ADP cana-591 90 10 the the DET cana-591 90 11 decision decision NOUN cana-591 90 12 attribute attribute NOUN cana-591 90 13 , , PUNCT cana-591 90 14 identify identify VERB cana-591 90 15 all all DET cana-591 90 16 the the DET cana-591 90 17 tuples tuple NOUN cana-591 90 18 associated associate VERB cana-591 90 19 with with ADP cana-591 90 20 that that DET cana-591 90 21 attribute attribute NOUN cana-591 90 22 . . PUNCT cana-591 91 1 step step NOUN cana-591 91 2 3 3 NUM cana-591 91 3 : : PUNCT cana-591 91 4 select select VERB cana-591 91 5 the the DET cana-591 91 6 condition condition NOUN cana-591 91 7 attributes attribute VERB cana-591 91 8 . . PUNCT cana-591 92 1 determine determine VERB cana-591 92 2 the the DET cana-591 92 3 lower low ADJ cana-591 92 4 approximation approximation NOUN cana-591 92 5 i.e. i.e. X cana-591 92 6 indiscernible indiscernible ADJ cana-591 92 7 with with ADP cana-591 92 8 respect respect NOUN cana-591 92 9 to to ADP cana-591 92 10 the the DET cana-591 92 11 selected select VERB cana-591 92 12 attributes attribute NOUN cana-591 92 13 . . PUNCT cana-591 93 1 step step NOUN cana-591 93 2 4 4 NUM cana-591 93 3 : : PUNCT cana-591 93 4 estimate estimate VERB cana-591 93 5 the the DET cana-591 93 6 upper upper ADJ cana-591 93 7 approximation approximation NOUN cana-591 93 8 i.e. i.e. X cana-591 93 9 the the DET cana-591 93 10 objects object NOUN cana-591 93 11 in in ADP cana-591 93 12 the the DET cana-591 93 13 boundary boundary ADJ cana-591 93 14 region region NOUN cana-591 93 15 are be AUX cana-591 93 16 indiscernible indiscernible ADJ cana-591 93 17 . . PUNCT cana-591 94 1 step step NOUN cana-591 94 2 5 5 NUM cana-591 94 3 : : PUNCT cana-591 94 4 find find VERB cana-591 94 5 the the DET cana-591 94 6 rough rough ADJ cana-591 94 7 set set NOUN cana-591 94 8 step step NOUN cana-591 94 9 6 6 NUM cana-591 94 10 : : PUNCT cana-591 94 11 identify identify VERB cana-591 94 12 the the DET cana-591 94 13 reduct reduct NOUN cana-591 94 14 ( ( PUNCT cana-591 94 15 minimal minimal ADJ cana-591 94 16 subset subset NOUN cana-591 94 17 of of ADP cana-591 94 18 relevant relevant ADJ cana-591 94 19 attributes attribute NOUN cana-591 94 20 ) ) PUNCT cana-591 94 21 communications communication NOUN cana-591 94 22 on on ADP cana-591 94 23 applied apply VERB cana-591 94 24 nonlinear nonlinear ADJ cana-591 94 25 analysis analysis NOUN cana-591 94 26 issn issn NOUN cana-591 94 27 : : PUNCT cana-591 94 28 1074 1074 NUM cana-591 94 29 - - PUNCT cana-591 94 30 133x 133x NUM cana-591 94 31 vol vol NOUN cana-591 94 32 31 31 NUM cana-591 94 33 no no NOUN cana-591 94 34 . . PUNCT cana-591 95 1 2s 2s NUM cana-591 95 2 ( ( PUNCT cana-591 95 3 2024 2024 NUM cana-591 95 4 ) ) PUNCT cana-591 95 5 37 37 NUM cana-591 95 6 https://internationalpubls.com https://internationalpubls.com X cana-591 95 7 3 3 X cana-591 95 8 . . X cana-591 95 9 implementation implementation NOUN cana-591 95 10 of of ADP cana-591 95 11 proposed propose VERB cana-591 95 12 algorithm algorithm NOUN cana-591 95 13 consider consider VERB cana-591 95 14 implementing implement VERB cana-591 95 15 the the DET cana-591 95 16 aforementioned aforementioned ADJ cana-591 95 17 technique technique NOUN cana-591 95 18 using use VERB cana-591 95 19 a a DET cana-591 95 20 table table NOUN cana-591 95 21 - - PUNCT cana-591 95 22 based base VERB cana-591 95 23 information information NOUN cana-591 95 24 system system NOUN cana-591 95 25 . . PUNCT cana-591 96 1 the the DET cana-591 96 2 condition condition NOUN cana-591 96 3 and and CCONJ cana-591 96 4 decision decision NOUN cana-591 96 5 attributes attribute NOUN cana-591 96 6 make make VERB cana-591 96 7 up up ADP cana-591 96 8 the the DET cana-591 96 9 information information NOUN cana-591 96 10 system system NOUN cana-591 96 11 's 's PART cana-591 96 12 column column NOUN cana-591 96 13 . . PUNCT cana-591 97 1 the the DET cana-591 97 2 values value NOUN cana-591 97 3 that that PRON cana-591 97 4 the the DET cana-591 97 5 condition condition NOUN cana-591 97 6 and and CCONJ cana-591 97 7 decision decision NOUN cana-591 97 8 attribute attribute NOUN cana-591 97 9 can can AUX cana-591 97 10 take take VERB cana-591 97 11 from from ADP cana-591 97 12 the the DET cana-591 97 13 discourse discourse NOUN cana-591 97 14 universe universe NOUN cana-591 97 15 are be AUX cana-591 97 16 represented represent VERB cana-591 97 17 by by ADP cana-591 97 18 the the DET cana-591 97 19 rows row NOUN cana-591 97 20 of of ADP cana-591 97 21 the the DET cana-591 97 22 information information NOUN cana-591 97 23 system system NOUN cana-591 97 24 . . PUNCT cana-591 98 1 table table NOUN cana-591 98 2 2 2 NUM cana-591 98 3 shows show VERB cana-591 98 4 that that SCONJ cana-591 98 5 the the DET cana-591 98 6 universe universe NOUN cana-591 98 7 consists consist VERB cana-591 98 8 of of ADP cana-591 98 9 twelve twelve NUM cana-591 98 10 elements element NOUN cana-591 98 11 in in ADP cana-591 98 12 total total NOUN cana-591 98 13 . . PUNCT cana-591 99 1 the the DET cana-591 99 2 condition condition NOUN cana-591 99 3 attributes attribute VERB cana-591 99 4 ' ' PART cana-591 99 5 value value NOUN cana-591 99 6 sets set NOUN cana-591 99 7 consist consist VERB cana-591 99 8 of of ADP cana-591 99 9 : : PUNCT cana-591 99 10 π‘Ž π‘Ž NOUN cana-591 99 11 = = NOUN cana-591 99 12 𝑋1 𝑋1 NOUN cana-591 99 13 = = SYM cana-591 99 14 { { PUNCT cana-591 99 15 π‘₯1 π‘₯1 NOUN cana-591 99 16 , , PUNCT cana-591 99 17 π‘₯3 π‘₯3 NOUN cana-591 99 18 , , PUNCT cana-591 99 19 π‘₯4 π‘₯4 NOUN cana-591 99 20 } } PUNCT cana-591 99 21 𝑏 𝑏 NOUN cana-591 99 22 = = PUNCT cana-591 99 23 𝑋2 𝑋2 VERB cana-591 99 24 = = PUNCT cana-591 99 25 { { PUNCT cana-591 99 26 π‘₯2 π‘₯2 NOUN cana-591 99 27 } } PUNCT cana-591 99 28 𝑐 𝑐 NOUN cana-591 99 29 = = PUNCT cana-591 99 30 𝑋3 𝑋3 NOUN cana-591 99 31 = = PUNCT cana-591 99 32 { { PUNCT cana-591 99 33 π‘₯5 π‘₯5 PROPN cana-591 99 34 } } PUNCT cana-591 99 35 𝑑 𝑑 NOUN cana-591 99 36 = = NOUN cana-591 99 37 𝑋4 𝑋4 NOUN cana-591 99 38 = = SYM cana-591 99 39 { { PUNCT cana-591 99 40 π‘₯6 π‘₯6 PROPN cana-591 99 41 , , PUNCT cana-591 99 42 π‘₯9 π‘₯9 PROPN cana-591 99 43 , , PUNCT cana-591 99 44 π‘₯10 π‘₯10 NOUN cana-591 99 45 } } PUNCT cana-591 99 46 decision decision NOUN cana-591 99 47 attribute attribute NOUN cana-591 99 48 can can AUX cana-591 99 49 take take VERB cana-591 99 50 values value NOUN cana-591 99 51 : : PUNCT cana-591 99 52 𝑒0 𝑒0 VERB cana-591 99 53 = = SYM cana-591 99 54 𝑋5 𝑋5 PROPN cana-591 99 55 = = SYM cana-591 99 56 { { PUNCT cana-591 99 57 π‘₯8 π‘₯8 NOUN cana-591 99 58 , , PUNCT cana-591 99 59 π‘₯11 π‘₯11 ADV cana-591 99 60 , , PUNCT cana-591 99 61 π‘₯12 π‘₯12 VERB cana-591 99 62 } } PUNCT cana-591 99 63 table table NOUN cana-591 99 64 2 2 NUM cana-591 99 65 . . PUNCT cana-591 99 66 information information NOUN cana-591 99 67 system system NOUN cana-591 99 68 π‘ˆ π‘ˆ PROPN cana-591 99 69 π‘Ž π‘Ž PUNCT cana-591 99 70 𝑏 𝑏 PROPN cana-591 99 71 𝑐 𝑐 PROPN cana-591 99 72 𝑑 𝑑 PROPN cana-591 99 73 𝑒 𝑒 PROPN cana-591 99 74 π‘₯1 π‘₯1 NOUN cana-591 99 75 1 1 NUM cana-591 99 76 0 0 NUM cana-591 99 77 0 0 NUM cana-591 99 78 0 0 NUM cana-591 99 79 1 1 NUM cana-591 99 80 π‘₯2 π‘₯2 NOUN cana-591 99 81 0 0 NUM cana-591 99 82 1 1 NUM cana-591 99 83 0 0 NUM cana-591 99 84 0 0 NUM cana-591 99 85 1 1 NUM cana-591 99 86 π‘₯3 π‘₯3 NOUN cana-591 99 87 1 1 NUM cana-591 99 88 0 0 NUM cana-591 99 89 0 0 NUM cana-591 99 90 0 0 NUM cana-591 99 91 1 1 NUM cana-591 99 92 π‘₯4 π‘₯4 NOUN cana-591 99 93 1 1 NUM cana-591 99 94 0 0 NUM cana-591 99 95 0 0 NUM cana-591 99 96 0 0 NUM cana-591 99 97 1 1 NUM cana-591 99 98 π‘₯5 π‘₯5 NOUN cana-591 99 99 0 0 NUM cana-591 99 100 0 0 NUM cana-591 99 101 1 1 NUM cana-591 99 102 0 0 NUM cana-591 99 103 1 1 NUM cana-591 99 104 π‘₯6 π‘₯6 NOUN cana-591 99 105 0 0 NUM cana-591 99 106 0 0 SYM cana-591 99 107 0 0 NUM cana-591 99 108 1 1 NUM cana-591 99 109 1 1 NUM cana-591 99 110 π‘₯7 π‘₯7 VERB cana-591 99 111 0 0 NUM cana-591 99 112 0 0 NUM cana-591 99 113 0 0 NUM cana-591 99 114 0 0 NUM cana-591 99 115 1 1 NUM cana-591 99 116 π‘₯8 π‘₯8 NOUN cana-591 99 117 0 0 NUM cana-591 99 118 0 0 NUM cana-591 99 119 0 0 NUM cana-591 99 120 0 0 SYM cana-591 99 121 0 0 NUM cana-591 99 122 π‘₯9 π‘₯9 NOUN cana-591 99 123 0 0 NUM cana-591 99 124 0 0 NUM cana-591 99 125 0 0 NUM cana-591 99 126 1 1 NUM cana-591 99 127 1 1 NUM cana-591 99 128 π‘₯10 π‘₯10 NUM cana-591 99 129 0 0 NUM cana-591 99 130 0 0 NUM cana-591 99 131 0 0 NUM cana-591 99 132 1 1 NUM cana-591 99 133 1 1 NUM cana-591 99 134 π‘₯11 π‘₯11 ADV cana-591 99 135 0 0 NUM cana-591 99 136 0 0 NUM cana-591 99 137 0 0 NUM cana-591 99 138 0 0 NUM cana-591 99 139 0 0 NUM cana-591 99 140 π‘₯12 π‘₯12 VERB cana-591 99 141 0 0 NUM cana-591 99 142 0 0 NUM cana-591 99 143 0 0 NUM cana-591 99 144 0 0 NUM cana-591 99 145 0 0 NUM cana-591 99 146 using use VERB cana-591 99 147 our our PRON cana-591 99 148 approach approach NOUN cana-591 99 149 , , PUNCT cana-591 99 150 the the DET cana-591 99 151 first first ADJ cana-591 99 152 condition condition NOUN cana-591 99 153 attribute attribute NOUN cana-591 99 154 , , PUNCT cana-591 99 155 " " PUNCT cana-591 99 156 π‘Ž π‘Ž X cana-591 99 157 , , PUNCT cana-591 99 158 " " PUNCT cana-591 99 159 is be AUX cana-591 99 160 removed remove VERB cana-591 99 161 from from ADP cana-591 99 162 table table NOUN cana-591 99 163 2 2 NUM cana-591 99 164 and and CCONJ cana-591 99 165 the the DET cana-591 99 166 consistency consistency NOUN cana-591 99 167 of of ADP cana-591 99 168 the the DET cana-591 99 169 remaining remain VERB cana-591 99 170 table table NOUN cana-591 99 171 , , PUNCT cana-591 99 172 table table NOUN cana-591 99 173 3 3 NUM cana-591 99 174 , , PUNCT cana-591 99 175 is be AUX cana-591 99 176 checked check VERB cana-591 99 177 . . PUNCT cana-591 100 1 when when SCONJ cana-591 100 2 we we PRON cana-591 100 3 have have VERB cana-591 100 4 identical identical ADJ cana-591 100 5 options option NOUN cana-591 100 6 for for ADP cana-591 100 7 two two NUM cana-591 100 8 or or CCONJ cana-591 100 9 more more ADJ cana-591 100 10 rows row NOUN cana-591 100 11 or or CCONJ cana-591 100 12 cases case NOUN cana-591 100 13 with with ADP cana-591 100 14 the the DET cana-591 100 15 same same ADJ cana-591 100 16 values value NOUN cana-591 100 17 of of ADP cana-591 100 18 condition condition NOUN cana-591 100 19 characteristics characteristic NOUN cana-591 100 20 , , PUNCT cana-591 100 21 a a DET cana-591 100 22 table table NOUN cana-591 100 23 is be AUX cana-591 100 24 considered consider VERB cana-591 100 25 to to PART cana-591 100 26 be be AUX cana-591 100 27 consistent consistent ADJ cana-591 100 28 ; ; PUNCT cana-591 100 29 if if SCONJ cana-591 100 30 not not PART cana-591 100 31 , , PUNCT cana-591 100 32 it it PRON cana-591 100 33 is be AUX cana-591 100 34 inconsistent inconsistent ADJ cana-591 100 35 . . PUNCT cana-591 101 1 table table NOUN cana-591 101 2 3 3 NUM cana-591 101 3 . . X cana-591 101 4 attribute attribute NOUN cana-591 101 5 ' ' PUNCT cana-591 101 6 π‘Ž π‘Ž X cana-591 101 7 ' ' PUNCT cana-591 101 8 is be AUX cana-591 101 9 eliminated eliminate VERB cana-591 101 10 π‘ˆ π‘ˆ PROPN cana-591 101 11 𝑏 𝑏 PROPN cana-591 101 12 𝑐 𝑐 PROPN cana-591 101 13 𝑑 𝑑 PROPN cana-591 101 14 𝑒 𝑒 PROPN cana-591 101 15 π‘₯1 π‘₯1 NOUN cana-591 101 16 0 0 NUM cana-591 101 17 0 0 NUM cana-591 101 18 0 0 NUM cana-591 101 19 1 1 NUM cana-591 101 20 π‘₯2 π‘₯2 NOUN cana-591 101 21 1 1 NUM cana-591 101 22 0 0 NUM cana-591 101 23 0 0 NUM cana-591 101 24 1 1 NUM cana-591 101 25 π‘₯3 π‘₯3 NOUN cana-591 101 26 0 0 NUM cana-591 101 27 0 0 NUM cana-591 101 28 0 0 NUM cana-591 101 29 1 1 NUM cana-591 101 30 π‘₯4 π‘₯4 NOUN cana-591 101 31 0 0 NUM cana-591 101 32 0 0 NUM cana-591 101 33 0 0 NUM cana-591 101 34 1 1 NUM cana-591 101 35 π‘₯5 π‘₯5 NOUN cana-591 101 36 0 0 NUM cana-591 101 37 1 1 NUM cana-591 101 38 0 0 NUM cana-591 101 39 1 1 NUM cana-591 101 40 π‘₯6 π‘₯6 NOUN cana-591 101 41 0 0 NUM cana-591 101 42 0 0 NUM cana-591 101 43 1 1 NUM cana-591 101 44 1 1 NUM cana-591 101 45 communications communication NOUN cana-591 101 46 on on ADP cana-591 101 47 applied apply VERB cana-591 101 48 nonlinear nonlinear ADJ cana-591 101 49 analysis analysis NOUN cana-591 101 50 issn issn NOUN cana-591 101 51 : : PUNCT cana-591 101 52 1074 1074 NUM cana-591 101 53 - - PUNCT cana-591 101 54 133x 133x NUM cana-591 101 55 vol vol NOUN cana-591 101 56 31 31 NUM cana-591 101 57 no no NOUN cana-591 101 58 . . PUNCT cana-591 102 1 2s 2s NUM cana-591 102 2 ( ( PUNCT cana-591 102 3 2024 2024 NUM cana-591 102 4 ) ) PUNCT cana-591 102 5 38 38 NUM cana-591 102 6 https://internationalpubls.com https://internationalpubls.com X cana-591 102 7 π‘₯7 π‘₯7 VERB cana-591 102 8 0 0 NUM cana-591 102 9 0 0 NUM cana-591 102 10 0 0 NUM cana-591 102 11 1 1 NUM cana-591 102 12 π‘₯8 π‘₯8 NOUN cana-591 102 13 0 0 NUM cana-591 102 14 0 0 NUM cana-591 102 15 0 0 NUM cana-591 102 16 0 0 NUM cana-591 103 1 π‘₯9 π‘₯9 NOUN cana-591 103 2 0 0 NUM cana-591 103 3 0 0 NUM cana-591 103 4 1 1 NUM cana-591 103 5 1 1 NUM cana-591 103 6 π‘₯10 π‘₯10 NUM cana-591 103 7 0 0 NUM cana-591 103 8 0 0 NUM cana-591 103 9 1 1 NUM cana-591 103 10 1 1 NUM cana-591 103 11 π‘₯11 π‘₯11 ADV cana-591 103 12 0 0 NUM cana-591 103 13 0 0 NUM cana-591 103 14 0 0 NUM cana-591 103 15 0 0 NUM cana-591 103 16 π‘₯12 π‘₯12 VERB cana-591 103 17 0 0 NUM cana-591 103 18 0 0 NUM cana-591 103 19 0 0 NUM cana-591 103 20 0 0 NUM cana-591 103 21 table table NOUN cana-591 103 22 3 3 NUM cana-591 103 23 is be AUX cana-591 103 24 created create VERB cana-591 103 25 by by ADP cana-591 103 26 removing remove VERB cana-591 103 27 the the DET cana-591 103 28 condition condition NOUN cana-591 103 29 attribute attribute NOUN cana-591 103 30 ' ' PUNCT cana-591 103 31 π‘Ž π‘Ž NOUN cana-591 103 32 ' ' PUNCT cana-591 103 33 from from ADP cana-591 103 34 table table NOUN cana-591 103 35 2 2 NUM cana-591 103 36 . . PUNCT cana-591 103 37 upon upon SCONJ cana-591 103 38 examining examine VERB cana-591 103 39 table table NOUN cana-591 103 40 3 3 NUM cana-591 103 41 , , PUNCT cana-591 103 42 it it PRON cana-591 103 43 becomes become VERB cana-591 103 44 evident evident ADJ cana-591 103 45 that that SCONJ cana-591 103 46 the the DET cana-591 103 47 removal removal NOUN cana-591 103 48 of of ADP cana-591 103 49 attribute attribute NOUN cana-591 103 50 ' ' PUNCT cana-591 103 51 π‘Ž π‘Ž NOUN cana-591 103 52 ' ' PUNCT cana-591 103 53 from from ADP cana-591 103 54 table table NOUN cana-591 103 55 2 2 NUM cana-591 103 56 results result NOUN cana-591 103 57 in in ADP cana-591 103 58 inconsistency inconsistency NOUN cana-591 103 59 since since SCONJ cana-591 103 60 , , PUNCT cana-591 103 61 for for SCONJ cana-591 103 62 each each PRON cana-591 103 63 of of ADP cana-591 103 64 the the DET cana-591 103 65 following follow VERB cana-591 103 66 values value NOUN cana-591 103 67 of of ADP cana-591 103 68 the the DET cana-591 103 69 condition condition NOUN cana-591 103 70 attributes attribute VERB cana-591 103 71 : : PUNCT cana-591 103 72 ' ' PUNCT cana-591 103 73 𝑏 𝑏 NOUN cana-591 103 74 ' ' PUNCT cana-591 103 75 , , PUNCT cana-591 103 76 ' ' PUNCT cana-591 103 77 𝑐 𝑐 NOUN cana-591 103 78 ' ' PUNCT cana-591 103 79 , , PUNCT cana-591 103 80 ' ' PUNCT cana-591 103 81 𝑑 𝑑 PRON cana-591 103 82 ' ' PUNCT cana-591 103 83 the the DET cana-591 103 84 value value NOUN cana-591 103 85 of of ADP cana-591 103 86 the the DET cana-591 103 87 decision decision NOUN cana-591 103 88 attribute attribute NOUN cana-591 103 89 , , PUNCT cana-591 103 90 ' ' PUNCT cana-591 103 91 𝑒 𝑒 X cana-591 103 92 ' ' PUNCT cana-591 103 93 , , PUNCT cana-591 103 94 differs differ VERB cana-591 103 95 for for ADP cana-591 103 96 π‘₯1 π‘₯1 PROPN cana-591 103 97 , , PUNCT cana-591 103 98 π‘₯3 π‘₯3 NOUN cana-591 103 99 , , PUNCT cana-591 103 100 π‘₯4 π‘₯4 NOUN cana-591 103 101 and and CCONJ cana-591 103 102 π‘₯8 π‘₯8 NOUN cana-591 103 103 , , PUNCT cana-591 103 104 π‘₯11 π‘₯11 ADV cana-591 103 105 , , PUNCT cana-591 103 106 π‘₯12 π‘₯12 VERB cana-591 103 107 . . PUNCT cana-591 104 1 π‘₯1 π‘₯1 PROPN cana-591 104 2 , , PUNCT cana-591 104 3 π‘₯3 π‘₯3 NOUN cana-591 104 4 , , PUNCT cana-591 104 5 π‘₯4 π‘₯4 ADJ cana-591 104 6 : : PUNCT cana-591 104 7 𝑏0𝑐0𝑑0 𝑏0𝑐0𝑑0 NOUN cana-591 104 8 β†’ β†’ SYM cana-591 104 9 𝑒1 𝑒1 NOUN cana-591 104 10 π‘₯8 π‘₯8 NOUN cana-591 104 11 , , PUNCT cana-591 104 12 π‘₯11 π‘₯11 ADV cana-591 104 13 , , PUNCT cana-591 104 14 π‘₯12 π‘₯12 VERB cana-591 104 15 : : PUNCT cana-591 104 16 𝑏0𝑐0𝑑0 𝑏0𝑐0𝑑0 NOUN cana-591 104 17 β†’ β†’ SYM cana-591 104 18 𝑒0 𝑒0 PROPN cana-591 104 19 thus thus ADV cana-591 104 20 , , PUNCT cana-591 104 21 core core NOUN cana-591 104 22 is be AUX cana-591 104 23 used use VERB cana-591 104 24 with with ADP cana-591 104 25 condition condition NOUN cana-591 104 26 attribute attribute NOUN cana-591 104 27 ' ' PUNCT cana-591 104 28 π‘Ž π‘Ž PRON cana-591 104 29 ' ' PUNCT cana-591 104 30 . . PUNCT cana-591 105 1 table table NOUN cana-591 105 2 4 4 NUM cana-591 105 3 remains remain VERB cana-591 105 4 after after ADP cana-591 105 5 removing remove VERB cana-591 105 6 characteristic characteristic ADJ cana-591 105 7 ' ' PUNCT cana-591 105 8 𝑏 𝑏 NOUN cana-591 105 9 ' ' PUNCT cana-591 105 10 from from ADP cana-591 105 11 table table NOUN cana-591 105 12 2 2 NUM cana-591 105 13 . . PUNCT cana-591 105 14 table table NOUN cana-591 105 15 4 4 NUM cana-591 105 16 . . PUNCT cana-591 105 17 attribute attribute NOUN cana-591 105 18 ' ' PUNCT cana-591 105 19 𝑏 𝑏 NOUN cana-591 105 20 ' ' PUNCT cana-591 105 21 is be AUX cana-591 105 22 eliminated eliminate VERB cana-591 105 23 π‘ˆ π‘ˆ PROPN cana-591 105 24 π‘Ž π‘Ž PROPN cana-591 105 25 𝑐 𝑐 NOUN cana-591 105 26 𝑑 𝑑 PROPN cana-591 105 27 𝑒 𝑒 PROPN cana-591 105 28 π‘₯1 π‘₯1 NOUN cana-591 105 29 1 1 NUM cana-591 105 30 0 0 NUM cana-591 105 31 0 0 NUM cana-591 105 32 1 1 NUM cana-591 105 33 π‘₯2 π‘₯2 NOUN cana-591 105 34 0 0 NUM cana-591 105 35 0 0 NUM cana-591 105 36 0 0 NUM cana-591 105 37 1 1 NUM cana-591 105 38 π‘₯3 π‘₯3 NOUN cana-591 105 39 1 1 NUM cana-591 105 40 0 0 NUM cana-591 105 41 0 0 NUM cana-591 105 42 1 1 NUM cana-591 105 43 π‘₯4 π‘₯4 NOUN cana-591 105 44 1 1 NUM cana-591 105 45 0 0 NUM cana-591 105 46 0 0 NUM cana-591 105 47 1 1 NUM cana-591 105 48 π‘₯5 π‘₯5 NOUN cana-591 105 49 0 0 NUM cana-591 105 50 1 1 NUM cana-591 105 51 0 0 NUM cana-591 105 52 1 1 NUM cana-591 105 53 π‘₯6 π‘₯6 NOUN cana-591 105 54 0 0 NUM cana-591 105 55 0 0 NUM cana-591 105 56 1 1 NUM cana-591 105 57 1 1 NUM cana-591 105 58 π‘₯7 π‘₯7 VERB cana-591 105 59 0 0 NUM cana-591 105 60 0 0 NUM cana-591 105 61 0 0 NUM cana-591 105 62 1 1 NUM cana-591 105 63 π‘₯8 π‘₯8 NOUN cana-591 105 64 0 0 NUM cana-591 105 65 0 0 NUM cana-591 105 66 0 0 NUM cana-591 105 67 0 0 NUM cana-591 105 68 π‘₯9 π‘₯9 NOUN cana-591 105 69 0 0 NUM cana-591 105 70 0 0 NUM cana-591 105 71 1 1 NUM cana-591 105 72 1 1 NUM cana-591 105 73 π‘₯10 π‘₯10 NUM cana-591 105 74 0 0 NUM cana-591 105 75 0 0 NUM cana-591 105 76 1 1 NUM cana-591 105 77 1 1 NUM cana-591 105 78 π‘₯11 π‘₯11 ADV cana-591 105 79 0 0 NUM cana-591 105 80 0 0 NUM cana-591 105 81 0 0 NUM cana-591 105 82 0 0 NUM cana-591 105 83 π‘₯12 π‘₯12 VERB cana-591 105 84 0 0 NUM cana-591 105 85 0 0 NUM cana-591 105 86 0 0 NUM cana-591 105 87 0 0 NUM cana-591 105 88 upon upon SCONJ cana-591 105 89 examination examination NOUN cana-591 105 90 , , PUNCT cana-591 105 91 table table NOUN cana-591 105 92 4 4 NUM cana-591 105 93 appears appear VERB cana-591 105 94 to to PART cana-591 105 95 be be AUX cana-591 105 96 devoid devoid ADJ cana-591 105 97 of of ADP cana-591 105 98 any any DET cana-591 105 99 discrepancies discrepancy NOUN cana-591 105 100 . . PUNCT cana-591 106 1 eliminating eliminate VERB cana-591 106 2 the the DET cana-591 106 3 characteristic characteristic NOUN cana-591 106 4 ' ' PUNCT cana-591 106 5 𝑏 𝑏 NOUN cana-591 106 6 ' ' PUNCT cana-591 106 7 results result NOUN cana-591 106 8 in in ADP cana-591 106 9 no no DET cana-591 106 10 inconsistency inconsistency NOUN cana-591 106 11 . . PUNCT cana-591 107 1 hence hence ADV cana-591 107 2 , , PUNCT cana-591 107 3 according accord VERB cana-591 107 4 on on ADP cana-591 107 5 the the DET cana-591 107 6 information information NOUN cana-591 107 7 , , PUNCT cana-591 107 8 attribute attribute NOUN cana-591 107 9 ' ' PUNCT cana-591 107 10 𝑏 𝑏 NOUN cana-591 107 11 ' ' PUNCT cana-591 107 12 is be AUX cana-591 107 13 not not PART cana-591 107 14 a a DET cana-591 107 15 core core NOUN cana-591 107 16 . . PUNCT cana-591 108 1 reduct reduct PROPN cana-591 108 2 1 1 NUM cana-591 108 3 = = PUNCT cana-591 108 4 { { PUNCT cana-591 108 5 a a X cana-591 108 6 , , PUNCT cana-591 108 7 c c NOUN cana-591 108 8 , , PUNCT cana-591 108 9 d d NOUN cana-591 108 10 } } PUNCT cana-591 108 11 table table NOUN cana-591 108 12 5 5 NUM cana-591 108 13 remains remain VERB cana-591 108 14 after after ADP cana-591 108 15 removing remove VERB cana-591 108 16 attribute attribute NOUN cana-591 108 17 ' ' PUNCT cana-591 108 18 𝑐 𝑐 NOUN cana-591 108 19 ' ' PUNCT cana-591 108 20 from from ADP cana-591 108 21 table table NOUN cana-591 108 22 2 2 NUM cana-591 108 23 . . PUNCT cana-591 109 1 communications communication NOUN cana-591 109 2 on on ADP cana-591 109 3 applied apply VERB cana-591 109 4 nonlinear nonlinear ADJ cana-591 109 5 analysis analysis NOUN cana-591 109 6 issn issn NOUN cana-591 109 7 : : PUNCT cana-591 109 8 1074 1074 NUM cana-591 109 9 - - PUNCT cana-591 109 10 133x 133x NUM cana-591 109 11 vol vol NOUN cana-591 109 12 31 31 NUM cana-591 109 13 no no NOUN cana-591 109 14 . . PUNCT cana-591 110 1 2s 2s NUM cana-591 110 2 ( ( PUNCT cana-591 110 3 2024 2024 NUM cana-591 110 4 ) ) PUNCT cana-591 110 5 39 39 NUM cana-591 110 6 https://internationalpubls.com https://internationalpubls.com X cana-591 110 7 table table NOUN cana-591 110 8 5 5 NUM cana-591 110 9 . . PUNCT cana-591 110 10 attribute attribute NOUN cana-591 110 11 ' ' PUNCT cana-591 110 12 𝑐 𝑐 PROPN cana-591 110 13 ' ' PUNCT cana-591 110 14 is be AUX cana-591 110 15 eliminated eliminate VERB cana-591 110 16 π‘ˆ π‘ˆ PROPN cana-591 110 17 π‘Ž π‘Ž PROPN cana-591 110 18 𝑏 𝑏 PROPN cana-591 110 19 𝑑 𝑑 PROPN cana-591 110 20 𝑒 𝑒 PROPN cana-591 110 21 π‘₯1 π‘₯1 NOUN cana-591 110 22 1 1 NUM cana-591 110 23 0 0 NUM cana-591 110 24 0 0 NUM cana-591 110 25 1 1 NUM cana-591 110 26 π‘₯2 π‘₯2 NOUN cana-591 110 27 0 0 NUM cana-591 110 28 1 1 NUM cana-591 110 29 0 0 NUM cana-591 110 30 1 1 NUM cana-591 110 31 π‘₯3 π‘₯3 NOUN cana-591 110 32 1 1 NUM cana-591 110 33 0 0 NUM cana-591 110 34 0 0 NUM cana-591 110 35 1 1 NUM cana-591 110 36 π‘₯4 π‘₯4 NOUN cana-591 110 37 1 1 NUM cana-591 110 38 0 0 NUM cana-591 110 39 0 0 NUM cana-591 110 40 1 1 NUM cana-591 110 41 π‘₯5 π‘₯5 NOUN cana-591 110 42 0 0 NUM cana-591 110 43 0 0 NUM cana-591 110 44 0 0 NUM cana-591 110 45 1 1 NUM cana-591 110 46 π‘₯6 π‘₯6 NOUN cana-591 110 47 0 0 NUM cana-591 110 48 0 0 NUM cana-591 110 49 1 1 NUM cana-591 110 50 1 1 NUM cana-591 110 51 π‘₯7 π‘₯7 VERB cana-591 110 52 0 0 NUM cana-591 110 53 0 0 NUM cana-591 110 54 0 0 NUM cana-591 110 55 1 1 NUM cana-591 110 56 π‘₯8 π‘₯8 NOUN cana-591 110 57 0 0 NUM cana-591 110 58 0 0 NUM cana-591 110 59 0 0 NUM cana-591 110 60 0 0 NUM cana-591 110 61 π‘₯9 π‘₯9 NOUN cana-591 110 62 0 0 NUM cana-591 110 63 0 0 NUM cana-591 110 64 1 1 NUM cana-591 110 65 1 1 NUM cana-591 110 66 π‘₯10 π‘₯10 NUM cana-591 110 67 0 0 NUM cana-591 110 68 0 0 NUM cana-591 110 69 1 1 NUM cana-591 110 70 1 1 NUM cana-591 110 71 π‘₯11 π‘₯11 ADV cana-591 110 72 0 0 NUM cana-591 110 73 0 0 NUM cana-591 110 74 0 0 NUM cana-591 110 75 0 0 NUM cana-591 110 76 π‘₯12 π‘₯12 VERB cana-591 110 77 0 0 NUM cana-591 110 78 0 0 NUM cana-591 110 79 0 0 NUM cana-591 110 80 0 0 NUM cana-591 111 1 the the DET cana-591 111 2 removal removal NOUN cana-591 111 3 of of ADP cana-591 111 4 the the DET cana-591 111 5 attribute attribute NOUN cana-591 111 6 ' ' PUNCT cana-591 111 7 𝑐 𝑐 NOUN cana-591 111 8 ' ' PUNCT cana-591 111 9 does do AUX cana-591 111 10 n't not PART cana-591 111 11 result result VERB cana-591 111 12 in in ADP cana-591 111 13 inconsistent inconsistent ADJ cana-591 111 14 data datum NOUN cana-591 111 15 . . PUNCT cana-591 112 1 as as ADP cana-591 112 2 a a DET cana-591 112 3 result result NOUN cana-591 112 4 , , PUNCT cana-591 112 5 condition condition NOUN cana-591 112 6 characteristic characteristic ADJ cana-591 112 7 ' ' PUNCT cana-591 112 8 𝑐 𝑐 NOUN cana-591 112 9 ' ' PUNCT cana-591 112 10 is be AUX cana-591 112 11 not not PART cana-591 112 12 utilized utilize VERB cana-591 112 13 as as ADP cana-591 112 14 the the DET cana-591 112 15 core core NOUN cana-591 112 16 . . PUNCT cana-591 113 1 however however ADV cana-591 113 2 , , PUNCT cana-591 113 3 table table NOUN cana-591 113 4 5 5 NUM cana-591 113 5 's 's PART cana-591 113 6 remaining remain VERB cana-591 113 7 condition condition NOUN cana-591 113 8 attribute attribute NOUN cana-591 113 9 is be AUX cana-591 113 10 regarded regard VERB cana-591 113 11 as as ADP cana-591 113 12 reduct reduct NOUN cana-591 113 13 . . PUNCT cana-591 114 1 hence hence ADV cana-591 114 2 , , PUNCT cana-591 114 3 reduct reduct PROPN cana-591 114 4 2 2 NUM cana-591 114 5 = = SYM cana-591 114 6 { { PUNCT cana-591 114 7 a a PRON cana-591 114 8 , , PUNCT cana-591 114 9 b b NOUN cana-591 114 10 , , PUNCT cana-591 114 11 d d NOUN cana-591 114 12 } } PUNCT cana-591 114 13 table table NOUN cana-591 114 14 6 6 NUM cana-591 114 15 . . PUNCT cana-591 114 16 attribute attribute NOUN cana-591 114 17 ' ' PUNCT cana-591 114 18 𝑑 𝑑 PRON cana-591 114 19 ' ' PUNCT cana-591 114 20 is be AUX cana-591 114 21 eliminated eliminate VERB cana-591 114 22 π‘ˆ π‘ˆ PROPN cana-591 114 23 π‘Ž π‘Ž PUNCT cana-591 114 24 𝑏 𝑏 PROPN cana-591 114 25 𝑐 𝑐 PROPN cana-591 114 26 𝑒 𝑒 PROPN cana-591 114 27 π‘₯1 π‘₯1 NOUN cana-591 114 28 1 1 NUM cana-591 114 29 0 0 NUM cana-591 114 30 0 0 NUM cana-591 114 31 1 1 NUM cana-591 114 32 π‘₯2 π‘₯2 NOUN cana-591 114 33 0 0 NUM cana-591 114 34 1 1 NUM cana-591 114 35 0 0 NUM cana-591 114 36 1 1 NUM cana-591 114 37 π‘₯3 π‘₯3 NOUN cana-591 114 38 1 1 NUM cana-591 114 39 0 0 NUM cana-591 114 40 0 0 NUM cana-591 114 41 1 1 NUM cana-591 114 42 π‘₯4 π‘₯4 NOUN cana-591 114 43 1 1 NUM cana-591 114 44 0 0 NUM cana-591 114 45 0 0 NUM cana-591 114 46 1 1 NUM cana-591 114 47 π‘₯5 π‘₯5 NOUN cana-591 114 48 0 0 NUM cana-591 114 49 0 0 NUM cana-591 114 50 1 1 NUM cana-591 114 51 1 1 NUM cana-591 114 52 π‘₯6 π‘₯6 NOUN cana-591 114 53 0 0 NUM cana-591 114 54 0 0 SYM cana-591 114 55 0 0 SYM cana-591 114 56 1 1 NUM cana-591 114 57 π‘₯7 π‘₯7 VERB cana-591 114 58 0 0 NUM cana-591 114 59 0 0 NUM cana-591 114 60 0 0 NUM cana-591 114 61 1 1 NUM cana-591 114 62 π‘₯8 π‘₯8 NOUN cana-591 114 63 0 0 NUM cana-591 114 64 0 0 NUM cana-591 114 65 0 0 NUM cana-591 114 66 0 0 NUM cana-591 114 67 π‘₯9 π‘₯9 NOUN cana-591 114 68 0 0 NUM cana-591 114 69 0 0 NUM cana-591 114 70 0 0 NUM cana-591 114 71 1 1 NUM cana-591 114 72 π‘₯10 π‘₯10 NUM cana-591 114 73 0 0 NUM cana-591 114 74 0 0 NUM cana-591 114 75 0 0 NUM cana-591 114 76 1 1 NUM cana-591 114 77 π‘₯11 π‘₯11 ADV cana-591 114 78 0 0 NUM cana-591 114 79 0 0 NUM cana-591 114 80 0 0 NUM cana-591 114 81 0 0 NUM cana-591 114 82 π‘₯12 π‘₯12 VERB cana-591 114 83 0 0 NUM cana-591 114 84 0 0 NUM cana-591 114 85 0 0 NUM cana-591 114 86 0 0 NUM cana-591 115 1 there there PRON cana-591 115 2 is be VERB cana-591 115 3 no no DET cana-591 115 4 inconsistency inconsistency NOUN cana-591 115 5 in in ADP cana-591 115 6 the the DET cana-591 115 7 dataset dataset NOUN cana-591 115 8 when when SCONJ cana-591 115 9 condition condition NOUN cana-591 115 10 attribute attribute NOUN cana-591 115 11 ' ' PUNCT cana-591 115 12 𝑑 𝑑 PRON cana-591 115 13 ' ' PUNCT cana-591 115 14 is be AUX cana-591 115 15 removed remove VERB cana-591 115 16 from from ADP cana-591 115 17 table table NOUN cana-591 115 18 6 6 NUM cana-591 115 19 . . PUNCT cana-591 116 1 as as ADP cana-591 116 2 a a DET cana-591 116 3 result result NOUN cana-591 116 4 of of ADP cana-591 116 5 this this PRON cana-591 116 6 , , PUNCT cana-591 116 7 attribute attribute NOUN cana-591 116 8 ' ' PUNCT cana-591 116 9 𝑑 𝑑 PRON cana-591 116 10 ' ' PUNCT cana-591 116 11 is be AUX cana-591 116 12 not not PART cana-591 116 13 a a DET cana-591 116 14 core core NOUN cana-591 116 15 . . PUNCT cana-591 117 1 reduct reduct PROPN cana-591 117 2 3 3 NUM cana-591 117 3 = = SYM cana-591 117 4 { { PUNCT cana-591 117 5 a a PRON cana-591 117 6 , , PUNCT cana-591 117 7 b b NOUN cana-591 117 8 , , PUNCT cana-591 117 9 c c NOUN cana-591 117 10 } } PUNCT cana-591 117 11 characteristic characteristic ADJ cana-591 117 12 ' ' PUNCT cana-591 117 13 π‘Ž π‘Ž NOUN cana-591 117 14 ' ' PUNCT cana-591 117 15 is be AUX cana-591 117 16 the the DET cana-591 117 17 only only ADJ cana-591 117 18 essential essential ADJ cana-591 117 19 characteristic characteristic NOUN cana-591 117 20 . . PUNCT cana-591 117 21 ' ' PUNCT cana-591 118 1 π‘Ž π‘Ž X cana-591 118 2 ' ' PUNCT cana-591 118 3 also also ADV cana-591 118 4 appears appear VERB cana-591 118 5 in in ADP cana-591 118 6 each each DET cana-591 118 7 reduct reduct NOUN cana-591 118 8 set set PROPN cana-591 118 9 . . PUNCT cana-591 119 1 communications communication NOUN cana-591 119 2 on on ADP cana-591 119 3 applied apply VERB cana-591 119 4 nonlinear nonlinear ADJ cana-591 119 5 analysis analysis NOUN cana-591 119 6 issn issn NOUN cana-591 119 7 : : PUNCT cana-591 119 8 1074 1074 NUM cana-591 119 9 - - PUNCT cana-591 119 10 133x 133x NUM cana-591 119 11 vol vol NOUN cana-591 119 12 31 31 NUM cana-591 119 13 no no NOUN cana-591 119 14 . . PUNCT cana-591 120 1 2s 2s NUM cana-591 120 2 ( ( PUNCT cana-591 120 3 2024 2024 NUM cana-591 120 4 ) ) PUNCT cana-591 120 5 40 40 NUM cana-591 120 6 https://internationalpubls.com https://internationalpubls.com X cana-591 120 7 additionally additionally ADV cana-591 120 8 , , PUNCT cana-591 120 9 we we PRON cana-591 120 10 understand understand VERB cana-591 120 11 that that SCONJ cana-591 120 12 core core NOUN cana-591 120 13 = = NOUN cana-591 120 14 ∩ ∩ NOUN cana-591 120 15 reducts reduct NOUN cana-591 120 16 core⁑(c core⁑(c PROPN cana-591 120 17 ) ) PUNCT cana-591 120 18 = = NOUN cana-591 120 19 ∩ ∩ X cana-591 120 20 { { PUNCT cana-591 120 21 { { PUNCT cana-591 120 22 reduct reduct PROPN cana-591 120 23 1 1 NUM cana-591 120 24 } } PUNCT cana-591 120 25 { { PUNCT cana-591 120 26 reduct reduct PROPN cana-591 120 27 2 2 NUM cana-591 120 28 } } PUNCT cana-591 120 29 { { PUNCT cana-591 120 30 reduct reduct PROPN cana-591 120 31 3 3 NUM cana-591 120 32 } } PUNCT cana-591 120 33 } } PUNCT cana-591 120 34 and and CCONJ cana-591 120 35 the the DET cana-591 120 36 reduct reduct NOUN cana-591 120 37 sets set NOUN cana-591 120 38 are be AUX cana-591 120 39 reduct reduct PROPN cana-591 120 40 1 1 NUM cana-591 120 41 = = SYM cana-591 120 42 { { PUNCT cana-591 120 43 a a X cana-591 120 44 , , PUNCT cana-591 120 45 c c NOUN cana-591 120 46 , , PUNCT cana-591 120 47 d d PROPN cana-591 120 48 } } PUNCT cana-591 120 49 reduct reduct NOUN cana-591 120 50 2 2 NUM cana-591 120 51 = = SYM cana-591 120 52 { { PUNCT cana-591 120 53 a a PRON cana-591 120 54 , , PUNCT cana-591 120 55 b b NOUN cana-591 120 56 , , PUNCT cana-591 120 57 d d PROPN cana-591 120 58 } } PUNCT cana-591 120 59 reduct reduct NOUN cana-591 120 60 3 3 NUM cana-591 120 61 = = SYM cana-591 120 62 { { PUNCT cana-591 120 63 a a PRON cana-591 120 64 , , PUNCT cana-591 120 65 b b NOUN cana-591 120 66 , , PUNCT cana-591 120 67 c c NOUN cana-591 120 68 } } PUNCT cana-591 120 69 core⁑(c core⁑(c PROPN cana-591 120 70 ) ) PUNCT cana-591 120 71 = = PRON cana-591 121 1 { { PUNCT cana-591 121 2 a a X cana-591 121 3 } } PUNCT cana-591 121 4 this this PRON cana-591 121 5 further far ADV cana-591 121 6 demonstrates demonstrate VERB cana-591 121 7 that that SCONJ cana-591 121 8 our our PRON cana-591 121 9 algorithm algorithm NOUN cana-591 121 10 is be AUX cana-591 121 11 accurate accurate ADJ cana-591 121 12 . . PUNCT cana-591 122 1 4 4 X cana-591 122 2 . . X cana-591 122 3 conclusion conclusion VERB cana-591 122 4 the the DET cana-591 122 5 application application NOUN cana-591 122 6 of of ADP cana-591 122 7 rough rough ADJ cana-591 122 8 set set NOUN cana-591 122 9 theory theory NOUN cana-591 122 10 to to ADP cana-591 122 11 the the DET cana-591 122 12 task task NOUN cana-591 122 13 of of ADP cana-591 122 14 finding find VERB cana-591 122 15 the the DET cana-591 122 16 best good ADJ cana-591 122 17 bike bike NOUN cana-591 122 18 in in ADP cana-591 122 19 different different ADJ cana-591 122 20 cubic cubic ADJ cana-591 122 21 centimeters centimeter NOUN cana-591 122 22 ( ( PUNCT cana-591 122 23 cc cc NOUN cana-591 122 24 ) ) PUNCT cana-591 122 25 has have AUX cana-591 122 26 provided provide VERB cana-591 122 27 valuable valuable ADJ cana-591 122 28 insights insight NOUN cana-591 122 29 in in ADP cana-591 122 30 this this DET cana-591 122 31 paper paper NOUN cana-591 122 32 . . PUNCT cana-591 123 1 by by ADP cana-591 123 2 employing employ VERB cana-591 123 3 rough rough ADJ cana-591 123 4 sets set NOUN cana-591 123 5 , , PUNCT cana-591 123 6 we we PRON cana-591 123 7 can can AUX cana-591 123 8 effectively effectively ADV cana-591 123 9 analyze analyze VERB cana-591 123 10 and and CCONJ cana-591 123 11 categorize categorize VERB cana-591 123 12 bikes bike NOUN cana-591 123 13 based base VERB cana-591 123 14 on on ADP cana-591 123 15 various various ADJ cana-591 123 16 attributes attribute NOUN cana-591 123 17 and and CCONJ cana-591 123 18 features feature VERB cana-591 123 19 relevant relevant ADJ cana-591 123 20 to to ADP cana-591 123 21 different different ADJ cana-591 123 22 cc cc ADP cana-591 123 23 categories category NOUN cana-591 123 24 . . PUNCT cana-591 124 1 this this DET cana-591 124 2 approach approach NOUN cana-591 124 3 helps help VERB cana-591 124 4 us we PRON cana-591 124 5 to to PART cana-591 124 6 identify identify VERB cana-591 124 7 the the DET cana-591 124 8 essential essential ADJ cana-591 124 9 attributes attribute NOUN cana-591 124 10 that that PRON cana-591 124 11 contribute contribute VERB cana-591 124 12 to to ADP cana-591 124 13 the the DET cana-591 124 14 superiority superiority NOUN cana-591 124 15 of of ADP cana-591 124 16 a a DET cana-591 124 17 bike bike NOUN cana-591 124 18 within within ADP cana-591 124 19 a a DET cana-591 124 20 specific specific ADJ cana-591 124 21 cc cc NOUN cana-591 124 22 range range NOUN cana-591 124 23 . . PUNCT cana-591 125 1 through through ADP cana-591 125 2 the the DET cana-591 125 3 reduction reduction NOUN cana-591 125 4 of of ADP cana-591 125 5 redundant redundant ADJ cana-591 125 6 information information NOUN cana-591 125 7 and and CCONJ cana-591 125 8 the the DET cana-591 125 9 extraction extraction NOUN cana-591 125 10 of of ADP cana-591 125 11 essential essential ADJ cana-591 125 12 characteristics characteristic NOUN cana-591 125 13 , , PUNCT cana-591 125 14 rough rough ADJ cana-591 125 15 set set NOUN cana-591 125 16 theory theory NOUN cana-591 125 17 streamlines streamline VERB cana-591 125 18 the the DET cana-591 125 19 decision decision NOUN cana-591 125 20 - - PUNCT cana-591 125 21 making make VERB cana-591 125 22 process process NOUN cana-591 125 23 for for ADP cana-591 125 24 selecting select VERB cana-591 125 25 the the DET cana-591 125 26 optimal optimal ADJ cana-591 125 27 bike bike NOUN cana-591 125 28 in in ADP cana-591 125 29 each each DET cana-591 125 30 cc cc NOUN cana-591 125 31 category category NOUN cana-591 125 32 . . PUNCT cana-591 126 1 overall overall ADJ cana-591 126 2 , , PUNCT cana-591 126 3 utilizing utilize VERB cana-591 126 4 rough rough ADJ cana-591 126 5 set set NOUN cana-591 126 6 theory theory NOUN cana-591 126 7 enhances enhance VERB cana-591 126 8 our our PRON cana-591 126 9 ability ability NOUN cana-591 126 10 to to PART cana-591 126 11 make make VERB cana-591 126 12 informed informed ADJ cana-591 126 13 choices choice NOUN cana-591 126 14 while while SCONJ cana-591 126 15 considering consider VERB cana-591 126 16 the the DET cana-591 126 17 intricate intricate ADJ cana-591 126 18 relationships relationship NOUN cana-591 126 19 between between ADP cana-591 126 20 attributes attribute NOUN cana-591 126 21 and and CCONJ cana-591 126 22 bike bike NOUN cana-591 126 23 performance performance NOUN cana-591 126 24 in in ADP cana-591 126 25 different different ADJ cana-591 126 26 cubic cubic ADJ cana-591 126 27 centimeter centimeter NOUN cana-591 126 28 ranges range NOUN cana-591 126 29 . . PUNCT cana-591 127 1 references reference NOUN cana-591 127 2 [ [ X cana-591 127 3 1 1 NUM cana-591 127 4 ] ] PUNCT cana-591 127 5 pawlak pawlak ADJ cana-591 127 6 , , PUNCT cana-591 127 7 z. z. PROPN cana-591 127 8 ( ( PUNCT cana-591 127 9 1982 1982 NUM cana-591 127 10 ) ) PUNCT cana-591 127 11 . . PUNCT cana-591 128 1 rough rough ADJ cana-591 128 2 sets set NOUN cana-591 128 3 , , PUNCT cana-591 128 4 international international ADJ cana-591 128 5 journal journal NOUN cana-591 128 6 of of ADP cana-591 128 7 computer computer NOUN cana-591 128 8 and and CCONJ cana-591 128 9 information information NOUN cana-591 128 10 sciences science NOUN cana-591 128 11 , , PUNCT cana-591 128 12 11 11 NUM cana-591 128 13 , , PUNCT cana-591 128 14 341–356 341–356 NUM cana-591 128 15 . . PUNCT cana-591 129 1 [ [ X cana-591 129 2 2 2 NUM cana-591 129 3 ] ] PUNCT cana-591 129 4 pawlak pawlak ADJ cana-591 129 5 , , PUNCT cana-591 129 6 z. z. PROPN cana-591 129 7 rough rough ADJ cana-591 129 8 sets set NOUN cana-591 129 9 - - PUNCT cana-591 129 10 theoretical theoretical ADJ cana-591 129 11 aspects aspect NOUN cana-591 129 12 of of ADP cana-591 129 13 reasoning reasoning NOUN cana-591 129 14 about about ADP cana-591 129 15 data datum NOUN cana-591 129 16 , , PUNCT cana-591 129 17 kluwer kluwer NOUN cana-591 129 18 academic academic ADJ cana-591 129 19 publishers publisher NOUN cana-591 129 20 , , PUNCT cana-591 129 21 boston boston PROPN cana-591 129 22 , , PUNCT cana-591 129 23 ma ma PROPN cana-591 129 24 , , PUNCT cana-591 129 25 1991 1991 NUM cana-591 129 26 . . PUNCT cana-591 130 1 [ [ X cana-591 130 2 3 3 NUM cana-591 130 3 ] ] X cana-591 130 4 thangavel thangavel NOUN cana-591 130 5 , , PUNCT cana-591 130 6 k. k. PROPN cana-591 130 7 , , PUNCT cana-591 130 8 & & CCONJ cana-591 130 9 pethalakshmi pethalakshmi PROPN cana-591 130 10 , , PUNCT cana-591 130 11 a. a. NOUN cana-591 130 12 ( ( PUNCT cana-591 130 13 2009 2009 NUM cana-591 130 14 ) ) PUNCT cana-591 130 15 . . PUNCT cana-591 131 1 dimensionality dimensionality NOUN cana-591 131 2 reduction reduction NOUN cana-591 131 3 based base VERB cana-591 131 4 on on ADP cana-591 131 5 rough rough ADJ cana-591 131 6 set set NOUN cana-591 131 7 theory theory NOUN cana-591 131 8 : : PUNCT cana-591 131 9 a a DET cana-591 131 10 review review NOUN cana-591 131 11 . . PUNCT cana-591 131 12 applied apply VERB cana-591 131 13 soft soft ADJ cana-591 131 14 computing computing NOUN cana-591 131 15 , , PUNCT cana-591 131 16 9(1 9(1 NUM cana-591 131 17 ) ) PUNCT cana-591 131 18 , , PUNCT cana-591 131 19 1 1 NUM cana-591 131 20 - - SYM cana-591 131 21 12 12 NUM cana-591 131 22 . . PUNCT cana-591 132 1 [ [ X cana-591 132 2 4 4 NUM cana-591 132 3 ] ] X cana-591 132 4 qian qian PROPN cana-591 132 5 , , PUNCT cana-591 132 6 y. y. PROPN cana-591 132 7 , , PUNCT cana-591 132 8 liang liang PROPN cana-591 132 9 , , PUNCT cana-591 132 10 j. j. PROPN cana-591 132 11 , , PUNCT cana-591 132 12 yao yao PROPN cana-591 132 13 , , PUNCT cana-591 132 14 y. y. PROPN cana-591 132 15 , , PUNCT cana-591 132 16 & & CCONJ cana-591 132 17 dang dang PROPN cana-591 132 18 , , PUNCT cana-591 132 19 c. c. PROPN cana-591 132 20 ( ( PUNCT cana-591 132 21 2010 2010 NUM cana-591 132 22 ) ) PUNCT cana-591 132 23 . . PUNCT cana-591 133 1 mgrs mgrs PROPN cana-591 133 2 : : PUNCT cana-591 133 3 a a DET cana-591 133 4 multi multi ADJ cana-591 133 5 - - ADJ cana-591 133 6 granulation granulation ADJ cana-591 133 7 rough rough ADJ cana-591 133 8 set set NOUN cana-591 133 9 . . PUNCT cana-591 134 1 information information NOUN cana-591 134 2 sciences sciences PROPN cana-591 134 3 , , PUNCT cana-591 134 4 180(6 180(6 NUM cana-591 134 5 ) ) PUNCT cana-591 134 6 , , PUNCT cana-591 134 7 949 949 NUM cana-591 134 8 - - SYM cana-591 134 9 970 970 NUM cana-591 134 10 . . PUNCT cana-591 135 1 [ [ X cana-591 135 2 5 5 NUM cana-591 135 3 ] ] X cana-591 135 4 qian qian PROPN cana-591 135 5 , , PUNCT cana-591 135 6 j. j. PROPN cana-591 135 7 , , PUNCT cana-591 135 8 han han PROPN cana-591 135 9 , , PUNCT cana-591 135 10 x. x. PROPN cana-591 135 11 , , PUNCT cana-591 135 12 yu yu PROPN cana-591 135 13 , , PUNCT cana-591 135 14 y. y. PROPN cana-591 135 15 , , PUNCT cana-591 135 16 & & CCONJ cana-591 135 17 liu liu PROPN cana-591 135 18 , , PUNCT cana-591 135 19 c. c. PROPN cana-591 135 20 ( ( PUNCT cana-591 135 21 2023 2023 NUM cana-591 135 22 ) ) PUNCT cana-591 135 23 . . PUNCT cana-591 136 1 multi multi ADJ cana-591 136 2 - - ADJ cana-591 136 3 granularity granularity NOUN cana-591 136 4 decision decision NOUN cana-591 136 5 - - PUNCT cana-591 136 6 theoretic theoretic NOUN cana-591 136 7 rough rough ADJ cana-591 136 8 sets set NOUN cana-591 136 9 based base VERB cana-591 136 10 on on ADP cana-591 136 11 the the DET cana-591 136 12 fuzzy fuzzy ADJ cana-591 136 13 tequivalence tequivalence NOUN cana-591 136 14 relation relation NOUN cana-591 136 15 with with ADP cana-591 136 16 new new ADJ cana-591 136 17 strategies strategy NOUN cana-591 136 18 . . PUNCT cana-591 137 1 journal journal NOUN cana-591 137 2 of of ADP cana-591 137 3 intelligent intelligent ADJ cana-591 137 4 & & CCONJ cana-591 137 5 fuzzy fuzzy ADJ cana-591 137 6 systems system NOUN cana-591 137 7 , , PUNCT cana-591 137 8 ( ( PUNCT cana-591 137 9 preprint preprint NOUN cana-591 137 10 ) ) PUNCT cana-591 137 11 , , PUNCT cana-591 137 12 1 1 NUM cana-591 137 13 - - SYM cana-591 137 14 15 15 NUM cana-591 137 15 . . PUNCT cana-591 138 1 [ [ X cana-591 138 2 6 6 NUM cana-591 138 3 ] ] X cana-591 138 4 liang liang PROPN cana-591 138 5 , , PUNCT cana-591 138 6 d. d. PROPN cana-591 138 7 , , PUNCT cana-591 138 8 liu liu PROPN cana-591 138 9 , , PUNCT cana-591 138 10 d. d. PROPN cana-591 138 11 , , PUNCT cana-591 138 12 pedrycz pedrycz NOUN cana-591 138 13 , , PUNCT cana-591 138 14 w. w. PROPN cana-591 138 15 , , PUNCT cana-591 138 16 & & CCONJ cana-591 138 17 hu hu PROPN cana-591 138 18 , , PUNCT cana-591 138 19 p. p. NOUN cana-591 138 20 ( ( PUNCT cana-591 138 21 2013 2013 NUM cana-591 138 22 ) ) PUNCT cana-591 138 23 . . PUNCT cana-591 138 24 triangular triangular NOUN cana-591 138 25 fuzzy fuzzy ADJ cana-591 138 26 decision decision NOUN cana-591 138 27 - - PUNCT cana-591 138 28 theoretic theoretic NOUN cana-591 138 29 rough rough ADJ cana-591 138 30 sets set NOUN cana-591 138 31 . . PUNCT cana-591 139 1 international international ADJ cana-591 139 2 journal journal PROPN cana-591 139 3 of of ADP cana-591 139 4 approximate approximate ADJ cana-591 139 5 reasoning reasoning NOUN cana-591 139 6 , , PUNCT cana-591 139 7 54(8 54(8 NUM cana-591 139 8 ) ) PUNCT cana-591 139 9 , , PUNCT cana-591 139 10 1087 1087 NUM cana-591 139 11 - - SYM cana-591 139 12 1106 1106 NUM cana-591 139 13 . . PUNCT cana-591 140 1 [ [ X cana-591 140 2 7 7 NUM cana-591 140 3 ] ] SYM cana-591 140 4 yao yao NOUN cana-591 140 5 , , PUNCT cana-591 140 6 y. y. PROPN cana-591 140 7 , , PUNCT cana-591 140 8 & & CCONJ cana-591 140 9 yao yao PROPN cana-591 140 10 , , PUNCT cana-591 140 11 b. b. PROPN cana-591 140 12 ( ( PUNCT cana-591 140 13 2012 2012 NUM cana-591 140 14 ) ) PUNCT cana-591 140 15 . . PUNCT cana-591 141 1 covering cover VERB cana-591 141 2 based base VERB cana-591 141 3 rough rough ADJ cana-591 141 4 set set NOUN cana-591 141 5 approximations approximation NOUN cana-591 141 6 . . PUNCT cana-591 142 1 information information NOUN cana-591 142 2 sciences sciences PROPN cana-591 142 3 , , PUNCT cana-591 142 4 200 200 NUM cana-591 142 5 , , PUNCT cana-591 142 6 91 91 NUM cana-591 142 7 - - SYM cana-591 142 8 107 107 NUM cana-591 142 9 . . PUNCT cana-591 143 1 [ [ X cana-591 143 2 8 8 NUM cana-591 143 3 ] ] SYM cana-591 143 4 yao yao NOUN cana-591 143 5 , , PUNCT cana-591 143 6 y. y. PROPN cana-591 143 7 ( ( PUNCT cana-591 143 8 2011 2011 NUM cana-591 143 9 ) ) PUNCT cana-591 143 10 . . PUNCT cana-591 144 1 the the DET cana-591 144 2 superiority superiority NOUN cana-591 144 3 of of ADP cana-591 144 4 three three NUM cana-591 144 5 - - PUNCT cana-591 144 6 way way NOUN cana-591 144 7 decisions decision NOUN cana-591 144 8 in in ADP cana-591 144 9 probabilistic probabilistic ADJ cana-591 144 10 rough rough ADJ cana-591 144 11 set set NOUN cana-591 144 12 models model NOUN cana-591 144 13 . . PUNCT cana-591 145 1 information information NOUN cana-591 145 2 sciences sciences PROPN cana-591 145 3 , , PUNCT cana-591 145 4 181(6 181(6 NUM cana-591 145 5 ) ) PUNCT cana-591 145 6 , , PUNCT cana-591 145 7 1080 1080 NUM cana-591 145 8 - - SYM cana-591 145 9 1096 1096 NUM cana-591 145 10 . . PUNCT cana-591 146 1 [ [ X cana-591 146 2 9 9 NUM cana-591 146 3 ] ] X cana-591 146 4 raghavan raghavan PROPN cana-591 146 5 , , PUNCT cana-591 146 6 r. r. PROPN cana-591 146 7 , , PUNCT cana-591 146 8 & & CCONJ cana-591 146 9 tripathy tripathy PROPN cana-591 146 10 , , PUNCT cana-591 146 11 b. b. PROPN cana-591 146 12 k. k. PROPN cana-591 146 13 ( ( PUNCT cana-591 146 14 2011 2011 NUM cana-591 146 15 ) ) PUNCT cana-591 146 16 . . PUNCT cana-591 147 1 on on ADP cana-591 147 2 some some DET cana-591 147 3 topological topological ADJ cana-591 147 4 properties property NOUN cana-591 147 5 of of ADP cana-591 147 6 multigranular multigranular ADJ cana-591 147 7 rough rough ADJ cana-591 147 8 sets set NOUN cana-591 147 9 . . PUNCT cana-591 148 1 advances advance NOUN cana-591 148 2 in in ADP cana-591 148 3 applied apply VERB cana-591 148 4 science science NOUN cana-591 148 5 research research NOUN cana-591 148 6 , , PUNCT cana-591 148 7 2(3 2(3 NUM cana-591 148 8 ) ) PUNCT cana-591 148 9 , , PUNCT cana-591 148 10 536 536 NUM cana-591 148 11 - - SYM cana-591 148 12 543 543 NUM cana-591 148 13 . . PUNCT cana-591 149 1 communications communication NOUN cana-591 149 2 on on ADP cana-591 149 3 applied apply VERB cana-591 149 4 nonlinear nonlinear ADJ cana-591 149 5 analysis analysis NOUN cana-591 149 6 issn issn NOUN cana-591 149 7 : : PUNCT cana-591 149 8 1074 1074 NUM cana-591 149 9 - - PUNCT cana-591 149 10 133x 133x NUM cana-591 149 11 vol vol NOUN cana-591 149 12 31 31 NUM cana-591 149 13 no no NOUN cana-591 149 14 . . PUNCT cana-591 150 1 2s 2s NUM cana-591 150 2 ( ( PUNCT cana-591 150 3 2024 2024 NUM cana-591 150 4 ) ) PUNCT cana-591 150 5 41 41 NUM cana-591 150 6 https://internationalpubls.com https://internationalpubls.com X cana-591 151 1 [ [ X cana-591 151 2 10 10 NUM cana-591 151 3 ] ] X cana-591 151 4 jupon jupon NOUN cana-591 151 5 , , PUNCT cana-591 151 6 r. r. PROPN cana-591 151 7 m. m. PROPN cana-591 151 8 , , PUNCT cana-591 151 9 wati wati PROPN cana-591 151 10 , , PUNCT cana-591 151 11 r. r. PROPN cana-591 151 12 , , PUNCT cana-591 151 13 kristina kristina PROPN cana-591 151 14 , , PUNCT cana-591 151 15 m. m. NOUN cana-591 151 16 , , PUNCT cana-591 151 17 & & CCONJ cana-591 151 18 nagara nagara PROPN cana-591 151 19 , , PUNCT cana-591 151 20 e. e. PROPN cana-591 151 21 s. s. PROPN cana-591 151 22 ( ( PUNCT cana-591 151 23 2023 2023 NUM cana-591 151 24 ) ) PUNCT cana-591 151 25 . . PUNCT cana-591 152 1 determining determine VERB cana-591 152 2 the the DET cana-591 152 3 purchase purchase NOUN cana-591 152 4 of of ADP cana-591 152 5 used use VERB cana-591 152 6 motorcycles motorcycle NOUN cana-591 152 7 using use VERB cana-591 152 8 the the DET cana-591 152 9 wp wp PROPN cana-591 152 10 method method NOUN cana-591 152 11 based base VERB cana-591 152 12 on on ADP cana-591 152 13 mobile mobile ADJ cana-591 152 14 web web NOUN cana-591 152 15 . . PUNCT cana-591 152 16 international international ADJ cana-591 152 17 journal journal NOUN cana-591 152 18 of of ADP cana-591 152 19 multidisciplinary multidisciplinary ADJ cana-591 152 20 research research NOUN cana-591 152 21 , , PUNCT cana-591 152 22 1(1 1(1 NUM cana-591 152 23 ) ) PUNCT cana-591 152 24 , , PUNCT cana-591 152 25 1 1 NUM cana-591 152 26 - - SYM cana-591 152 27 12 12 NUM cana-591 152 28 . . PUNCT cana-591 153 1 [ [ X cana-591 153 2 11 11 NUM cana-591 153 3 ] ] SYM cana-591 153 4 pfaffenbichler pfaffenbichler NOUN cana-591 153 5 , , PUNCT cana-591 153 6 p. p. NOUN cana-591 153 7 , , PUNCT cana-591 153 8 & & CCONJ cana-591 153 9 circella circella PROPN cana-591 153 10 , , PUNCT cana-591 153 11 g. g. PROPN cana-591 153 12 ( ( PUNCT cana-591 153 13 2009 2009 NUM cana-591 153 14 ) ) PUNCT cana-591 153 15 . . PUNCT cana-591 154 1 the the DET cana-591 154 2 role role NOUN cana-591 154 3 of of ADP cana-591 154 4 motorized motorize VERB cana-591 154 5 2 2 NUM cana-591 154 6 - - PUNCT cana-591 154 7 wheelers wheeler NOUN cana-591 154 8 in in ADP cana-591 154 9 an an DET cana-591 154 10 energy energy NOUN cana-591 154 11 efficient efficient ADJ cana-591 154 12 transport transport NOUN cana-591 154 13 system system NOUN cana-591 154 14 . . PUNCT cana-591 155 1 proc proc NOUN cana-591 155 2 . . PUNCT cana-591 156 1 of of ADP cana-591 156 2 the the DET cana-591 156 3 european european PROPN cana-591 156 4 council council PROPN cana-591 156 5 for for ADP cana-591 156 6 an an DET cana-591 156 7 energy energy NOUN cana-591 156 8 efficient efficient ADJ cana-591 156 9 economy economy NOUN cana-591 156 10 , , PUNCT cana-591 156 11 le le X cana-591 156 12 colle colle PROPN cana-591 156 13 sur sur PROPN cana-591 156 14 loup loup PROPN cana-591 156 15 , , PUNCT cana-591 156 16 cΓ΄te cΓ΄te PROPN cana-591 156 17 d'azur d'azur PROPN cana-591 156 18 , , PUNCT cana-591 156 19 1345 1345 NUM cana-591 156 20 - - SYM cana-591 156 21 1354 1354 NUM cana-591 157 1 . . PUNCT cana-591 158 1 [ [ X cana-591 158 2 12 12 NUM cana-591 158 3 ] ] PUNCT cana-591 158 4 butalia butalia NOUN cana-591 158 5 , , PUNCT cana-591 158 6 a. a. NOUN cana-591 158 7 , , PUNCT cana-591 158 8 dhore dhore NOUN cana-591 158 9 , , PUNCT cana-591 158 10 m. m. NOUN cana-591 158 11 , , PUNCT cana-591 158 12 & & CCONJ cana-591 158 13 tewani tewani PROPN cana-591 158 14 , , PUNCT cana-591 158 15 g. g. PROPN cana-591 158 16 ( ( PUNCT cana-591 158 17 2008 2008 NUM cana-591 158 18 ) ) PUNCT cana-591 158 19 . . PUNCT cana-591 159 1 applications application NOUN cana-591 159 2 of of ADP cana-591 159 3 rough rough ADJ cana-591 159 4 sets set NOUN cana-591 159 5 in in ADP cana-591 159 6 the the DET cana-591 159 7 field field NOUN cana-591 159 8 of of ADP cana-591 159 9 data datum NOUN cana-591 159 10 mining mining NOUN cana-591 159 11 . . PUNCT cana-591 160 1 in in ADP cana-591 160 2 2008 2008 NUM cana-591 160 3 first first ADJ cana-591 160 4 international international ADJ cana-591 160 5 conference conference NOUN cana-591 160 6 on on ADP cana-591 160 7 emerging emerge VERB cana-591 160 8 trends trend NOUN cana-591 160 9 in in ADP cana-591 160 10 engineering engineering NOUN cana-591 160 11 and and CCONJ cana-591 160 12 technology technology NOUN cana-591 160 13 ( ( PUNCT cana-591 160 14 pp pp ADJ cana-591 160 15 . . PUNCT cana-591 160 16 498 498 NUM cana-591 160 17 - - SYM cana-591 160 18 503 503 NUM cana-591 160 19 ) ) PUNCT cana-591 160 20 . . PUNCT cana-591 161 1 ieee ieee PROPN cana-591 161 2 . . PUNCT cana-591 162 1 [ [ X cana-591 162 2 13 13 NUM cana-591 162 3 ] ] SYM cana-591 162 4 vashist vashist NOUN cana-591 162 5 , , PUNCT cana-591 162 6 r. r. PROPN cana-591 162 7 ( ( PUNCT cana-591 162 8 2015 2015 NUM cana-591 162 9 ) ) PUNCT cana-591 162 10 . . PUNCT cana-591 163 1 an an DET cana-591 163 2 algorithm algorithm NOUN cana-591 163 3 for for ADP cana-591 163 4 finding find VERB cana-591 163 5 the the DET cana-591 163 6 reduct reduct NOUN cana-591 163 7 and and CCONJ cana-591 163 8 core core NOUN cana-591 163 9 of of ADP cana-591 163 10 the the DET cana-591 163 11 consistent consistent ADJ cana-591 163 12 dataset dataset NOUN cana-591 163 13 . . PUNCT cana-591 164 1 in in ADP cana-591 164 2 2015 2015 NUM cana-591 164 3 international international ADJ cana-591 164 4 conference conference NOUN cana-591 164 5 on on ADP cana-591 164 6 computational computational ADJ cana-591 164 7 intelligence intelligence NOUN cana-591 164 8 and and CCONJ cana-591 164 9 communication communication NOUN cana-591 164 10 networks network NOUN cana-591 164 11 ( ( PUNCT cana-591 164 12 cicn cicn PROPN cana-591 164 13 ) ) PUNCT cana-591 164 14 ( ( PUNCT cana-591 164 15 pp pp ADJ cana-591 164 16 . . PUNCT cana-591 165 1 741 741 NUM cana-591 165 2 - - NUM cana-591 165 3 745 745 NUM cana-591 165 4 ) ) PUNCT cana-591 165 5 . . PUNCT cana-591 166 1 ieee ieee NOUN cana-591 166 2 . . PUNCT cana-591 167 1 [ [ X cana-591 167 2 14 14 NUM cana-591 167 3 ] ] SYM cana-591 167 4 wu wu PROPN cana-591 167 5 , , PUNCT cana-591 167 6 w. w. PROPN cana-591 167 7 z. z. PROPN cana-591 167 8 , , PUNCT cana-591 167 9 & & CCONJ cana-591 167 10 mi mi PROPN cana-591 167 11 , , PUNCT cana-591 167 12 j. j. PROPN cana-591 167 13 s. s. PROPN cana-591 167 14 ( ( PUNCT cana-591 167 15 2011 2011 NUM cana-591 167 16 ) ) PUNCT cana-591 167 17 . . PUNCT cana-591 168 1 some some DET cana-591 168 2 mathematical mathematical ADJ cana-591 168 3 structures structure NOUN cana-591 168 4 of of ADP cana-591 168 5 generalized generalized ADJ cana-591 168 6 rough rough ADJ cana-591 168 7 sets set NOUN cana-591 168 8 in in ADP cana-591 168 9 infinite infinite ADJ cana-591 168 10 universes universe NOUN cana-591 168 11 of of ADP cana-591 168 12 discourse discourse NOUN cana-591 168 13 . . PUNCT cana-591 169 1 in in ADP cana-591 169 2 transactions transaction NOUN cana-591 169 3 on on ADP cana-591 169 4 rough rough ADJ cana-591 169 5 sets set NOUN cana-591 169 6 xiii xiii PROPN cana-591 169 7 ( ( PUNCT cana-591 169 8 pp pp ADJ cana-591 169 9 . . PUNCT cana-591 169 10 175 175 NUM cana-591 169 11 - - SYM cana-591 169 12 206 206 NUM cana-591 169 13 ) ) PUNCT cana-591 169 14 . . PUNCT cana-591 170 1 springer springer PROPN cana-591 170 2 berlin berlin PROPN cana-591 170 3 heidelberg heidelberg PROPN cana-591 170 4 . . PUNCT