id sid tid token lemma pos cana-5770 1 1 algebraic algebraic ADJ cana-5770 1 2 structure structure NOUN cana-5770 1 3 of of ADP cana-5770 1 4 relations relation NOUN cana-5770 1 5 on on ADP cana-5770 1 6 fuzzy fuzzy ADJ cana-5770 1 7 soft soft ADJ cana-5770 1 8 sets set NOUN cana-5770 1 9 anju anju PROPN cana-5770 1 10 s s PART cana-5770 1 11 mattam mattam PROPN cana-5770 1 12 assistant assistant PROPN cana-5770 1 13 professor professor NOUN cana-5770 1 14 little little ADJ cana-5770 1 15 flower flower NOUN cana-5770 1 16 college college NOUN cana-5770 1 17 guruvayoor guruvayoor NOUN cana-5770 1 18 , , PUNCT cana-5770 1 19 thrissur thrissur PROPN cana-5770 1 20 , , PUNCT cana-5770 1 21 kerala kerala PROPN cana-5770 1 22 . . PUNCT cana-5770 2 1 anju@littleflowercollege.edu.in anju@littleflowercollege.edu.in PROPN cana-5770 2 2 ; ; PUNCT cana-5770 2 3 τu(ε τu(ε PUNCT cana-5770 2 4 ) ) PUNCT cana-5770 3 1 = = SYM cana-5770 3 2   NOUN cana-5770 3 3 γu(ε γu(ε PUNCT cana-5770 3 4 if if SCONJ cana-5770 3 5 u u NOUN cana-5770 3 6 ) ) PUNCT cana-5770 3 7 ∈ ∈ PROPN cana-5770 3 8 ℘− ℘− NOUN cana-5770 3 9 ℘ξ ℘ξ VERB cana-5770 3 10 ξu(ε ξu(ε ADV cana-5770 3 11 if if SCONJ cana-5770 3 12 u u NOUN cana-5770 3 13 ) ) PUNCT cana-5770 3 14 ∈ ∈ PROPN cana-5770 3 15 ℘ξ ℘ξ NOUN cana-5770 3 16 − − NOUN cana-5770 3 17 ℘ ℘ PROPN cana-5770 3 18 γu(ε γu(ε NUM cana-5770 3 19 ) ) PUNCT cana-5770 3 20 ∨ ∨ NUM cana-5770 3 21 ξu(ε ξu(ε CCONJ cana-5770 3 22 ) ) PUNCT cana-5770 3 23 if if SCONJ cana-5770 3 24 u u PROPN cana-5770 3 25 ∈ ∈ PROPN cana-5770 3 26 ℘ ℘ PROPN cana-5770 3 27 ∩ ∩ NOUN cana-5770 3 28 ℘ξ ℘ξ ADJ cana-5770 3 29 definition definition NOUN cana-5770 3 30 2.3 2.3 NUM cana-5770 3 31 . . PUNCT cana-5770 4 1 fs f NOUN cana-5770 4 2 - - PUNCT cana-5770 4 3 intersection intersection NOUN cana-5770 4 4 of of ADP cana-5770 4 5 fs f NOUN cana-5770 4 6 - - PUNCT cana-5770 4 7 sets set NOUN cana-5770 4 8 ( ( PUNCT cana-5770 4 9 γ,℘ γ,℘ ADV cana-5770 4 10 ) ) PUNCT cana-5770 4 11 and and CCONJ cana-5770 4 12 ( ( PUNCT cana-5770 4 13 ξ,℘ξ ξ,℘ξ NUM cana-5770 4 14 ) ) PUNCT cana-5770 4 15 over over ADP cana-5770 4 16 z z PROPN cana-5770 4 17 is be AUX cana-5770 4 18 defined define VERB cana-5770 4 19 as as ADP cana-5770 4 20 the the DET cana-5770 4 21 fs fs NOUN cana-5770 4 22 - - PUNCT cana-5770 4 23 set set NOUN cana-5770 4 24 ( ( PUNCT cana-5770 4 25 τ τ PROPN cana-5770 4 26 , , PUNCT cana-5770 4 27 u u NOUN cana-5770 4 28 ) ) PUNCT cana-5770 4 29 = = SYM cana-5770 4 30 ( ( PUNCT cana-5770 4 31 γ,℘ γ,℘ X cana-5770 4 32 ) ) PUNCT cana-5770 5 1 ∩ ∩ NOUN cana-5770 5 2 ( ( PUNCT cana-5770 5 3 ξ,℘ξ ξ,℘ξ NUM cana-5770 5 4 ) ) PUNCT cana-5770 5 5 where where SCONJ cana-5770 5 6 u u NOUN cana-5770 5 7 = = PUNCT cana-5770 5 8 ℘ ℘ NOUN cana-5770 5 9 ∩ ∩ NOUN cana-5770 5 10 s s NOUN cana-5770 5 11 and and CCONJ cana-5770 5 12 for for ADP cana-5770 5 13 all all DET cana-5770 5 14 u u PROPN cana-5770 5 15 ∈ ∈ PROPN cana-5770 5 16 u u NOUN cana-5770 5 17 , , PUNCT cana-5770 5 18 τu(ε τu(ε PUNCT cana-5770 5 19 ) ) PUNCT cana-5770 5 20 = = SYM cana-5770 5 21 γu(ε γu(ε NUM cana-5770 5 22 ) ) PUNCT cana-5770 5 23 ∧ ∧ PROPN cana-5770 5 24 ξu(ε ξu(ε NOUN cana-5770 5 25 ) ) PUNCT cana-5770 5 26 communications communication NOUN cana-5770 5 27 on on ADP cana-5770 5 28 applied apply VERB cana-5770 5 29 nonlinear nonlinear ADJ cana-5770 5 30 analysis analysis NOUN cana-5770 5 31 issn issn NOUN cana-5770 5 32 : : PUNCT cana-5770 5 33 1074 1074 NUM cana-5770 5 34 - - PUNCT cana-5770 5 35 133x 133x NUM cana-5770 5 36 vol vol NOUN cana-5770 5 37 32 32 NUM cana-5770 5 38 no no NOUN cana-5770 5 39 . . PUNCT cana-5770 6 1 9s 9s NUM cana-5770 6 2 ( ( PUNCT cana-5770 6 3 2025 2025 NUM cana-5770 6 4 ) ) PUNCT cana-5770 6 5 received receive VERB cana-5770 6 6 : : PUNCT cana-5770 6 7 12 12 NUM cana-5770 6 8 - - SYM cana-5770 6 9 01 01 NUM cana-5770 6 10 - - PUNCT cana-5770 6 11 2025 2025 NUM cana-5770 6 12 abstract abstract NOUN cana-5770 6 13 : : PUNCT cana-5770 6 14 algebraic algebraic ADJ cana-5770 6 15 properties property NOUN cana-5770 6 16 of of ADP cana-5770 6 17 operations operation NOUN cana-5770 6 18 on on ADP cana-5770 6 19 fuzzy fuzzy ADJ cana-5770 6 20 soft soft ADJ cana-5770 6 21 relations relation NOUN cana-5770 6 22 are be AUX cana-5770 6 23 investigated investigate VERB cana-5770 6 24 article article NOUN cana-5770 6 25 history history NOUN cana-5770 6 26 : : PUNCT cana-5770 6 27 revised revise VERB cana-5770 6 28 : : PUNCT cana-5770 6 29 15 15 NUM cana-5770 6 30 - - NUM cana-5770 6 31 02 02 NUM cana-5770 6 32 - - PUNCT cana-5770 6 33 2025 2025 NUM cana-5770 6 34 and and CCONJ cana-5770 6 35 the the DET cana-5770 6 36 lattice lattice NOUN cana-5770 6 37 structure structure NOUN cana-5770 6 38 associated associate VERB cana-5770 6 39 with with ADP cana-5770 6 40 fuzzy fuzzy ADJ cana-5770 6 41 soft soft ADJ cana-5770 6 42 relations relation NOUN cana-5770 6 43 and and CCONJ cana-5770 6 44 fuzzy fuzzy ADJ cana-5770 6 45 soft soft ADJ cana-5770 6 46 equivalence equivalence NOUN cana-5770 6 47 accepted accept VERB cana-5770 6 48 : : PUNCT cana-5770 6 49 10 10 NUM cana-5770 6 50 - - SYM cana-5770 6 51 03 03 NUM cana-5770 6 52 - - PUNCT cana-5770 6 53 2025 2025 NUM cana-5770 6 54 relations relation NOUN cana-5770 6 55 are be AUX cana-5770 6 56 established establish VERB cana-5770 6 57 . . PUNCT cana-5770 7 1 keywords keyword NOUN cana-5770 7 2 : : PUNCT cana-5770 7 3 fuzzy fuzzy ADJ cana-5770 7 4 soft soft ADJ cana-5770 7 5 set set NOUN cana-5770 7 6 , , PUNCT cana-5770 7 7 fuzzy fuzzy ADJ cana-5770 7 8 soft soft ADJ cana-5770 7 9 relation relation NOUN cana-5770 7 10 , , PUNCT cana-5770 7 11 fuzzy fuzzy ADJ cana-5770 7 12 soft soft ADJ cana-5770 7 13 equivalence equivalence NOUN cana-5770 7 14 relation relation NOUN cana-5770 7 15 . . PUNCT cana-5770 8 1 1 1 X cana-5770 8 2 . . X cana-5770 8 3 introduction introduction NOUN cana-5770 8 4 . . PUNCT cana-5770 9 1 the the DET cana-5770 9 2 concept concept NOUN cana-5770 9 3 of of ADP cana-5770 9 4 soft soft ADJ cana-5770 9 5 set set NOUN cana-5770 9 6 [ [ X cana-5770 9 7 1 1 NUM cana-5770 9 8 ] ] PUNCT cana-5770 9 9 is be AUX cana-5770 9 10 gaining gain VERB cana-5770 9 11 popularity popularity NOUN cana-5770 9 12 among among ADP cana-5770 9 13 the the DET cana-5770 9 14 researchers researcher NOUN cana-5770 9 15 operating operate VERB cana-5770 9 16 in in ADP cana-5770 9 17 multidisciplinary multidisciplinary ADJ cana-5770 9 18 areas area NOUN cana-5770 9 19 . . PUNCT cana-5770 10 1 embedded embed VERB cana-5770 10 2 with with ADP cana-5770 10 3 recent recent ADJ cana-5770 10 4 developments development NOUN cana-5770 10 5 theory theory NOUN cana-5770 10 6 of of ADP cana-5770 10 7 soft soft ADJ cana-5770 10 8 sets set NOUN cana-5770 10 9 is be AUX cana-5770 10 10 getting get VERB cana-5770 10 11 richer rich ADJ cana-5770 10 12 and and CCONJ cana-5770 10 13 richer rich ADJ cana-5770 10 14 everyday[2 everyday[2 NOUN cana-5770 10 15 , , PUNCT cana-5770 10 16 3 3 NUM cana-5770 10 17 ] ] PUNCT cana-5770 10 18 . . PUNCT cana-5770 11 1 fuzzification fuzzification NOUN cana-5770 11 2 of of ADP cana-5770 11 3 soft soft ADJ cana-5770 11 4 sets set NOUN cana-5770 11 5 [ [ X cana-5770 11 6 4 4 NUM cana-5770 11 7 , , PUNCT cana-5770 11 8 5 5 NUM cana-5770 11 9 ] ] PUNCT cana-5770 11 10 also also ADV cana-5770 11 11 play play VERB cana-5770 11 12 a a DET cana-5770 11 13 very very ADV cana-5770 11 14 important important ADJ cana-5770 11 15 role role NOUN cana-5770 11 16 in in ADP cana-5770 11 17 fuzzy fuzzy ADJ cana-5770 11 18 logic logic NOUN cana-5770 11 19 and and CCONJ cana-5770 11 20 it it PRON cana-5770 11 21 has have VERB cana-5770 11 22 the the DET cana-5770 11 23 potential potential NOUN cana-5770 11 24 of of ADP cana-5770 11 25 hybridization hybridization NOUN cana-5770 11 26 . . PUNCT cana-5770 12 1 in in ADP cana-5770 12 2 this this DET cana-5770 12 3 aspect aspect NOUN cana-5770 12 4 fuzzy fuzzy ADJ cana-5770 12 5 soft soft ADJ cana-5770 12 6 set set NOUN cana-5770 12 7 among among ADP cana-5770 12 8 with with ADP cana-5770 12 9 its its PRON cana-5770 12 10 application application NOUN cana-5770 12 11 [ [ X cana-5770 12 12 6 6 NUM cana-5770 12 13 , , PUNCT cana-5770 12 14 7]have 7]have VERB cana-5770 12 15 been be AUX cana-5770 12 16 probed probe VERB cana-5770 12 17 many many ADJ cana-5770 12 18 authors author NOUN cana-5770 12 19 . . PUNCT cana-5770 13 1 relations relation NOUN cana-5770 13 2 on on ADP cana-5770 13 3 collection collection NOUN cana-5770 13 4 of of ADP cana-5770 13 5 fuzzy fuzzy ADJ cana-5770 13 6 soft soft ADJ cana-5770 13 7 sets set NOUN cana-5770 13 8 [ [ X cana-5770 13 9 8 8 NUM cana-5770 13 10 ] ] PUNCT cana-5770 13 11 are be AUX cana-5770 13 12 structured structure VERB cana-5770 13 13 using use VERB cana-5770 13 14 minimum minimum ADJ cana-5770 13 15 function function NOUN cana-5770 13 16 . . PUNCT cana-5770 14 1 it it PRON cana-5770 14 2 provides provide VERB cana-5770 14 3 a a DET cana-5770 14 4 broad broad ADJ cana-5770 14 5 and and CCONJ cana-5770 14 6 flexible flexible ADJ cana-5770 14 7 technique technique NOUN cana-5770 14 8 for for ADP cana-5770 14 9 molding mold VERB cana-5770 14 10 any any DET cana-5770 14 11 decision decision NOUN cana-5770 14 12 making make VERB cana-5770 14 13 process process NOUN cana-5770 14 14 . . PUNCT cana-5770 15 1 in in ADP cana-5770 15 2 section section NOUN cana-5770 15 3 ii ii PROPN cana-5770 15 4 adequate adequate ADJ cana-5770 15 5 concepts concept NOUN cana-5770 15 6 related relate VERB cana-5770 15 7 to to ADP cana-5770 15 8 fuzzy fuzzy ADJ cana-5770 15 9 soft soft ADJ cana-5770 15 10 sets set NOUN cana-5770 15 11 are be AUX cana-5770 15 12 given give VERB cana-5770 15 13 . . PUNCT cana-5770 16 1 in in ADP cana-5770 16 2 the the DET cana-5770 16 3 next next ADJ cana-5770 16 4 section section NOUN cana-5770 16 5 different different ADJ cana-5770 16 6 types type NOUN cana-5770 16 7 of of ADP cana-5770 16 8 relations relation NOUN cana-5770 16 9 that that PRON cana-5770 16 10 can can AUX cana-5770 16 11 be be AUX cana-5770 16 12 defined define VERB cana-5770 16 13 on on ADP cana-5770 16 14 the the DET cana-5770 16 15 collection collection NOUN cana-5770 16 16 of of ADP cana-5770 16 17 fuzzy fuzzy ADJ cana-5770 16 18 soft soft ADJ cana-5770 16 19 sets set NOUN cana-5770 16 20 are be AUX cana-5770 16 21 investigated investigate VERB cana-5770 16 22 with with ADP cana-5770 16 23 a a DET cana-5770 16 24 detailed detailed ADJ cana-5770 16 25 study study NOUN cana-5770 16 26 on on ADP cana-5770 16 27 its its PRON cana-5770 16 28 properties property NOUN cana-5770 16 29 . . PUNCT cana-5770 17 1 section section NOUN cana-5770 17 2 4 4 NUM cana-5770 17 3 is be AUX cana-5770 17 4 entirely entirely ADV cana-5770 17 5 devoted devoted ADJ cana-5770 17 6 to to ADP cana-5770 17 7 the the DET cana-5770 17 8 study study NOUN cana-5770 17 9 of of ADP cana-5770 17 10 fuzzy fuzzy ADJ cana-5770 17 11 soft soft ADJ cana-5770 17 12 equivalence equivalence NOUN cana-5770 17 13 relations relation NOUN cana-5770 17 14 containing contain VERB cana-5770 17 15 the the DET cana-5770 17 16 concepts concept NOUN cana-5770 17 17 of of ADP cana-5770 17 18 fuzzy fuzzy ADJ cana-5770 17 19 soft soft ADJ cana-5770 17 20 reflexive reflexive ADJ cana-5770 17 21 , , PUNCT cana-5770 17 22 fuzzy fuzzy ADJ cana-5770 17 23 soft soft ADJ cana-5770 17 24 symmetric symmetric ADJ cana-5770 17 25 and and CCONJ cana-5770 17 26 fuzzy fuzzy ADJ cana-5770 17 27 soft soft ADJ cana-5770 17 28 transitive transitive ADJ cana-5770 17 29 relations relation NOUN cana-5770 17 30 . . PUNCT cana-5770 18 1 in in ADP cana-5770 18 2 the the DET cana-5770 18 3 last last ADJ cana-5770 18 4 section section NOUN cana-5770 18 5 the the DET cana-5770 18 6 lattice lattice NOUN cana-5770 18 7 structure structure NOUN cana-5770 18 8 of of ADP cana-5770 18 9 fuzzy fuzzy ADJ cana-5770 18 10 soft soft ADJ cana-5770 18 11 relations relation NOUN cana-5770 18 12 and and CCONJ cana-5770 18 13 fuzzy fuzzy ADJ cana-5770 18 14 soft soft ADJ cana-5770 18 15 equivalence equivalence NOUN cana-5770 18 16 relations relation NOUN cana-5770 18 17 are be AUX cana-5770 18 18 also also ADV cana-5770 18 19 studied study VERB cana-5770 18 20 . . PUNCT cana-5770 19 1 2 2 X cana-5770 19 2 . . NUM cana-5770 19 3 preliminaries preliminary NOUN cana-5770 19 4 . . PUNCT cana-5770 20 1 let let VERB cana-5770 20 2 z z NOUN cana-5770 20 3 and and CCONJ cana-5770 20 4 ℘ ℘ PROPN cana-5770 20 5 be be VERB cana-5770 20 6 the the DET cana-5770 20 7 universal universal ADJ cana-5770 20 8 set set NOUN cana-5770 20 9 and and CCONJ cana-5770 20 10 the the DET cana-5770 20 11 parameter parameter NOUN cana-5770 20 12 set set VERB cana-5770 20 13 respectively respectively ADV cana-5770 20 14 and and CCONJ cana-5770 20 15 let let VERB cana-5770 20 16 the the DET cana-5770 20 17 collection collection NOUN cana-5770 20 18 of of ADP cana-5770 20 19 all all DET cana-5770 20 20 fuzzy fuzzy ADJ cana-5770 20 21 subsets subset NOUN cana-5770 20 22 of of ADP cana-5770 20 23 z z NOUN cana-5770 20 24 be be AUX cana-5770 20 25 denoted denote VERB cana-5770 20 26 as as ADP cana-5770 20 27 iz iz INTJ cana-5770 20 28 . . PUNCT cana-5770 21 1 a a DET cana-5770 21 2 fuzzy fuzzy ADJ cana-5770 21 3 soft soft ADJ cana-5770 21 4 set set NOUN cana-5770 21 5 ( ( PUNCT cana-5770 21 6 fs fs NOUN cana-5770 21 7 - - PUNCT cana-5770 21 8 set set NOUN cana-5770 21 9 ) ) PUNCT cana-5770 21 10 over over ADP cana-5770 21 11 z z PROPN cana-5770 21 12 is be AUX cana-5770 21 13 a a DET cana-5770 21 14 pair pair NOUN cana-5770 21 15 ( ( PUNCT cana-5770 21 16 γ,℘ γ,℘ ADV cana-5770 21 17 ) ) PUNCT cana-5770 21 18 where where SCONJ cana-5770 21 19 function function NOUN cana-5770 21 20 γ γ PROPN cana-5770 21 21 is be AUX cana-5770 21 22 defined define VERB cana-5770 21 23 from from ADP cana-5770 21 24 ℘ ℘ PROPN cana-5770 21 25 to to ADP cana-5770 21 26 iz iz INTJ cana-5770 21 27 . . PUNCT cana-5770 22 1 definition definition NOUN cana-5770 22 2 2.1 2.1 NUM cana-5770 22 3 . . PUNCT cana-5770 23 1 the the DET cana-5770 23 2 fuzzy fuzzy ADJ cana-5770 23 3 set set VERB cana-5770 23 4 in in ADP cana-5770 23 5 ( ( PUNCT cana-5770 23 6 γ,℘ γ,℘ ADV cana-5770 23 7 ) ) PUNCT cana-5770 23 8 corresponding correspond VERB cana-5770 23 9 to to ADP cana-5770 23 10 the the DET cana-5770 23 11 parameter parameter NOUN cana-5770 23 12 t t PROPN cana-5770 23 13 ∈ ∈ PROPN cana-5770 23 14 ℘ ℘ PROPN cana-5770 23 15 is be AUX cana-5770 23 16 called call VERB cana-5770 23 17 the the DET cana-5770 23 18 fs fs NOUN cana-5770 23 19 - - PUNCT cana-5770 23 20 element element NOUN cana-5770 23 21 denoted denote VERB cana-5770 23 22 by by ADP cana-5770 23 23 γt γt NOUN cana-5770 23 24 , , PUNCT cana-5770 23 25 where where SCONJ cana-5770 23 26 γt γt NOUN cana-5770 23 27 is be AUX cana-5770 23 28 a a DET cana-5770 23 29 function function NOUN cana-5770 23 30 from from ADP cana-5770 23 31 z z NOUN cana-5770 23 32 to to ADP cana-5770 23 33 [ [ X cana-5770 23 34 0,1 0,1 NUM cana-5770 23 35 ] ] PUNCT cana-5770 23 36 . . PUNCT cana-5770 24 1 the the DET cana-5770 24 2 collection collection NOUN cana-5770 24 3 of of ADP cana-5770 24 4 all all DET cana-5770 24 5 fs f NOUN cana-5770 24 6 - - NOUN cana-5770 24 7 sets set NOUN cana-5770 24 8 over over ADP cana-5770 24 9 the the DET cana-5770 24 10 universal universal ADJ cana-5770 24 11 set set NOUN cana-5770 24 12 z z PROPN cana-5770 24 13 and and CCONJ cana-5770 24 14 parameter parameter NOUN cana-5770 24 15 set set VERB cana-5770 24 16 ℘ ℘ PROPN cana-5770 24 17 is be AUX cana-5770 24 18 denoted denote VERB cana-5770 24 19 by by ADP cana-5770 24 20 fss(z,℘ fss(z,℘ PROPN cana-5770 24 21 ) ) PUNCT cana-5770 24 22 . . PUNCT cana-5770 25 1 the the DET cana-5770 25 2 fs fs ADJ cana-5770 25 3 - - PUNCT cana-5770 25 4 set set VERB cana-5770 25 5 ˜(γ,℘ ˜(γ,℘ NOUN cana-5770 25 6 ) ) PUNCT cana-5770 25 7 is be AUX cana-5770 25 8 called call VERB cana-5770 25 9 a a DET cana-5770 25 10 null null ADJ cana-5770 25 11 fs fs NOUN cana-5770 25 12 - - PUNCT cana-5770 25 13 set set ADJ cana-5770 25 14 , , PUNCT cana-5770 25 15 denoted denote VERB cana-5770 25 16 by by ADP cana-5770 25 17 0℘ 0℘ PROPN cana-5770 25 18 , , PUNCT cana-5770 25 19 if if SCONJ cana-5770 25 20 γt(ε)=0 γt(ε)=0 NUM cana-5770 25 21 , , PUNCT cana-5770 25 22 ∀ ∀ X cana-5770 25 23 t t NOUN cana-5770 25 24 ∈ ∈ PROPN cana-5770 25 25 ℘ ℘ PROPN cana-5770 25 26 and and CCONJ cana-5770 25 27 ∀ ∀ NUM cana-5770 25 28 ε ε PROPN cana-5770 25 29 ∈ ∈ PROPN cana-5770 25 30 z. z. PROPN cana-5770 26 1 the the DET cana-5770 26 2 fs fs PROPN cana-5770 26 3 - - PUNCT cana-5770 26 4 set set VERB cana-5770 26 5 ˜(γ,℘ ˜(γ,℘ NOUN cana-5770 26 6 ) ) PUNCT cana-5770 26 7 is be AUX cana-5770 26 8 called call VERB cana-5770 26 9 the the DET cana-5770 26 10 whole whole ADJ cana-5770 26 11 fs fs NOUN cana-5770 26 12 - - PUNCT cana-5770 26 13 set set ADJ cana-5770 26 14 , , PUNCT cana-5770 26 15 denoted denote VERB cana-5770 26 16 by by ADP cana-5770 26 17 1℘ 1℘ PRON cana-5770 26 18 , , PUNCT cana-5770 26 19 if if SCONJ cana-5770 26 20 γt(ε)= γt(ε)= PROPN cana-5770 26 21 1 1 NUM cana-5770 26 22 , , PUNCT cana-5770 26 23 ∀ ∀ X cana-5770 26 24 t t NOUN cana-5770 26 25 ∈ ∈ PROPN cana-5770 26 26 ℘ ℘ PROPN cana-5770 26 27 and and CCONJ cana-5770 26 28 ∀ ∀ NUM cana-5770 26 29 ε ε PROPN cana-5770 26 30 ∈ ∈ PROPN cana-5770 26 31 z. z. PROPN cana-5770 26 32 complement complement NOUN cana-5770 26 33 of of ADP cana-5770 26 34 fs fs NOUN cana-5770 26 35 - - PUNCT cana-5770 26 36 set set VERB cana-5770 26 37 ( ( PUNCT cana-5770 26 38 γ,℘ γ,℘ ADV cana-5770 26 39 ) ) PUNCT cana-5770 26 40 over over ADP cana-5770 26 41 z z PROPN cana-5770 26 42 is be AUX cana-5770 26 43 given give VERB cana-5770 26 44 by by ADP cana-5770 26 45 ( ( PUNCT cana-5770 26 46 γc,℘ γc,℘ NUM cana-5770 26 47 ) ) PUNCT cana-5770 27 1 where where SCONJ cana-5770 27 2 γct(ε)= γct(ε)= ADP cana-5770 27 3 1 1 NUM cana-5770 27 4 - - NUM cana-5770 27 5 γt(ε γt(ε NUM cana-5770 27 6 ) ) PUNCT cana-5770 27 7 . . PUNCT cana-5770 28 1 ˜ ˜ PROPN cana-5770 28 2 ˜ ˜ PROPN cana-5770 29 1 ˜ ˜ PROPN cana-5770 29 2 ˜note ˜note VERB cana-5770 29 3 that that SCONJ cana-5770 29 4 0 0 NUM cana-5770 29 5 c c NOUN cana-5770 29 6 = = SYM cana-5770 29 7 1 1 NUM cana-5770 29 8 and and CCONJ cana-5770 29 9 1 1 NUM cana-5770 29 10 c c NOUN cana-5770 29 11 = = SYM cana-5770 29 12 0℘ 0℘ NUM cana-5770 30 1 ℘ ℘ PROPN cana-5770 30 2 ℘ ℘ NUM cana-5770 30 3 ℘ ℘ PROPN cana-5770 30 4 definition definition NOUN cana-5770 30 5 2.2 2.2 NUM cana-5770 30 6 . . PUNCT cana-5770 31 1 fs fs PROPN cana-5770 31 2 - - PUNCT cana-5770 31 3 union union NOUN cana-5770 31 4 of of ADP cana-5770 31 5 two two NUM cana-5770 31 6 fs f NOUN cana-5770 31 7 - - PUNCT cana-5770 31 8 sets set NOUN cana-5770 31 9 ( ( PUNCT cana-5770 31 10 γ,℘ γ,℘ ADV cana-5770 31 11 ) ) PUNCT cana-5770 31 12 and and CCONJ cana-5770 31 13 ( ( PUNCT cana-5770 31 14 ξ,℘ξ ξ,℘ξ NUM cana-5770 31 15 ) ) PUNCT cana-5770 31 16 over over ADP cana-5770 31 17 z z PROPN cana-5770 31 18 is be AUX cana-5770 31 19 defined define VERB cana-5770 31 20 as as ADP cana-5770 31 21 the the DET cana-5770 31 22 fs fs NOUN cana-5770 31 23 - - PUNCT cana-5770 31 24 set set NOUN cana-5770 31 25 ( ( PUNCT cana-5770 31 26 τ τ PROPN cana-5770 31 27 , , PUNCT cana-5770 31 28 u u NOUN cana-5770 31 29 ) ) PUNCT cana-5770 31 30 = = SYM cana-5770 32 1 ( ( PUNCT cana-5770 32 2 γ,℘ γ,℘ ADV cana-5770 32 3 ) ) PUNCT cana-5770 32 4 ∪ ∪ NOUN cana-5770 32 5 ( ( PUNCT cana-5770 32 6 ξ,℘ξ ξ,℘ξ NUM cana-5770 32 7 ) ) PUNCT cana-5770 32 8 where where SCONJ cana-5770 32 9 u u NOUN cana-5770 32 10 = = NOUN cana-5770 32 11 ℘ ℘ PROPN cana-5770 32 12 ∪ ∪ ADJ cana-5770 32 13 ℘ξ ℘ξ NOUN cana-5770 32 14 and and CCONJ cana-5770 32 15 for for ADP cana-5770 32 16 all all DET cana-5770 32 17 u u NOUN cana-5770 32 18 ∈ ∈ PROPN cana-5770 32 19 u u NOUN cana-5770 32 20 https://internationalpubls.com https://internationalpubls.com X cana-5770 32 21 3196 3196 NUM cana-5770 32 22 anju anju PROPN cana-5770 32 23 rajath rajath NOUN cana-5770 32 24 pencil pencil NOUN cana-5770 32 25 definition definition NOUN cana-5770 32 26 2.4 2.4 NUM cana-5770 32 27 . . PUNCT cana-5770 33 1 let let VERB cana-5770 33 2 ( ( PUNCT cana-5770 33 3 γ,℘ γ,℘ ADV cana-5770 33 4 ) ) PUNCT cana-5770 33 5 and and CCONJ cana-5770 33 6 ( ( PUNCT cana-5770 33 7 ξ,℘ξ ξ,℘ξ X cana-5770 33 8 ) ) PUNCT cana-5770 33 9 be be VERB cana-5770 33 10 two two NUM cana-5770 33 11 fs f NOUN cana-5770 33 12 - - PUNCT cana-5770 33 13 sets set NOUN cana-5770 33 14 over over ADP cana-5770 33 15 z. z. PROPN cana-5770 33 16 then then ADV cana-5770 33 17 product product NOUN cana-5770 33 18 of of ADP cana-5770 33 19 ( ( PUNCT cana-5770 33 20 γ,℘ γ,℘ ADV cana-5770 33 21 ) ) PUNCT cana-5770 33 22 and and CCONJ cana-5770 33 23 ( ( PUNCT cana-5770 33 24 ξ,℘ξ ξ,℘ξ X cana-5770 33 25 ) ) PUNCT cana-5770 33 26 is be AUX cana-5770 33 27 defined define VERB cana-5770 33 28 as as ADP cana-5770 33 29 ( ( PUNCT cana-5770 33 30 γ,℘ γ,℘ ADV cana-5770 33 31 ) ) PUNCT cana-5770 33 32 x x X cana-5770 33 33 ( ( PUNCT cana-5770 33 34 ξ,℘ξ ξ,℘ξ NUM cana-5770 33 35 ) ) PUNCT cana-5770 33 36 = = SYM cana-5770 34 1 ( ( PUNCT cana-5770 34 2 k k X cana-5770 34 3 , , PUNCT cana-5770 34 4 ℘ ℘ NOUN cana-5770 34 5 x x SYM cana-5770 34 6 ℘ξ ℘ξ NOUN cana-5770 34 7 ) ) PUNCT cana-5770 34 8 where where SCONJ cana-5770 34 9 k k NOUN cana-5770 34 10 : : PUNCT cana-5770 34 11 ℘ ℘ NUM cana-5770 34 12 x x SYM cana-5770 34 13 ℘ξ ℘ξ VERB cana-5770 34 14 → → SYM cana-5770 34 15 ix ix ADV cana-5770 34 16 and and CCONJ cana-5770 34 17 ∀ ∀ NUM cana-5770 34 18 ( ( PUNCT cana-5770 34 19 t t PROPN cana-5770 34 20 , , PUNCT cana-5770 34 21 s s PART cana-5770 34 22 ) ) PUNCT cana-5770 34 23 ∈ ∈ PROPN cana-5770 34 24 ℘ ℘ PROPN cana-5770 34 25 x x SYM cana-5770 34 26 ℘ξ ℘ξ VERB cana-5770 34 27 k(t k(t PROPN cana-5770 34 28 , , PUNCT cana-5770 34 29 s)(ε s)(ε PUNCT cana-5770 34 30 ) ) PUNCT cana-5770 34 31 = = PRON cana-5770 34 32 { { PUNCT cana-5770 34 33 1 1 NUM cana-5770 34 34 , , PUNCT cana-5770 34 35 if if SCONJ cana-5770 34 36 t t PROPN cana-5770 34 37 = = SYM cana-5770 34 38 s s PROPN cana-5770 34 39 min(γt(ε),ξs(ε min(γt(ε),ξs(ε PROPN cana-5770 34 40 ) ) PUNCT cana-5770 34 41 ) ) PUNCT cana-5770 34 42 , , PUNCT cana-5770 34 43 if if SCONJ cana-5770 34 44 t t PROPN cana-5770 34 45 6= 6= SYM cana-5770 34 46 s s X cana-5770 34 47 . . NOUN cana-5770 35 1 3 3 X cana-5770 35 2 . . X cana-5770 35 3 fuzzy fuzzy ADJ cana-5770 35 4 soft soft ADJ cana-5770 35 5 relation relation NOUN cana-5770 35 6 . . PUNCT cana-5770 36 1 definition definition NOUN cana-5770 36 2 3.1 3.1 NUM cana-5770 36 3 . . PUNCT cana-5770 37 1 let let VERB cana-5770 37 2 ( ( PUNCT cana-5770 37 3 γ,℘ γ,℘ ADV cana-5770 37 4 ) ) PUNCT cana-5770 37 5 and and CCONJ cana-5770 37 6 ( ( PUNCT cana-5770 37 7 ξ ξ X cana-5770 37 8 , , PUNCT cana-5770 37 9 s s PART cana-5770 37 10 ) ) PUNCT cana-5770 37 11 be be AUX cana-5770 37 12 the the DET cana-5770 37 13 fs f NOUN cana-5770 37 14 - - PUNCT cana-5770 37 15 sets set NOUN cana-5770 37 16 over over ADP cana-5770 37 17 z. z. PROPN cana-5770 37 18 fuzzy fuzzy ADJ cana-5770 37 19 soft soft ADJ cana-5770 37 20 relation relation NOUN cana-5770 37 21 ( ( PUNCT cana-5770 37 22 fs fs NOUN cana-5770 37 23 - - PUNCT cana-5770 37 24 relation relation NOUN cana-5770 37 25 ) ) PUNCT cana-5770 37 26 from from ADP cana-5770 37 27 ( ( PUNCT cana-5770 37 28 γ,℘ γ,℘ ADV cana-5770 37 29 ) ) PUNCT cana-5770 37 30 to to ADP cana-5770 37 31 ( ( PUNCT cana-5770 37 32 ξ ξ X cana-5770 37 33 , , PUNCT cana-5770 37 34 s s PART cana-5770 37 35 ) ) PUNCT cana-5770 37 36 is be AUX cana-5770 37 37 the the DET cana-5770 37 38 fs fs NOUN cana-5770 37 39 - - PUNCT cana-5770 37 40 subset subset NOUN cana-5770 37 41 of of ADP cana-5770 37 42 ( ( PUNCT cana-5770 37 43 γ,℘ γ,℘ ADV cana-5770 37 44 ) ) PUNCT cana-5770 38 1 x x X cana-5770 38 2 ( ( PUNCT cana-5770 38 3 ξ ξ PROPN cana-5770 38 4 , , PUNCT cana-5770 38 5 s s PART cana-5770 38 6 ) ) PUNCT cana-5770 38 7 and and CCONJ cana-5770 38 8 usually usually ADV cana-5770 38 9 denoted denote VERB cana-5770 38 10 by by ADP cana-5770 38 11 < < X cana-5770 38 12 . . PUNCT cana-5770 39 1 if if SCONJ cana-5770 39 2 < < X cana-5770 39 3 is be AUX cana-5770 39 4 a a DET cana-5770 39 5 fs fs NOUN cana-5770 39 6 - - PUNCT cana-5770 39 7 subset subset NOUN cana-5770 39 8 of of ADP cana-5770 39 9 product product NOUN cana-5770 39 10 ( ( PUNCT cana-5770 39 11 γ,℘ γ,℘ ADV cana-5770 39 12 ) ) PUNCT cana-5770 39 13 x x X cana-5770 39 14 ( ( PUNCT cana-5770 39 15 γ,℘ γ,℘ ADV cana-5770 39 16 ) ) PUNCT cana-5770 39 17 then then ADV cana-5770 39 18 < < X cana-5770 39 19 is be AUX cana-5770 39 20 called call VERB cana-5770 39 21 a a DET cana-5770 39 22 fs fs NOUN cana-5770 39 23 - - PUNCT cana-5770 39 24 relation relation NOUN cana-5770 39 25 on on ADP cana-5770 39 26 ( ( PUNCT cana-5770 39 27 γ,℘ γ,℘ NUM cana-5770 39 28 ) ) PUNCT cana-5770 39 29 . . PUNCT cana-5770 40 1 inverse inverse NOUN cana-5770 40 2 of of ADP cana-5770 40 3 a a DET cana-5770 40 4 fs fs NOUN cana-5770 40 5 - - PUNCT cana-5770 40 6 relation relation NOUN cana-5770 40 7 < < X cana-5770 40 8 is be AUX cana-5770 40 9 defined define VERB cana-5770 40 10 by by ADP cana-5770 40 11 < < X cana-5770 40 12 −1ts −1ts PROPN cana-5770 40 13 = = PROPN cana-5770 40 14 < < X cana-5770 40 15 st st PROPN cana-5770 40 16 , , PUNCT cana-5770 40 17 ∀ ∀ X cana-5770 40 18 ( ( PUNCT cana-5770 40 19 t t PROPN cana-5770 40 20 , , PUNCT cana-5770 40 21 s s PART cana-5770 40 22 ) ) PUNCT cana-5770 40 23 ∈ ∈ PROPN cana-5770 40 24 ℘xs ℘xs PROPN cana-5770 40 25 . . PUNCT cana-5770 41 1 null null ADJ cana-5770 41 2 fuzzy fuzzy ADJ cana-5770 41 3 soft soft ADJ cana-5770 41 4 relation relation NOUN cana-5770 41 5 õ õ NOUN cana-5770 41 6 on on ADP cana-5770 41 7 ( ( PUNCT cana-5770 41 8 γ,℘ γ,℘ ADV cana-5770 41 9 ) ) PUNCT cana-5770 41 10 is be AUX cana-5770 41 11 defined define VERB cana-5770 41 12 as as ADP cana-5770 41 13 õts(z)=0 õts(z)=0 ADJ cana-5770 41 14 , , PUNCT cana-5770 41 15 ∀ ∀ NOUN cana-5770 41 16 ε ε NOUN cana-5770 41 17 ∈ ∈ PROPN cana-5770 41 18 x x X cana-5770 41 19 and and CCONJ cana-5770 41 20 t t PROPN cana-5770 41 21 , , PUNCT cana-5770 41 22 s s PART cana-5770 41 23 ∈ ∈ PROPN cana-5770 41 24 ℘. ℘. PROPN cana-5770 41 25 theorem theorem VERB cana-5770 41 26 3.2 3.2 NUM cana-5770 41 27 . . PUNCT cana-5770 42 1 let let VERB cana-5770 42 2 < < X cana-5770 42 3 be be AUX cana-5770 42 4 a a DET cana-5770 42 5 fs fs NOUN cana-5770 42 6 - - PUNCT cana-5770 42 7 relation relation NOUN cana-5770 42 8 from from ADP cana-5770 42 9 ( ( PUNCT cana-5770 42 10 γ,℘ γ,℘ ADV cana-5770 42 11 ) ) PUNCT cana-5770 42 12 to to ADP cana-5770 42 13 ( ( PUNCT cana-5770 42 14 ξ ξ PROPN cana-5770 42 15 , , PUNCT cana-5770 42 16 s s PART cana-5770 42 17 ) ) PUNCT cana-5770 42 18 . . PUNCT cana-5770 43 1 then then ADV cana-5770 43 2 the the DET cana-5770 43 3 fs fs NOUN cana-5770 43 4 - - PUNCT cana-5770 43 5 relation relation NOUN cana-5770 43 6 < < NOUN cana-5770 43 7 −1 −1 NOUN cana-5770 43 8 is be AUX cana-5770 43 9 from from ADP cana-5770 43 10 ( ( PUNCT cana-5770 43 11 ξ ξ PROPN cana-5770 43 12 , , PUNCT cana-5770 43 13 s s PART cana-5770 43 14 ) ) PUNCT cana-5770 43 15 to to PART cana-5770 43 16 ( ( PUNCT cana-5770 43 17 γ,℘ γ,℘ ADV cana-5770 43 18 ) ) PUNCT cana-5770 43 19 . . PUNCT cana-5770 44 1 proof proof NOUN cana-5770 44 2 fs f NOUN cana-5770 44 3 - - PUNCT cana-5770 44 4 relation relation NOUN cana-5770 44 5 < < X cana-5770 44 6 is be AUX cana-5770 44 7 from from ADP cana-5770 44 8 ( ( PUNCT cana-5770 44 9 γ,℘ γ,℘ ADV cana-5770 44 10 ) ) PUNCT cana-5770 44 11 to to ADP cana-5770 44 12 ( ( PUNCT cana-5770 44 13 ξ ξ PROPN cana-5770 44 14 , , PUNCT cana-5770 44 15 s s PART cana-5770 44 16 ) ) PUNCT cana-5770 45 1 = = AUX cana-5770 45 2 ⇒ ⇒ VERB cana-5770 45 3 < < X cana-5770 45 4 ⊆ ⊆ NUM cana-5770 45 5 ( ( PUNCT cana-5770 45 6 γ,℘ γ,℘ ADV cana-5770 45 7 ) ) PUNCT cana-5770 45 8 x x X cana-5770 45 9 ( ( PUNCT cana-5770 45 10 ξ ξ PROPN cana-5770 45 11 , , PUNCT cana-5770 45 12 s s NOUN cana-5770 45 13 ) ) PUNCT cana-5770 45 14 . . PUNCT cana-5770 46 1 < < X cana-5770 46 2 −1ts −1ts X cana-5770 46 3 = = X cana-5770 46 4 < < X cana-5770 46 5 st st PROPN cana-5770 46 6 ≤ ≤ PROPN cana-5770 46 7 min(ξs min(ξs NOUN cana-5770 46 8 , , PUNCT cana-5770 46 9 γt γt NOUN cana-5770 46 10 ) ) PUNCT cana-5770 46 11 , , PUNCT cana-5770 46 12 ∀ ∀ X cana-5770 46 13 ( ( PUNCT cana-5770 46 14 t t PROPN cana-5770 46 15 , , PUNCT cana-5770 46 16 s s PART cana-5770 46 17 ) ) PUNCT cana-5770 46 18 ∈ ∈ PROPN cana-5770 46 19 ℘xs ℘xs PROPN cana-5770 46 20 . . PUNCT cana-5770 47 1 hence hence ADV cana-5770 47 2 < < X cana-5770 47 3 −1 −1 NOUN cana-5770 47 4 is be AUX cana-5770 47 5 a a DET cana-5770 47 6 fs fs NOUN cana-5770 47 7 - - PUNCT cana-5770 47 8 relation relation NOUN cana-5770 47 9 from from ADP cana-5770 47 10 ( ( PUNCT cana-5770 47 11 ξ ξ PROPN cana-5770 47 12 , , PUNCT cana-5770 47 13 s s PART cana-5770 47 14 ) ) PUNCT cana-5770 47 15 to to PART cana-5770 47 16 ( ( PUNCT cana-5770 47 17 γ,℘ γ,℘ NUM cana-5770 47 18 ) ) PUNCT cana-5770 47 19 . . PUNCT cana-5770 48 1 definition definition NOUN cana-5770 48 2 3.3 3.3 NUM cana-5770 48 3 . . PUNCT cana-5770 49 1 union union NOUN cana-5770 49 2 and and CCONJ cana-5770 49 3 intersections intersection NOUN cana-5770 49 4 of of ADP cana-5770 49 5 fs f NOUN cana-5770 49 6 - - PUNCT cana-5770 49 7 relations relation NOUN cana-5770 49 8 < < NOUN cana-5770 49 9 1 1 NUM cana-5770 49 10 and and CCONJ cana-5770 49 11 < < X cana-5770 49 12 2 2 NUM cana-5770 49 13 defined define VERB cana-5770 49 14 on on ADP cana-5770 49 15 the the DET cana-5770 49 16 fs fs NOUN cana-5770 49 17 - - PUNCT cana-5770 49 18 set set VERB cana-5770 49 19 ( ( PUNCT cana-5770 49 20 γ,℘ γ,℘ ADV cana-5770 49 21 ) ) PUNCT cana-5770 49 22 are be AUX cana-5770 49 23 defined define VERB cana-5770 49 24 as as SCONJ cana-5770 49 25 follows follow VERB cana-5770 49 26 . . PUNCT cana-5770 50 1 ( ( PUNCT cana-5770 50 2 < < X cana-5770 50 3 1 1 NUM cana-5770 50 4 ∪ ∪ ADP cana-5770 50 5 < < NOUN cana-5770 50 6 2)ts(ε 2)ts(ε NUM cana-5770 50 7 ) ) PUNCT cana-5770 50 8 = = NOUN cana-5770 50 9 ( ( PUNCT cana-5770 50 10 < < X cana-5770 50 11 1)ts(ε 1)ts(ε NUM cana-5770 50 12 ) ) PUNCT cana-5770 50 13 ∨ ∨ NOUN cana-5770 50 14 ( ( PUNCT cana-5770 50 15 < < X cana-5770 50 16 2)ts(ε 2)ts(ε NUM cana-5770 50 17 ) ) PUNCT cana-5770 50 18 ( ( PUNCT cana-5770 50 19 < < X cana-5770 50 20 1 1 NUM cana-5770 50 21 ∩ ∩ NOUN cana-5770 50 22 < < NOUN cana-5770 50 23 2)ts(ε 2)ts(ε NUM cana-5770 50 24 ) ) PUNCT cana-5770 50 25 = = NOUN cana-5770 50 26 ( ( PUNCT cana-5770 50 27 < < X cana-5770 50 28 1)ts(ε 1)ts(ε NUM cana-5770 50 29 ) ) PUNCT cana-5770 50 30 ∧ ∧ NOUN cana-5770 50 31 ( ( PUNCT cana-5770 50 32 < < X cana-5770 50 33 2)ts(ε 2)ts(ε NUM cana-5770 50 34 ) ) PUNCT cana-5770 50 35 , , PUNCT cana-5770 50 36 ∀ ∀ PUNCT cana-5770 50 37 ε ε PROPN cana-5770 50 38 ∈ ∈ PROPN cana-5770 50 39 z z PROPN cana-5770 50 40 and and CCONJ cana-5770 50 41 ∀ ∀ NUM cana-5770 50 42 ( ( PUNCT cana-5770 50 43 t t PROPN cana-5770 50 44 , , PUNCT cana-5770 50 45 s s PART cana-5770 50 46 ) ) PUNCT cana-5770 50 47 ∈ ∈ PROPN cana-5770 50 48 ℘ ℘ PROPN cana-5770 50 49 x x SYM cana-5770 50 50 ℘. ℘. PROPN cana-5770 50 51 the the DET cana-5770 50 52 partial partial ADJ cana-5770 50 53 ordering order VERB cana-5770 50 54 ≤ ≤ NOUN cana-5770 50 55 in in ADP cana-5770 50 56 the the DET cana-5770 50 57 set set NOUN cana-5770 50 58 of of ADP cana-5770 50 59 all all DET cana-5770 50 60 fs f NOUN cana-5770 50 61 - - PUNCT cana-5770 50 62 relations relation NOUN cana-5770 50 63 on on ADP cana-5770 50 64 ( ( PUNCT cana-5770 50 65 γ,℘ γ,℘ ADV cana-5770 50 66 ) ) PUNCT cana-5770 50 67 denoted denote VERB cana-5770 50 68 as as ADP cana-5770 50 69 < < X cana-5770 50 70 ( ( PUNCT cana-5770 50 71 γ,℘ γ,℘ ADV cana-5770 50 72 ) ) PUNCT cana-5770 50 73 is be AUX cana-5770 50 74 given give VERB cana-5770 50 75 by by ADP cana-5770 50 76 , , PUNCT cana-5770 50 77 if if SCONJ cana-5770 50 78 < < X cana-5770 50 79 1 1 NUM cana-5770 50 80 and and CCONJ cana-5770 50 81 < < X cana-5770 50 82 2 2 NUM cana-5770 50 83 ∈ ∈ NOUN cana-5770 50 84 < < X cana-5770 50 85 ( ( PUNCT cana-5770 50 86 γ,℘ γ,℘ ADV cana-5770 50 87 ) ) PUNCT cana-5770 50 88 then then ADV cana-5770 50 89 < < X cana-5770 50 90 1 1 NUM cana-5770 50 91 ≤ ≤ NUM cana-5770 50 92 < < X cana-5770 50 93 2 2 NUM cana-5770 50 94 iff iff NOUN cana-5770 50 95 ( ( PUNCT cana-5770 50 96 < < X cana-5770 50 97 1)ts 1)ts PROPN cana-5770 50 98 ( ( PUNCT cana-5770 50 99 ε ε PROPN cana-5770 50 100 ) ) PUNCT cana-5770 50 101 ≤ ≤ NOUN cana-5770 50 102 ( ( PUNCT cana-5770 50 103 < < NOUN cana-5770 50 104 2)ts(ε 2)ts(ε NUM cana-5770 50 105 ) ) PUNCT cana-5770 50 106 , , PUNCT cana-5770 50 107 ∀ ∀ PUNCT cana-5770 50 108 ε ε PROPN cana-5770 50 109 ∈ ∈ PROPN cana-5770 50 110 z z PROPN cana-5770 50 111 and and CCONJ cana-5770 50 112 ∀ ∀ NUM cana-5770 50 113 ( ( PUNCT cana-5770 50 114 t t PROPN cana-5770 50 115 , , PUNCT cana-5770 50 116 s s PART cana-5770 50 117 ) ) PUNCT cana-5770 50 118 ∈ ∈ PROPN cana-5770 50 119 ℘ ℘ PROPN cana-5770 50 120 x x SYM cana-5770 50 121 ℘. ℘. PROPN cana-5770 50 122 identity identity NOUN cana-5770 50 123 fuzzy fuzzy ADJ cana-5770 50 124 soft soft ADJ cana-5770 50 125 relation relation NOUN cana-5770 50 126 ĩ ĩ PROPN cana-5770 50 127 on on ADP cana-5770 50 128 ( ( PUNCT cana-5770 50 129 γ,℘ γ,℘ ADV cana-5770 50 130 ) ) PUNCT cana-5770 50 131 is be AUX cana-5770 50 132 defined define VERB cana-5770 50 133 for for ADP cana-5770 50 134 any any DET cana-5770 50 135 t t NOUN cana-5770 50 136 , , PUNCT cana-5770 50 137 m m NOUN cana-5770 50 138 ∈ ∈ NOUN cana-5770 50 139 ℘ ℘ PROPN cana-5770 50 140 as as ADP cana-5770 50 141 ĩtm ĩtm NOUN cana-5770 50 142 = = PUNCT cana-5770 50 143 { { PUNCT cana-5770 50 144 0 0 NUM cana-5770 51 1 if if SCONJ cana-5770 51 2 t t PROPN cana-5770 51 3 6= 6= PROPN cana-5770 51 4 m m PROPN cana-5770 51 5 1 1 NUM cana-5770 51 6 if if SCONJ cana-5770 51 7 t t NOUN cana-5770 51 8 = = PUNCT cana-5770 51 9 m m PROPN cana-5770 51 10 definition definition NOUN cana-5770 51 11 3.4 3.4 NUM cana-5770 51 12 . . PUNCT cana-5770 52 1 consider consider VERB cana-5770 52 2 two two NUM cana-5770 52 3 fs f NOUN cana-5770 52 4 - - PUNCT cana-5770 52 5 relations relation NOUN cana-5770 52 6 < < NOUN cana-5770 52 7 1 1 NUM cana-5770 52 8 and and CCONJ cana-5770 52 9 < < X cana-5770 52 10 2 2 NUM cana-5770 52 11 from from ADP cana-5770 52 12 ( ( PUNCT cana-5770 52 13 γ,℘ γ,℘ ADV cana-5770 52 14 ) ) PUNCT cana-5770 52 15 to to ADP cana-5770 52 16 ( ( PUNCT cana-5770 52 17 ξ ξ PROPN cana-5770 52 18 , , PUNCT cana-5770 52 19 s s PART cana-5770 52 20 ) ) PUNCT cana-5770 52 21 and and CCONJ cana-5770 52 22 ( ( PUNCT cana-5770 52 23 ξ ξ X cana-5770 52 24 , , PUNCT cana-5770 52 25 s s PART cana-5770 52 26 ) ) PUNCT cana-5770 52 27 to to ADP cana-5770 52 28 ( ( PUNCT cana-5770 52 29 ζ ζ NOUN cana-5770 52 30 , , PUNCT cana-5770 52 31 m m NOUN cana-5770 52 32 ) ) PUNCT cana-5770 52 33 respectively respectively ADV cana-5770 52 34 . . PUNCT cana-5770 53 1 composition composition NOUN cana-5770 53 2 of of ADP cana-5770 53 3 fs f NOUN cana-5770 53 4 - - PUNCT cana-5770 53 5 relations relation NOUN cana-5770 53 6 < < NOUN cana-5770 53 7 1 1 NUM cana-5770 53 8 and and CCONJ cana-5770 53 9 < < X cana-5770 53 10 2 2 NUM cana-5770 53 11 denoted denote VERB cana-5770 53 12 by by ADP cana-5770 53 13 < < X cana-5770 53 14 1 1 NUM cana-5770 53 15 ◦ ◦ NOUN cana-5770 53 16 <2 <2 NOUN cana-5770 53 17 is be AUX cana-5770 53 18 a a DET cana-5770 53 19 fsrelation fsrelation NOUN cana-5770 53 20 from from ADP cana-5770 53 21 ( ( PUNCT cana-5770 53 22 γ,℘ γ,℘ ADV cana-5770 53 23 ) ) PUNCT cana-5770 53 24 to to ADP cana-5770 53 25 ( ( PUNCT cana-5770 53 26 ζ ζ NOUN cana-5770 53 27 , , PUNCT cana-5770 53 28 m m PRON cana-5770 53 29 ) ) PUNCT cana-5770 53 30 defined define VERB cana-5770 53 31 as as ADP cana-5770 53 32 ( ( PUNCT cana-5770 53 33 < < NOUN cana-5770 53 34 1 1 NUM cana-5770 53 35 ◦ ◦ NOUN cana-5770 53 36 <2)tm <2)tm ADJ cana-5770 53 37 = = SYM cana-5770 53 38 ∨ ∨ NUM cana-5770 53 39 s∈s s∈s NOUN cana-5770 53 40 min((<1)ts,(<2)sm min((<1)ts,(<2)sm PROPN cana-5770 53 41 ) ) PUNCT cana-5770 53 42 where where SCONJ cana-5770 53 43 ( ( PUNCT cana-5770 53 44 t t PROPN cana-5770 53 45 , , PUNCT cana-5770 53 46 s s PART cana-5770 53 47 ) ) PUNCT cana-5770 53 48 ∈ ∈ PROPN cana-5770 53 49 ℘xs ℘xs PROPN cana-5770 53 50 and and CCONJ cana-5770 53 51 ( ( PUNCT cana-5770 53 52 s s X cana-5770 53 53 , , PUNCT cana-5770 53 54 m m NOUN cana-5770 53 55 ) ) PUNCT cana-5770 53 56 ∈ ∈ PROPN cana-5770 53 57 sxm sxm PROPN cana-5770 53 58 . . PUNCT cana-5770 54 1 theorem theorem VERB cana-5770 54 2 3.5 3.5 NUM cana-5770 54 3 . . PUNCT cana-5770 55 1 if if SCONJ cana-5770 55 2 ĩ ĩ PROPN cana-5770 55 3 and and CCONJ cana-5770 55 4 0̃ 0̃ NOUN cana-5770 55 5 be be AUX cana-5770 55 6 the the DET cana-5770 55 7 whole whole ADJ cana-5770 55 8 and and CCONJ cana-5770 55 9 null null ADJ cana-5770 55 10 fuzzy fuzzy ADJ cana-5770 55 11 soft soft ADJ cana-5770 55 12 relations relation NOUN cana-5770 55 13 respectively respectively ADV cana-5770 55 14 on on ADP cana-5770 55 15 ( ( PUNCT cana-5770 55 16 γ,℘ γ,℘ ADV cana-5770 55 17 ) ) PUNCT cana-5770 55 18 over over ADP cana-5770 55 19 z z NOUN cana-5770 55 20 then then ADV cana-5770 55 21 1 1 X cana-5770 55 22 ) ) PUNCT cana-5770 55 23 ĩ−1 ĩ−1 PROPN cana-5770 55 24 = = SYM cana-5770 55 25 ĩ ĩ PROPN cana-5770 55 26 2 2 NUM cana-5770 55 27 ) ) PUNCT cana-5770 55 28 0̃−1 0̃−1 NUM cana-5770 56 1 = = SYM cana-5770 56 2 0̃ 0̃ NOUN cana-5770 56 3 3 3 NUM cana-5770 56 4 ) ) PUNCT cana-5770 56 5 ĩ ĩ NOUN cana-5770 56 6 ◦ ◦ VERB cana-5770 56 7 ĩ ĩ NOUN cana-5770 56 8 = = PUNCT cana-5770 56 9 ĩ ĩ PROPN cana-5770 56 10 4 4 NUM cana-5770 56 11 ) ) PUNCT cana-5770 56 12 0̃ 0̃ NOUN cana-5770 56 13 ◦ ◦ NOUN cana-5770 56 14 0̃ 0̃ NOUN cana-5770 56 15 = = SYM cana-5770 56 16 0 0 NUM cana-5770 56 17 proof proof NOUN cana-5770 56 18 proof proof NOUN cana-5770 56 19 of of ADP cana-5770 56 20 1 1 NUM cana-5770 56 21 and and CCONJ cana-5770 56 22 2 2 NUM cana-5770 56 23 follows follow VERB cana-5770 56 24 obviously obviously ADV cana-5770 56 25 . . PUNCT cana-5770 57 1 3 3 X cana-5770 57 2 ) ) PUNCT cana-5770 57 3 consider consider VERB cana-5770 57 4 the the DET cana-5770 57 5 parameters parameter NOUN cana-5770 57 6 t t PROPN cana-5770 57 7 and and CCONJ cana-5770 57 8 s s PROPN cana-5770 57 9 ∈ ∈ NOUN cana-5770 57 10 ℘ ℘ PROPN cana-5770 57 11 such such ADJ cana-5770 57 12 that that DET cana-5770 57 13 t t NOUN cana-5770 57 14 = = SYM cana-5770 57 15 s s PROPN cana-5770 57 16 , , PUNCT cana-5770 57 17 ( ( PUNCT cana-5770 57 18 ĩ ĩ NOUN cana-5770 57 19 ◦ ◦ VERB cana-5770 57 20 ĩ)tt ĩ)tt NOUN cana-5770 57 21 = = SYM cana-5770 57 22 ∨ ∨ PROPN cana-5770 57 23 m∈℘ m∈℘ PROPN cana-5770 57 24 ( ( PUNCT cana-5770 57 25 min(ĩ min(ĩ NOUN cana-5770 57 26 tm tm PROPN cana-5770 57 27 , , PUNCT cana-5770 57 28 ĩmt ĩmt NOUN cana-5770 57 29 ) ) PUNCT cana-5770 57 30 ) ) PUNCT cana-5770 58 1 = = PUNCT cana-5770 58 2 ∨ ∨ NUM cana-5770 58 3 m6 m6 PROPN cana-5770 58 4 = = PROPN cana-5770 58 5 t t PROPN cana-5770 58 6 ( ( PUNCT cana-5770 58 7 min(ĩ min(ĩ NOUN cana-5770 58 8 tm tm PROPN cana-5770 58 9 , , PUNCT cana-5770 58 10 ĩmt ĩmt NOUN cana-5770 58 11 ) ) PUNCT cana-5770 58 12 ) ) PUNCT cana-5770 58 13 ∨ ∨ PROPN cana-5770 58 14 min(ĩ min(ĩ PROPN cana-5770 58 15 tt tt PROPN cana-5770 58 16 , , PUNCT cana-5770 58 17 ĩ ĩ PROPN cana-5770 58 18 tt tt PROPN cana-5770 58 19 ) ) PUNCT cana-5770 58 20 = = PUNCT cana-5770 58 21 max(0,1 max(0,1 PROPN cana-5770 58 22 ) ) PUNCT cana-5770 58 23 = = SYM cana-5770 58 24 1 1 NUM cana-5770 58 25 for for ADP cana-5770 58 26 the the DET cana-5770 58 27 parameters parameter NOUN cana-5770 58 28 t t PROPN cana-5770 58 29 , , PUNCT cana-5770 58 30 s s PART cana-5770 58 31 ∈ ∈ NOUN cana-5770 58 32 ℘ ℘ PROPN cana-5770 58 33 , , PUNCT cana-5770 58 34 with with ADP cana-5770 58 35 t t PROPN cana-5770 58 36 6= 6= NUM cana-5770 58 37 s s PROPN cana-5770 58 38 , , PUNCT cana-5770 58 39 ( ( PUNCT cana-5770 58 40 ĩ ĩ PROPN cana-5770 58 41 ◦ ◦ VERB cana-5770 58 42 ĩ)ts ĩ)ts PROPN cana-5770 58 43 = = PUNCT cana-5770 58 44 ∨ ∨ NUM cana-5770 58 45 m∈℘ m∈℘ PROPN cana-5770 58 46 ( ( PUNCT cana-5770 58 47 min(ĩ min(ĩ NOUN cana-5770 58 48 tm tm PROPN cana-5770 58 49 , , PUNCT cana-5770 58 50 ĩms ĩms PROPN cana-5770 58 51 ) ) PUNCT cana-5770 58 52 ) ) PUNCT cana-5770 58 53 communications communication NOUN cana-5770 58 54 on on ADP cana-5770 58 55 applied apply VERB cana-5770 58 56 nonlinear nonlinear ADJ cana-5770 58 57 analysis analysis NOUN cana-5770 58 58 issn issn NOUN cana-5770 58 59 : : PUNCT cana-5770 58 60 1074 1074 NUM cana-5770 58 61 - - PUNCT cana-5770 58 62 133x 133x NUM cana-5770 58 63 vol vol NOUN cana-5770 58 64 32 32 NUM cana-5770 59 1 no no NOUN cana-5770 59 2 . . PUNCT cana-5770 60 1 9s 9s NUM cana-5770 60 2 ( ( PUNCT cana-5770 60 3 2025 2025 NUM cana-5770 60 4 ) ) PUNCT cana-5770 60 5 https://internationalpubls.com https://internationalpubls.com X cana-5770 60 6 3197 3197 NUM cana-5770 60 7 anju anju PROPN cana-5770 60 8 rajath rajath NOUN cana-5770 60 9 pencil pencil NOUN cana-5770 60 10 = = PROPN cana-5770 60 11 ∨ ∨ NUM cana-5770 60 12 m6 m6 PROPN cana-5770 60 13 = = PROPN cana-5770 60 14 t t PROPN cana-5770 60 15 , , PUNCT cana-5770 60 16 s s PART cana-5770 60 17 ( ( PUNCT cana-5770 60 18 min(ĩ min(ĩ NOUN cana-5770 60 19 tm tm PROPN cana-5770 60 20 , , PUNCT cana-5770 60 21 ĩms ĩms PROPN cana-5770 60 22 ) ) PUNCT cana-5770 60 23 ) ) PUNCT cana-5770 61 1 ∨ ∨ PROPN cana-5770 61 2 min(ĩ min(ĩ PROPN cana-5770 61 3 tt tt PROPN cana-5770 61 4 , , PUNCT cana-5770 61 5 ĩ ĩ PROPN cana-5770 61 6 ts ts NOUN cana-5770 61 7 ) ) PUNCT cana-5770 61 8 ∨ ∨ NUM cana-5770 61 9 min(ĩ min(ĩ NOUN cana-5770 61 10 ts ts NOUN cana-5770 61 11 , , PUNCT cana-5770 61 12 ĩss ĩs NOUN cana-5770 61 13 ) ) PUNCT cana-5770 61 14 = = PUNCT cana-5770 61 15 0 0 NUM cana-5770 61 16 ∨ ∨ NUM cana-5770 61 17 min(1,ĩ min(1,ĩ PROPN cana-5770 61 18 ts ts NOUN cana-5770 61 19 ) ) PUNCT cana-5770 61 20 ∨ ∨ PROPN cana-5770 61 21 min(ĩ min(ĩ NOUN cana-5770 61 22 ts,1 ts,1 PROPN cana-5770 61 23 ) ) PUNCT cana-5770 62 1 = = SYM cana-5770 62 2 0 0 NUM cana-5770 62 3 4 4 X cana-5770 62 4 ) ) PUNCT cana-5770 62 5 let let VERB cana-5770 62 6 parameters parameter NOUN cana-5770 62 7 t t PROPN cana-5770 62 8 , , PUNCT cana-5770 62 9 s s PART cana-5770 62 10 ∈ ∈ NOUN cana-5770 62 11 ℘ ℘ PROPN cana-5770 62 12 , , PUNCT cana-5770 62 13 ( ( PUNCT cana-5770 62 14 0̃ 0̃ NOUN cana-5770 62 15 ◦ ◦ NOUN cana-5770 62 16 0̃)ts 0̃)ts X cana-5770 62 17 = = PUNCT cana-5770 62 18 ∨ ∨ NUM cana-5770 62 19 m∈℘ m∈℘ PROPN cana-5770 62 20 ( ( PUNCT cana-5770 62 21 min(0̃tm,0̃ms min(0̃tm,0̃ms PROPN cana-5770 62 22 ) ) PUNCT cana-5770 62 23 ) ) PUNCT cana-5770 63 1 = = PUNCT cana-5770 64 1 ∨ ∨ NUM cana-5770 64 2 m∈℘ m∈℘ PROPN cana-5770 64 3 min(0,0 min(0,0 PROPN cana-5770 64 4 ) ) PUNCT cana-5770 64 5 = = SYM cana-5770 64 6 0 0 PUNCT cana-5770 64 7 = = SYM cana-5770 64 8 0̃ts 0̃ts NOUN cana-5770 64 9 theorem theorem VERB cana-5770 64 10 3.6 3.6 NUM cana-5770 64 11 . . PUNCT cana-5770 65 1 let let VERB cana-5770 65 2 s s PROPN cana-5770 65 3 , , PUNCT cana-5770 65 4 t t PROPN cana-5770 65 5 and and CCONJ cana-5770 65 6 < < AUX cana-5770 65 7 be be AUX cana-5770 65 8 the the DET cana-5770 65 9 fs f NOUN cana-5770 65 10 - - PUNCT cana-5770 65 11 relations relation NOUN cana-5770 65 12 defined define VERB cana-5770 65 13 on on ADP cana-5770 65 14 the the DET cana-5770 65 15 fs fs NOUN cana-5770 65 16 - - PUNCT cana-5770 65 17 set set VERB cana-5770 65 18 ( ( PUNCT cana-5770 65 19 γ,℘ γ,℘ ADV cana-5770 65 20 ) ) PUNCT cana-5770 65 21 then then ADV cana-5770 65 22 1 1 X cana-5770 65 23 ) ) PUNCT cana-5770 65 24 ( ( PUNCT cana-5770 65 25 s−1)−1 s−1)−1 NOUN cana-5770 65 26 = = SYM cana-5770 65 27 s s PART cana-5770 65 28 2 2 NUM cana-5770 65 29 ) ) PUNCT cana-5770 65 30 ( ( PUNCT cana-5770 65 31 sc)c sc)c NOUN cana-5770 65 32 = = SYM cana-5770 65 33 s s NOUN cana-5770 65 34 3 3 NUM cana-5770 65 35 ) ) PUNCT cana-5770 65 36 ( ( PUNCT cana-5770 65 37 sc)−1 sc)−1 SYM cana-5770 65 38 = = SYM cana-5770 65 39 ( ( PUNCT cana-5770 65 40 s−1)c s−1)c PROPN cana-5770 65 41 4 4 NUM cana-5770 65 42 ) ) PUNCT cana-5770 65 43 s s PART cana-5770 65 44 ⊆ ⊆ NUM cana-5770 65 45 t t NOUN cana-5770 65 46 = = NOUN cana-5770 65 47 ⇒ ⇒ VERB cana-5770 65 48 s−1 s−1 PROPN cana-5770 65 49 ⊆ ⊆ NUM cana-5770 65 50 t t NOUN cana-5770 65 51 −1 −1 NOUN cana-5770 65 52 5 5 NUM cana-5770 65 53 ) ) PUNCT cana-5770 65 54 ( ( PUNCT cana-5770 65 55 s s X cana-5770 65 56 ◦ ◦ NOUN cana-5770 65 57 t t PROPN cana-5770 65 58 ) ) PUNCT cana-5770 65 59 −1 −1 NOUN cana-5770 66 1 = = SYM cana-5770 66 2 t t NOUN cana-5770 66 3 −1 −1 NOUN cana-5770 66 4 ◦ ◦ NOUN cana-5770 66 5 s−1 s−1 PROPN cana-5770 66 6 6 6 NUM cana-5770 66 7 ) ) PUNCT cana-5770 66 8 s s PART cana-5770 66 9 ⊆ ⊆ NUM cana-5770 66 10 t t NOUN cana-5770 66 11 = = PRON cana-5770 66 12 ⇒ ⇒ NOUN cana-5770 66 13 s s PART cana-5770 66 14 ◦ ◦ NOUN cana-5770 66 15 < < X cana-5770 66 16 ⊆ ⊆ NUM cana-5770 66 17 t t NOUN cana-5770 66 18 ◦ ◦ NOUN cana-5770 66 19 < < X cana-5770 66 20 7)(s 7)(s NUM cana-5770 66 21 ◦ ◦ NOUN cana-5770 66 22 t t NOUN cana-5770 66 23 ) ) PUNCT cana-5770 67 1 ◦ ◦ VERB cana-5770 67 2 < < X cana-5770 67 3 = = SYM cana-5770 67 4 s s PART cana-5770 67 5 ◦ ◦ NOUN cana-5770 67 6 ( ( PUNCT cana-5770 67 7 t t NOUN cana-5770 67 8 ◦ ◦ NOUN cana-5770 67 9 < < X cana-5770 67 10 ) ) PUNCT cana-5770 67 11 8)(s 8)(s NOUN cana-5770 67 12 ∪ ∪ ADP cana-5770 67 13 t t PROPN cana-5770 67 14 ) ) PUNCT cana-5770 67 15 −1 −1 NOUN cana-5770 68 1 = = PUNCT cana-5770 68 2 s−1 s−1 PROPN cana-5770 68 3 ∪ ∪ VERB cana-5770 68 4 t t NOUN cana-5770 68 5 −1 −1 NOUN cana-5770 68 6 and and CCONJ cana-5770 68 7 ( ( PUNCT cana-5770 68 8 s s X cana-5770 68 9 ∩ ∩ ADJ cana-5770 68 10 t t NOUN cana-5770 68 11 ) ) PUNCT cana-5770 68 12 −1 −1 NOUN cana-5770 69 1 = = SYM cana-5770 70 1 s−1 s−1 NOUN cana-5770 70 2 ∩ ∩ NOUN cana-5770 70 3 t t NOUN cana-5770 70 4 −1 −1 NOUN cana-5770 70 5 9)(s 9)(s NUM cana-5770 70 6 ∪ ∪ ADP cana-5770 70 7 t t NOUN cana-5770 70 8 ) ) PUNCT cana-5770 70 9 c c NOUN cana-5770 70 10 = = SYM cana-5770 70 11 sc sc PROPN cana-5770 70 12 ∩ ∩ PROPN cana-5770 70 13 t t PROPN cana-5770 70 14 c c PROPN cana-5770 70 15 and and CCONJ cana-5770 70 16 ( ( PUNCT cana-5770 70 17 s s NOUN cana-5770 70 18 ∩ ∩ ADJ cana-5770 70 19 t t NOUN cana-5770 70 20 ) ) PUNCT cana-5770 70 21 c c NOUN cana-5770 70 22 = = PUNCT cana-5770 70 23 sc sc PROPN cana-5770 70 24 ∪ ∪ PROPN cana-5770 70 25 t t PROPN cana-5770 70 26 c. c. NOUN cana-5770 70 27 proof proof NOUN cana-5770 70 28 1)using 1)use VERB cana-5770 70 29 the the DET cana-5770 70 30 definition definition NOUN cana-5770 70 31 for for ADP cana-5770 70 32 inverse inverse NOUN cana-5770 70 33 of of ADP cana-5770 70 34 fs fs NOUN cana-5770 70 35 - - PUNCT cana-5770 70 36 relation relation NOUN cana-5770 70 37 ( ( PUNCT cana-5770 70 38 s−1)−1ts(ε s−1)−1ts(ε NOUN cana-5770 70 39 ) ) PUNCT cana-5770 70 40 is be AUX cana-5770 70 41 same same ADJ cana-5770 70 42 as as ADP cana-5770 70 43 ( ( PUNCT cana-5770 70 44 s−1)st(ε s−1)st(ε PROPN cana-5770 70 45 ) ) PUNCT cana-5770 70 46 which which PRON cana-5770 70 47 is be AUX cana-5770 70 48 equal equal ADJ cana-5770 70 49 to to ADP cana-5770 70 50 ( ( PUNCT cana-5770 70 51 s)ts(ε s)ts(ε NOUN cana-5770 70 52 ) ) PUNCT cana-5770 70 53 , , PUNCT cana-5770 70 54 ∀ ∀ X cana-5770 70 55 ε ε PROPN cana-5770 70 56 ∈z ∈z PROPN cana-5770 70 57 and and CCONJ cana-5770 70 58 t t PROPN cana-5770 70 59 , , PUNCT cana-5770 70 60 s s PART cana-5770 70 61 ∈ ∈ PROPN cana-5770 70 62 ℘ ℘ PROPN cana-5770 70 63 2)(sc)cts(ε 2)(sc)cts(ε NOUN cana-5770 70 64 ) ) PUNCT cana-5770 71 1 = = SYM cana-5770 71 2 1(sc)ts(ε 1(sc)ts(ε NUM cana-5770 71 3 ) ) PUNCT cana-5770 71 4 = = SYM cana-5770 71 5 1-(1sts(ε 1-(1sts(ε NUM cana-5770 71 6 ) ) PUNCT cana-5770 71 7 ) ) PUNCT cana-5770 72 1 = = SYM cana-5770 72 2 sts(ε sts(ε NOUN cana-5770 72 3 ) ) PUNCT cana-5770 72 4 , , PUNCT cana-5770 72 5 ∀ ∀ PUNCT cana-5770 72 6 ε ε PROPN cana-5770 72 7 ∈ ∈ PROPN cana-5770 72 8 z z PROPN cana-5770 72 9 and and CCONJ cana-5770 72 10 t t PROPN cana-5770 72 11 , , PUNCT cana-5770 72 12 s s PART cana-5770 72 13 ∈ ∈ PROPN cana-5770 72 14 ℘ ℘ PROPN cana-5770 72 15 3 3 NUM cana-5770 72 16 ) ) PUNCT cana-5770 72 17 ∀ ∀ PUNCT cana-5770 72 18 ε ε PROPN cana-5770 72 19 ∈ ∈ PROPN cana-5770 72 20 z z PROPN cana-5770 72 21 and and CCONJ cana-5770 72 22 t t PROPN cana-5770 72 23 , , PUNCT cana-5770 72 24 s s PART cana-5770 72 25 ∈ ∈ NOUN cana-5770 72 26 ℘ ℘ PROPN cana-5770 72 27 , , PUNCT cana-5770 72 28 ( ( PUNCT cana-5770 72 29 sc)−1ts(ε sc)−1ts(ε NOUN cana-5770 72 30 ) ) PUNCT cana-5770 72 31 = = PUNCT cana-5770 73 1 ( ( PUNCT cana-5770 73 2 sc)st(ε sc)st(ε PROPN cana-5770 73 3 ) ) PUNCT cana-5770 73 4 = = NOUN cana-5770 73 5 1 1 NUM cana-5770 73 6 sst(ε sst(ε NOUN cana-5770 73 7 ) ) PUNCT cana-5770 73 8 , , PUNCT cana-5770 73 9 ( ( PUNCT cana-5770 73 10 s−1)cts(ε s−1)cts(ε PROPN cana-5770 73 11 ) ) PUNCT cana-5770 73 12 = = SYM cana-5770 73 13 1 1 NUM cana-5770 73 14 ( ( PUNCT cana-5770 73 15 s−1)ts(ε s−1)ts(ε NOUN cana-5770 73 16 ) ) PUNCT cana-5770 73 17 = = SYM cana-5770 73 18 1sst(ε 1sst(ε NUM cana-5770 73 19 ) ) PUNCT cana-5770 73 20 , , PUNCT cana-5770 73 21 = = NOUN cana-5770 73 22 ⇒ ⇒ NOUN cana-5770 73 23 ( ( PUNCT cana-5770 73 24 sc)−1 sc)−1 SYM cana-5770 73 25 = = SYM cana-5770 73 26 ( ( PUNCT cana-5770 73 27 s−1)c s−1)c PROPN cana-5770 73 28 4)using 4)using NUM cana-5770 73 29 definition definition NOUN cana-5770 73 30 3.1 3.1 NUM cana-5770 73 31 we we PRON cana-5770 73 32 have have VERB cana-5770 73 33 ( ( PUNCT cana-5770 73 34 s−1)ts(ε s−1)ts(ε NOUN cana-5770 73 35 ) ) PUNCT cana-5770 73 36 is be AUX cana-5770 73 37 equal equal ADJ cana-5770 73 38 to to ADP cana-5770 73 39 ( ( PUNCT cana-5770 73 40 s)ts(ε s)ts(ε NOUN cana-5770 73 41 ) ) PUNCT cana-5770 73 42 which which PRON cana-5770 73 43 is be AUX cana-5770 73 44 less less ADJ cana-5770 73 45 than than ADP cana-5770 73 46 ( ( PUNCT cana-5770 73 47 t t NOUN cana-5770 73 48 ) ) PUNCT cana-5770 73 49 ts(ε ts(ε NUM cana-5770 73 50 ) ) PUNCT cana-5770 73 51 . . PUNCT cana-5770 74 1 using use VERB cana-5770 74 2 the the DET cana-5770 74 3 similarity similarity NOUN cana-5770 74 4 property property NOUN cana-5770 74 5 ( ( PUNCT cana-5770 74 6 t t NOUN cana-5770 74 7 ) ) PUNCT cana-5770 74 8 ts(ε ts(ε PUNCT cana-5770 74 9 ) ) PUNCT cana-5770 74 10 = = SYM cana-5770 74 11 ( ( PUNCT cana-5770 74 12 t t PROPN cana-5770 74 13 −1)ts(ε −1)ts(ε PROPN cana-5770 74 14 ) ) PUNCT cana-5770 74 15 , , PUNCT cana-5770 74 16 ∀ ∀ PUNCT cana-5770 74 17 ε ε PROPN cana-5770 74 18 ∈ ∈ PROPN cana-5770 74 19 z z PROPN cana-5770 74 20 and and CCONJ cana-5770 74 21 t t PROPN cana-5770 74 22 , , PUNCT cana-5770 74 23 s s AUX cana-5770 74 24 ∈ ∈ NOUN cana-5770 74 25 ℘ ℘ NOUN cana-5770 74 26 = = SYM cana-5770 74 27 ⇒ ⇒ VERB cana-5770 74 28 s−1 s−1 PROPN cana-5770 74 29 ⊆ ⊆ NUM cana-5770 74 30 t t NOUN cana-5770 74 31 −1 −1 NOUN cana-5770 74 32 5 5 NUM cana-5770 74 33 ) ) PUNCT cana-5770 74 34 ( ( PUNCT cana-5770 74 35 t t NOUN cana-5770 74 36 −1 −1 NOUN cana-5770 74 37 ◦ ◦ NOUN cana-5770 74 38 s−1)ts(ε s−1)ts(ε NOUN cana-5770 74 39 ) ) PUNCT cana-5770 74 40 = = PUNCT cana-5770 74 41 ∨ ∨ NUM cana-5770 74 42 m∈℘ m∈℘ PROPN cana-5770 74 43 ( ( PUNCT cana-5770 74 44 min(t min(t PROPN cana-5770 74 45 −1tm(ε −1tm(ε PROPN cana-5770 74 46 ) ) PUNCT cana-5770 74 47 , , PUNCT cana-5770 74 48 s−1ms(ε s−1ms(ε NOUN cana-5770 74 49 ) ) PUNCT cana-5770 74 50 ) ) PUNCT cana-5770 74 51 ) ) PUNCT cana-5770 75 1 = = PUNCT cana-5770 75 2 ∨ ∨ NUM cana-5770 75 3 m∈℘ m∈℘ PROPN cana-5770 75 4 ( ( PUNCT cana-5770 75 5 min(t min(t PROPN cana-5770 75 6 mt(ε mt(ε PROPN cana-5770 75 7 ) ) PUNCT cana-5770 75 8 , , PUNCT cana-5770 75 9 ssm(ε ssm(ε PROPN cana-5770 75 10 ) ) PUNCT cana-5770 75 11 ) ) PUNCT cana-5770 75 12 ) ) PUNCT cana-5770 76 1 = = PUNCT cana-5770 76 2 ∨ ∨ NUM cana-5770 76 3 m∈℘ m∈℘ PROPN cana-5770 76 4 ( ( PUNCT cana-5770 76 5 min(ssm(ε min(ssm(ε PROPN cana-5770 76 6 ) ) PUNCT cana-5770 76 7 , , PUNCT cana-5770 76 8 t t PROPN cana-5770 76 9 mt(ε mt(ε PROPN cana-5770 76 10 ) ) PUNCT cana-5770 76 11 ) ) PUNCT cana-5770 76 12 ) ) PUNCT cana-5770 77 1 = = PUNCT cana-5770 78 1 ( ( PUNCT cana-5770 78 2 s s NOUN cana-5770 78 3 ◦ ◦ NOUN cana-5770 78 4 t t PROPN cana-5770 78 5 ) ) PUNCT cana-5770 79 1 st(ε st(ε ADP cana-5770 79 2 ) ) PUNCT cana-5770 80 1 = = PUNCT cana-5770 80 2 ( ( PUNCT cana-5770 80 3 s s PROPN cana-5770 80 4 ◦ ◦ NOUN cana-5770 80 5 t t NOUN cana-5770 80 6 ) ) PUNCT cana-5770 80 7 −1ts(ε −1ts(ε PROPN cana-5770 80 8 ) ) PUNCT cana-5770 80 9 , , PUNCT cana-5770 80 10 ∀ ∀ PUNCT cana-5770 80 11 ε ε PROPN cana-5770 80 12 ∈ ∈ PROPN cana-5770 80 13 z z PROPN cana-5770 80 14 and and CCONJ cana-5770 80 15 t t PROPN cana-5770 80 16 , , PUNCT cana-5770 80 17 s s PART cana-5770 80 18 ∈ ∈ PROPN cana-5770 80 19 ℘ ℘ PROPN cana-5770 80 20 6 6 NUM cana-5770 80 21 ) ) PUNCT cana-5770 80 22 ( ( PUNCT cana-5770 80 23 s s AUX cana-5770 80 24 ◦ ◦ NOUN cana-5770 80 25 < < X cana-5770 80 26 ) ) PUNCT cana-5770 80 27 ts ts X cana-5770 80 28 = = PUNCT cana-5770 80 29 ∨ ∨ PROPN cana-5770 80 30 m∈℘ m∈℘ PROPN cana-5770 80 31 ( ( PUNCT cana-5770 80 32 min((s)tm min((s)tm PROPN cana-5770 80 33 , , PUNCT cana-5770 80 34 ( ( PUNCT cana-5770 80 35 < < NOUN cana-5770 80 36 ) ) PUNCT cana-5770 80 37 ms ms NOUN cana-5770 80 38 ) ) PUNCT cana-5770 80 39 ) ) PUNCT cana-5770 80 40 ≤ ≤ NUM cana-5770 80 41 ∨ ∨ NUM cana-5770 80 42 m∈℘ m∈℘ PROPN cana-5770 80 43 ( ( PUNCT cana-5770 80 44 min((t min((t INTJ cana-5770 80 45 ) ) PUNCT cana-5770 80 46 tm tm NOUN cana-5770 80 47 , , PUNCT cana-5770 80 48 ( ( PUNCT cana-5770 80 49 < < NOUN cana-5770 80 50 ) ) PUNCT cana-5770 80 51 ms ms NOUN cana-5770 80 52 ) ) PUNCT cana-5770 80 53 ) ) PUNCT cana-5770 80 54 ≤ ≤ NOUN cana-5770 80 55 ( ( PUNCT cana-5770 80 56 t t NOUN cana-5770 80 57 ◦ ◦ NOUN cana-5770 80 58 < < X cana-5770 80 59 ) ) PUNCT cana-5770 80 60 ts ts ADP cana-5770 80 61 7 7 NUM cana-5770 80 62 ) ) PUNCT cana-5770 80 63 ( ( PUNCT cana-5770 80 64 ( ( PUNCT cana-5770 80 65 s s X cana-5770 80 66 ◦ ◦ NOUN cana-5770 80 67 t t NOUN cana-5770 80 68 ) ) PUNCT cana-5770 81 1 ◦ ◦ NOUN cana-5770 81 2 < < X cana-5770 81 3 ) ) PUNCT cana-5770 81 4 ts ts X cana-5770 81 5 = = PUNCT cana-5770 81 6 ∨ ∨ PROPN cana-5770 81 7 m∈℘ m∈℘ PROPN cana-5770 81 8 ( ( PUNCT cana-5770 81 9 min((s min(( VERB cana-5770 81 10 ◦ ◦ PROPN cana-5770 81 11 t t PROPN cana-5770 81 12 ) ) PUNCT cana-5770 81 13 tm,(<)ms tm,(<)m NOUN cana-5770 81 14 ) ) PUNCT cana-5770 81 15 ) ) PUNCT cana-5770 82 1 = = PUNCT cana-5770 82 2 ∨ ∨ NUM cana-5770 82 3 m∈℘ m∈℘ PROPN cana-5770 82 4 ( ( PUNCT cana-5770 82 5 min min PROPN cana-5770 82 6 ( ( PUNCT cana-5770 82 7 ∨ ∨ NUM cana-5770 82 8 u∈t u∈t ADV cana-5770 82 9 ( ( PUNCT cana-5770 82 10 min((s)tu,(t min((s)tu,(t NOUN cana-5770 82 11 ) ) PUNCT cana-5770 82 12 um),(<)ms um),(<)ms ADJ cana-5770 82 13 ) ) PUNCT cana-5770 82 14 ) ) PUNCT cana-5770 82 15 ) ) PUNCT cana-5770 83 1 = = PUNCT cana-5770 83 2 ∨ ∨ NUM cana-5770 83 3 m∈℘ m∈℘ PROPN cana-5770 83 4 ∨ ∨ NUM cana-5770 83 5 u∈t u∈t ADV cana-5770 83 6 ( ( PUNCT cana-5770 83 7 min((s)tu min((s)tu X cana-5770 83 8 , , PUNCT cana-5770 83 9 min((t min((t PROPN cana-5770 83 10 ) ) PUNCT cana-5770 83 11 um um INTJ cana-5770 83 12 , , PUNCT cana-5770 83 13 ( ( PUNCT cana-5770 83 14 < < NOUN cana-5770 83 15 ) ) PUNCT cana-5770 83 16 ms ms NOUN cana-5770 83 17 ) ) PUNCT cana-5770 83 18 ) ) PUNCT cana-5770 83 19 ) ) PUNCT cana-5770 84 1 = = PUNCT cana-5770 84 2 ∨ ∨ NUM cana-5770 84 3 u∈t u∈t ADV cana-5770 84 4 min(stu min(stu PROPN cana-5770 84 5 , , PUNCT cana-5770 84 6 ∨ ∨ PROPN cana-5770 84 7 m∈℘ m∈℘ PROPN cana-5770 84 8 ( ( PUNCT cana-5770 84 9 min min PROPN cana-5770 84 10 ( ( PUNCT cana-5770 84 11 ( ( PUNCT cana-5770 84 12 t t NOUN cana-5770 84 13 ) ) PUNCT cana-5770 84 14 um um INTJ cana-5770 84 15 , , PUNCT cana-5770 84 16 ( ( PUNCT cana-5770 84 17 < < NOUN cana-5770 84 18 ) ) PUNCT cana-5770 84 19 ms ms NOUN cana-5770 84 20 ) ) PUNCT cana-5770 84 21 ) ) PUNCT cana-5770 84 22 ) ) PUNCT cana-5770 85 1 = = PUNCT cana-5770 85 2 ∨ ∨ NUM cana-5770 85 3 u∈t u∈t ADV cana-5770 85 4 ( ( PUNCT cana-5770 85 5 min min NOUN cana-5770 85 6 ( ( PUNCT cana-5770 85 7 stu stu PROPN cana-5770 85 8 , , PUNCT cana-5770 85 9 ( ( PUNCT cana-5770 85 10 t t NOUN cana-5770 85 11 ) ) PUNCT cana-5770 85 12 ◦ ◦ NOUN cana-5770 85 13 ( ( PUNCT cana-5770 85 14 < < NOUN cana-5770 85 15 ) ) PUNCT cana-5770 85 16 us we PRON cana-5770 85 17 ) ) PUNCT cana-5770 85 18 ) ) PUNCT cana-5770 86 1 = = PUNCT cana-5770 86 2 ( ( PUNCT cana-5770 86 3 s s AUX cana-5770 86 4 ◦ ◦ NOUN cana-5770 86 5 ( ( PUNCT cana-5770 86 6 ( ( PUNCT cana-5770 86 7 t t NOUN cana-5770 86 8 ) ) PUNCT cana-5770 86 9 ◦ ◦ NOUN cana-5770 86 10 ( ( PUNCT cana-5770 86 11 < < NOUN cana-5770 86 12 ) ) PUNCT cana-5770 86 13 ) ) PUNCT cana-5770 86 14 ) ) PUNCT cana-5770 86 15 ts ts ADP cana-5770 86 16 8) 8) NUM cana-5770 86 17 ( ( PUNCT cana-5770 86 18 s s NOUN cana-5770 86 19 ∪ ∪ PROPN cana-5770 86 20 t t NOUN cana-5770 86 21 ) ) PUNCT cana-5770 86 22 −1ts(ε −1ts(ε NOUN cana-5770 86 23 ) ) PUNCT cana-5770 86 24 = = PUNCT cana-5770 86 25 ( ( PUNCT cana-5770 86 26 s s X cana-5770 86 27 ∪ ∪ PROPN cana-5770 86 28 t t PROPN cana-5770 86 29 ) ) PUNCT cana-5770 86 30 st(ε st(ε ADP cana-5770 86 31 ) ) PUNCT cana-5770 86 32 = = SYM cana-5770 86 33 sst(ε sst(ε PROPN cana-5770 86 34 ) ) PUNCT cana-5770 86 35 ∨ ∨ PROPN cana-5770 86 36 t t PROPN cana-5770 86 37 st(ε st(ε PROPN cana-5770 86 38 ) ) PUNCT cana-5770 86 39 = = SYM cana-5770 86 40 s−1ts(ε s−1ts(ε PROPN cana-5770 86 41 ) ) PUNCT cana-5770 86 42 ∨ ∨ PROPN cana-5770 86 43 t t NOUN cana-5770 86 44 −1 −1 NOUN cana-5770 86 45 ts(ε ts(ε NOUN cana-5770 86 46 ) ) PUNCT cana-5770 86 47 = = SYM cana-5770 86 48 ( ( PUNCT cana-5770 86 49 s−1 s−1 PROPN cana-5770 86 50 ∪ ∪ VERB cana-5770 86 51 t t PROPN cana-5770 86 52 −1)ts(ε −1)ts(ε NOUN cana-5770 86 53 ) ) PUNCT cana-5770 86 54 , , PUNCT cana-5770 86 55 ∀ ∀ PUNCT cana-5770 86 56 ε ε PROPN cana-5770 86 57 ∈ ∈ PROPN cana-5770 86 58 z z PROPN cana-5770 86 59 and and CCONJ cana-5770 86 60 t t PROPN cana-5770 86 61 , , PUNCT cana-5770 86 62 s s PART cana-5770 86 63 ∈ ∈ PROPN cana-5770 86 64 ℘. ℘. PROPN cana-5770 86 65 = = SYM cana-5770 86 66 ⇒ ⇒ NOUN cana-5770 86 67 ( ( PUNCT cana-5770 86 68 s s X cana-5770 86 69 ∪ ∪ PROPN cana-5770 86 70 t t NOUN cana-5770 86 71 ) ) PUNCT cana-5770 86 72 −1 −1 NOUN cana-5770 86 73 = = PUNCT cana-5770 87 1 s−1 s−1 PROPN cana-5770 87 2 ∪ ∪ VERB cana-5770 87 3 t t NOUN cana-5770 87 4 −1 −1 NOUN cana-5770 87 5 ( ( PUNCT cana-5770 87 6 s s X cana-5770 87 7 ∩ ∩ ADJ cana-5770 87 8 t t NOUN cana-5770 87 9 ) ) PUNCT cana-5770 87 10 −1ts(ε −1ts(ε PROPN cana-5770 87 11 ) ) PUNCT cana-5770 87 12 = = PUNCT cana-5770 87 13 ( ( PUNCT cana-5770 87 14 s s X cana-5770 87 15 ∩ ∩ ADJ cana-5770 87 16 t t PROPN cana-5770 87 17 ) ) PUNCT cana-5770 87 18 st(ε st(ε ADP cana-5770 87 19 ) ) PUNCT cana-5770 87 20 = = SYM cana-5770 87 21 sst(ε sst(ε PROPN cana-5770 87 22 ) ) PUNCT cana-5770 87 23 ∧ ∧ PROPN cana-5770 87 24 t t PROPN cana-5770 87 25 st(ε st(ε PROPN cana-5770 87 26 ) ) PUNCT cana-5770 87 27 = = SYM cana-5770 87 28 s−1ts(ε s−1ts(ε ADJ cana-5770 87 29 ) ) PUNCT cana-5770 87 30 ∧ ∧ NOUN cana-5770 87 31 s−1ts(ε s−1ts(ε NOUN cana-5770 87 32 ) ) PUNCT cana-5770 87 33 = = SYM cana-5770 87 34 ( ( PUNCT cana-5770 87 35 s−1 s−1 PROPN cana-5770 87 36 ∩ ∩ X cana-5770 87 37 t t PROPN cana-5770 87 38 −1)ts(ε −1)ts(ε PROPN cana-5770 87 39 ) ) PUNCT cana-5770 87 40 , , PUNCT cana-5770 87 41 ∀ ∀ PUNCT cana-5770 87 42 ε ε PROPN cana-5770 87 43 ∈ ∈ PROPN cana-5770 87 44 z z PROPN cana-5770 87 45 and and CCONJ cana-5770 87 46 t t PROPN cana-5770 87 47 , , PUNCT cana-5770 87 48 s s PART cana-5770 88 1 ∈ ∈ PROPN cana-5770 88 2 ℘ ℘ NUM cana-5770 88 3 = = SYM cana-5770 88 4 ⇒ ⇒ NOUN cana-5770 88 5 ( ( PUNCT cana-5770 88 6 s s X cana-5770 88 7 ∩ ∩ ADJ cana-5770 88 8 t t NOUN cana-5770 88 9 ) ) PUNCT cana-5770 88 10 −1 −1 NOUN cana-5770 88 11 = = SYM cana-5770 89 1 s−1 s−1 NOUN cana-5770 89 2 ∩ ∩ NOUN cana-5770 89 3 t t NOUN cana-5770 89 4 −1 −1 NOUN cana-5770 89 5 9)(s 9)(s NUM cana-5770 89 6 ∪ ∪ ADP cana-5770 89 7 t t NOUN cana-5770 89 8 ) ) PUNCT cana-5770 89 9 cts(ε cts(ε NOUN cana-5770 89 10 ) ) PUNCT cana-5770 89 11 = = NOUN cana-5770 89 12 1(s 1(s NUM cana-5770 89 13 ∪ ∪ PROPN cana-5770 89 14 t t PROPN cana-5770 89 15 ) ) PUNCT cana-5770 89 16 ts(ε ts(ε PUNCT cana-5770 89 17 ) ) PUNCT cana-5770 89 18 = = SYM cana-5770 89 19 1(sts(ε)∨(t 1(sts(ε)∨(t PROPN cana-5770 89 20 ) ) PUNCT cana-5770 89 21 ts(ε ts(ε NUM cana-5770 89 22 ) ) PUNCT cana-5770 89 23 ) ) PUNCT cana-5770 90 1 = = SYM cana-5770 90 2 ( ( PUNCT cana-5770 90 3 1sts(ε 1sts(ε NOUN cana-5770 90 4 ) ) PUNCT cana-5770 90 5 ) ) PUNCT cana-5770 91 1 ∧ ∧ NOUN cana-5770 91 2 ( ( PUNCT cana-5770 91 3 1(t 1(t NUM cana-5770 91 4 ) ) PUNCT cana-5770 91 5 ts(ε ts(ε NUM cana-5770 91 6 ) ) PUNCT cana-5770 91 7 ) ) PUNCT cana-5770 92 1 = = SYM cana-5770 92 2 scts(ε scts(ε NOUN cana-5770 92 3 ) ) PUNCT cana-5770 92 4 ) ) PUNCT cana-5770 93 1 ∧ ∧ PROPN cana-5770 93 2 ( ( PUNCT cana-5770 93 3 t t NOUN cana-5770 93 4 ) ) PUNCT cana-5770 93 5 cts(ε cts(ε NOUN cana-5770 93 6 ) ) PUNCT cana-5770 93 7 = = SYM cana-5770 93 8 ( ( PUNCT cana-5770 93 9 sc sc PROPN cana-5770 93 10 ∩ ∩ PROPN cana-5770 93 11 t t PROPN cana-5770 93 12 c)ts(ε c)ts(ε NOUN cana-5770 93 13 ) ) PUNCT cana-5770 93 14 , , PUNCT cana-5770 93 15 ∀ ∀ PUNCT cana-5770 93 16 ε ε PROPN cana-5770 93 17 ∈ ∈ PROPN cana-5770 93 18 z z PROPN cana-5770 93 19 and and CCONJ cana-5770 93 20 t t PROPN cana-5770 93 21 , , PUNCT cana-5770 93 22 s s PART cana-5770 94 1 ∈ ∈ PROPN cana-5770 94 2 ℘ ℘ NUM cana-5770 94 3 = = SYM cana-5770 94 4 ⇒ ⇒ NOUN cana-5770 94 5 ( ( PUNCT cana-5770 94 6 s s X cana-5770 94 7 ∪ ∪ PROPN cana-5770 94 8 t t NOUN cana-5770 94 9 ) ) PUNCT cana-5770 94 10 c c NOUN cana-5770 94 11 = = SYM cana-5770 94 12 sc sc PROPN cana-5770 94 13 ∩ ∩ PROPN cana-5770 94 14 t t PROPN cana-5770 94 15 c c PROPN cana-5770 94 16 ( ( PUNCT cana-5770 94 17 s s X cana-5770 94 18 ∩ ∩ ADJ cana-5770 94 19 t t NOUN cana-5770 94 20 ) ) PUNCT cana-5770 94 21 cts(ε cts(ε NOUN cana-5770 94 22 ) ) PUNCT cana-5770 94 23 = = SYM cana-5770 94 24 1(s 1(s NUM cana-5770 94 25 ∩ ∩ PROPN cana-5770 94 26 t t PROPN cana-5770 94 27 ) ) PUNCT cana-5770 94 28 ts(ε ts(ε X cana-5770 94 29 ) ) PUNCT cana-5770 94 30 = = SYM cana-5770 94 31 1(sts(z)∧(t 1(sts(z)∧(t PROPN cana-5770 94 32 ) ) PUNCT cana-5770 94 33 ts(ε ts(ε NUM cana-5770 94 34 ) ) PUNCT cana-5770 94 35 ) ) PUNCT cana-5770 95 1 = = SYM cana-5770 95 2 ( ( PUNCT cana-5770 95 3 1sts(ε 1sts(ε NOUN cana-5770 95 4 ) ) PUNCT cana-5770 95 5 ) ) PUNCT cana-5770 96 1 ∨ ∨ NUM cana-5770 96 2 ( ( PUNCT cana-5770 96 3 1(t 1(t NUM cana-5770 96 4 ) ) PUNCT cana-5770 96 5 ts(ε ts(ε NUM cana-5770 96 6 ) ) PUNCT cana-5770 96 7 ) ) PUNCT cana-5770 97 1 = = SYM cana-5770 97 2 scts(ε scts(ε NOUN cana-5770 97 3 ) ) PUNCT cana-5770 97 4 ) ) PUNCT cana-5770 98 1 ∨ ∨ PROPN cana-5770 98 2 ( ( PUNCT cana-5770 98 3 t t NOUN cana-5770 98 4 ) ) PUNCT cana-5770 98 5 cts(ε cts(ε NOUN cana-5770 98 6 ) ) PUNCT cana-5770 98 7 communications communication NOUN cana-5770 98 8 on on ADP cana-5770 98 9 applied apply VERB cana-5770 98 10 nonlinear nonlinear ADJ cana-5770 98 11 analysis analysis NOUN cana-5770 98 12 issn issn NOUN cana-5770 98 13 : : PUNCT cana-5770 98 14 1074 1074 NUM cana-5770 98 15 - - PUNCT cana-5770 98 16 133x 133x NUM cana-5770 98 17 vol vol NOUN cana-5770 98 18 32 32 NUM cana-5770 98 19 no no NOUN cana-5770 98 20 . . PUNCT cana-5770 99 1 9s 9s NUM cana-5770 99 2 ( ( PUNCT cana-5770 99 3 2025 2025 NUM cana-5770 99 4 ) ) PUNCT cana-5770 99 5 https://internationalpubls.com https://internationalpubls.com X cana-5770 99 6 3198 3198 NUM cana-5770 99 7 anju anju PROPN cana-5770 99 8 rajath rajath NOUN cana-5770 99 9 pencil pencil NOUN cana-5770 99 10 = = SYM cana-5770 99 11 ( ( PUNCT cana-5770 99 12 sc sc PROPN cana-5770 99 13 ∪ ∪ X cana-5770 99 14 ( ( PUNCT cana-5770 99 15 t t NOUN cana-5770 99 16 ) ) PUNCT cana-5770 99 17 c)ts(ε c)ts(ε NOUN cana-5770 99 18 ) ) PUNCT cana-5770 99 19 , , PUNCT cana-5770 99 20 ∀ ∀ PUNCT cana-5770 99 21 ε ε PROPN cana-5770 99 22 ∈ ∈ PROPN cana-5770 99 23 z z PROPN cana-5770 99 24 and and CCONJ cana-5770 99 25 t t PROPN cana-5770 99 26 , , PUNCT cana-5770 99 27 s s PART cana-5770 100 1 ∈ ∈ PROPN cana-5770 100 2 ℘ ℘ NUM cana-5770 100 3 = = SYM cana-5770 100 4 ⇒ ⇒ NOUN cana-5770 100 5 ( ( PUNCT cana-5770 100 6 s s X cana-5770 100 7 ∩ ∩ NOUN cana-5770 100 8 t t NOUN cana-5770 100 9 ) ) PUNCT cana-5770 100 10 c c NOUN cana-5770 101 1 = = PUNCT cana-5770 101 2 sc sc PROPN cana-5770 101 3 ∪ ∪ ADP cana-5770 101 4 t t PROPN cana-5770 101 5 c c PROPN cana-5770 101 6 4 4 NUM cana-5770 101 7 . . PUNCT cana-5770 102 1 fs fs ADJ cana-5770 102 2 - - PUNCT cana-5770 102 3 equivalence equivalence NOUN cana-5770 102 4 relation relation NOUN cana-5770 102 5 . . PUNCT cana-5770 103 1 definition definition NOUN cana-5770 103 2 4.1 4.1 NUM cana-5770 103 3 . . PUNCT cana-5770 104 1 let let VERB cana-5770 104 2 < < X cana-5770 104 3 be be AUX cana-5770 104 4 a a DET cana-5770 104 5 fsrelation fsrelation NOUN cana-5770 104 6 defined define VERB cana-5770 104 7 on on ADP cana-5770 104 8 fs f NOUN cana-5770 104 9 - - PUNCT cana-5770 104 10 set set VERB cana-5770 104 11 ( ( PUNCT cana-5770 104 12 γ,℘ γ,℘ ADV cana-5770 104 13 ) ) PUNCT cana-5770 104 14 over over ADP cana-5770 104 15 z. z. PROPN cana-5770 104 16 1 1 NUM cana-5770 104 17 ) ) PUNCT cana-5770 104 18 if if SCONJ cana-5770 104 19 < < X cana-5770 104 20 ts(ε ts(ε NOUN cana-5770 104 21 ) ) PUNCT cana-5770 104 22 ≤ ≤ NOUN cana-5770 104 23 < < X cana-5770 104 24 tt(ε tt(ε NOUN cana-5770 104 25 ) ) PUNCT cana-5770 104 26 and and CCONJ cana-5770 104 27 < < X cana-5770 104 28 st(ε st(ε X cana-5770 104 29 ) ) PUNCT cana-5770 104 30 ≤ ≤ PUNCT cana-5770 104 31 < < X cana-5770 104 32 tt(ε tt(ε NOUN cana-5770 104 33 ) ) PUNCT cana-5770 104 34 , , PUNCT cana-5770 104 35 ∀ ∀ X cana-5770 104 36 t t PROPN cana-5770 104 37 , , PUNCT cana-5770 104 38 s s PART cana-5770 104 39 ∈ ∈ NOUN cana-5770 104 40 ℘ ℘ PROPN cana-5770 104 41 with with ADP cana-5770 104 42 t t PROPN cana-5770 104 43 6= 6= ADP cana-5770 104 44 s s NOUN cana-5770 104 45 and and CCONJ cana-5770 104 46 ∀ ∀ NUM cana-5770 104 47 ε ε PROPN cana-5770 104 48 ∈ ∈ PROPN cana-5770 105 1 z z PROPN cana-5770 105 2 , , PUNCT cana-5770 105 3 then then ADV cana-5770 105 4 the the DET cana-5770 105 5 fs fs NOUN cana-5770 105 6 - - PUNCT cana-5770 105 7 relation relation NOUN cana-5770 105 8 < < X cana-5770 105 9 is be AUX cana-5770 105 10 called call VERB cana-5770 105 11 fs fs ADJ cana-5770 105 12 - - PUNCT cana-5770 105 13 reflexive reflexive ADJ cana-5770 105 14 . . PUNCT cana-5770 106 1 2 2 X cana-5770 106 2 ) ) PUNCT cana-5770 106 3 if if SCONJ cana-5770 106 4 the the DET cana-5770 106 5 fs fs ADJ cana-5770 106 6 - - PUNCT cana-5770 106 7 reflexive reflexive ADJ cana-5770 106 8 relation relation NOUN cana-5770 106 9 < < X cana-5770 106 10 is be AUX cana-5770 106 11 such such ADJ cana-5770 106 12 that that SCONJ cana-5770 106 13 < < X cana-5770 106 14 tt(ε tt(ε NOUN cana-5770 106 15 ) ) PUNCT cana-5770 106 16 = = SYM cana-5770 106 17 1 1 NUM cana-5770 106 18 , , PUNCT cana-5770 106 19 ∀ ∀ NUM cana-5770 106 20 ε ε PROPN cana-5770 106 21 ∈ ∈ PROPN cana-5770 106 22 z z PROPN cana-5770 106 23 and and CCONJ cana-5770 106 24 ∀ ∀ NOUN cana-5770 106 25 t t NOUN cana-5770 106 26 ∈ ∈ PROPN cana-5770 106 27 ℘ ℘ PROPN cana-5770 106 28 , , PUNCT cana-5770 106 29 then then ADV cana-5770 106 30 < < X cana-5770 106 31 is be AUX cana-5770 106 32 called call VERB cana-5770 106 33 identically identically ADV cana-5770 106 34 fs fs ADJ cana-5770 106 35 - - PUNCT cana-5770 106 36 reflexive reflexive ADJ cana-5770 106 37 relation relation NOUN cana-5770 106 38 3 3 NUM cana-5770 106 39 ) ) PUNCT cana-5770 106 40 if if SCONJ cana-5770 106 41 < < X cana-5770 106 42 = = PUNCT cana-5770 106 43 < < X cana-5770 106 44 −1 −1 NOUN cana-5770 106 45 , , PUNCT cana-5770 106 46 < < X cana-5770 106 47 is be AUX cana-5770 106 48 called call VERB cana-5770 106 49 a a DET cana-5770 106 50 fs fs ADJ cana-5770 106 51 - - PUNCT cana-5770 106 52 symmetric symmetric ADJ cana-5770 106 53 relation relation NOUN cana-5770 106 54 4 4 NUM cana-5770 106 55 ) ) PUNCT cana-5770 106 56 if if SCONJ cana-5770 106 57 < < X cana-5770 106 58 ◦ ◦ NOUN cana-5770 106 59 < < X cana-5770 106 60 ⊆ ⊆ NUM cana-5770 106 61 < < X cana-5770 106 62 , , PUNCT cana-5770 106 63 then then ADV cana-5770 106 64 < < X cana-5770 106 65 is be AUX cana-5770 106 66 called call VERB cana-5770 106 67 a a DET cana-5770 106 68 fs fs ADJ cana-5770 106 69 - - PUNCT cana-5770 106 70 transitive transitive ADJ cana-5770 106 71 relation relation NOUN cana-5770 106 72 5 5 NUM cana-5770 106 73 ) ) PUNCT cana-5770 106 74 if if SCONJ cana-5770 106 75 the the DET cana-5770 106 76 relation relation NOUN cana-5770 106 77 < < X cana-5770 106 78 satisfies satisfy VERB cana-5770 106 79 the the DET cana-5770 106 80 conditions condition NOUN cana-5770 106 81 1,3,4 1,3,4 NUM cana-5770 106 82 then then ADV cana-5770 106 83 < < X cana-5770 106 84 is be AUX cana-5770 106 85 called call VERB cana-5770 106 86 a a DET cana-5770 106 87 fs fs ADJ cana-5770 106 88 - - PUNCT cana-5770 106 89 equivalence equivalence NOUN cana-5770 106 90 relation relation NOUN cana-5770 106 91 . . PUNCT cana-5770 107 1 theorem theorem VERB cana-5770 107 2 4.2 4.2 NUM cana-5770 107 3 . . PUNCT cana-5770 108 1 let let VERB cana-5770 108 2 < < X cana-5770 108 3 be be AUX cana-5770 108 4 a a DET cana-5770 108 5 fs fs NOUN cana-5770 108 6 - - PUNCT cana-5770 108 7 relation relation NOUN cana-5770 108 8 on on ADP cana-5770 108 9 fs fs ADJ cana-5770 108 10 - - PUNCT cana-5770 108 11 set set VERB cana-5770 108 12 ( ( PUNCT cana-5770 108 13 γ,℘ γ,℘ ADV cana-5770 108 14 ) ) PUNCT cana-5770 108 15 , , PUNCT cana-5770 108 16 then then ADV cana-5770 108 17 < < X cana-5770 108 18 −1 −1 NOUN cana-5770 108 19 and and CCONJ cana-5770 108 20 < < X cana-5770 108 21 ◦ ◦ NOUN cana-5770 108 22 < < X cana-5770 108 23 are be AUX cana-5770 108 24 fsequivalence fsequivalence NOUN cana-5770 108 25 relations relation NOUN cana-5770 108 26 on on ADP cana-5770 108 27 ( ( PUNCT cana-5770 108 28 γ,℘ γ,℘ ADV cana-5770 108 29 ) ) PUNCT cana-5770 108 30 proof proof NOUN cana-5770 108 31 for for ADP cana-5770 108 32 t t PROPN cana-5770 108 33 , , PUNCT cana-5770 108 34 s s PART cana-5770 108 35 ∈ ∈ NOUN cana-5770 108 36 ℘ ℘ PROPN cana-5770 108 37 with with ADP cana-5770 108 38 t t PROPN cana-5770 108 39 6= 6= SYM cana-5770 108 40 s s PROPN cana-5770 108 41 and and CCONJ cana-5770 108 42 for for ADP cana-5770 108 43 ε ε PROPN cana-5770 108 44 ∈ ∈ PROPN cana-5770 108 45 z z PROPN cana-5770 108 46 , , PUNCT cana-5770 108 47 < < X cana-5770 108 48 −1ts −1ts PROPN cana-5770 108 49 ( ( PUNCT cana-5770 108 50 ε ε PROPN cana-5770 108 51 ) ) PUNCT cana-5770 108 52 = = PUNCT cana-5770 109 1 < < X cana-5770 109 2 st(ε st(ε NOUN cana-5770 109 3 ) ) PUNCT cana-5770 109 4 ≤ ≤ PUNCT cana-5770 110 1 < < X cana-5770 110 2 tt(ε tt(ε NOUN cana-5770 110 3 ) ) PUNCT cana-5770 110 4 similarly similarly ADV cana-5770 110 5 < < X cana-5770 110 6 −1st −1st X cana-5770 110 7 ( ( PUNCT cana-5770 110 8 ε ε PROPN cana-5770 110 9 ) ) PUNCT cana-5770 110 10 ≤ ≤ NOUN cana-5770 111 1 < < X cana-5770 111 2 tt(ε tt(ε NOUN cana-5770 111 3 ) ) PUNCT cana-5770 111 4 = = AUX cana-5770 111 5 ⇒ ⇒ NOUN cana-5770 111 6 < < X cana-5770 111 7 −1 −1 NOUN cana-5770 111 8 is be AUX cana-5770 111 9 fs f NOUN cana-5770 111 10 - - PUNCT cana-5770 111 11 reflexive reflexive ADJ cana-5770 111 12 . . PUNCT cana-5770 112 1 since since SCONJ cana-5770 112 2 < < X cana-5770 112 3 is be AUX cana-5770 112 4 fs f NOUN cana-5770 112 5 - - ADJ cana-5770 112 6 symmetric symmetric ADJ cana-5770 112 7 we we PRON cana-5770 112 8 have have VERB cana-5770 112 9 < < X cana-5770 112 10 = = X cana-5770 112 11 < < X cana-5770 112 12 −1 −1 X cana-5770 112 13 hence hence ADV cana-5770 112 14 < < X cana-5770 112 15 −1 −1 NOUN cana-5770 112 16 = = PUNCT cana-5770 112 17 ( ( PUNCT cana-5770 112 18 < < X cana-5770 112 19 −1)−1 −1)−1 NOUN cana-5770 112 20 = = X cana-5770 112 21 < < X cana-5770 112 22 therefore therefore ADV cana-5770 112 23 the the DET cana-5770 112 24 fs fs NOUN cana-5770 112 25 - - PUNCT cana-5770 112 26 relation relation NOUN cana-5770 112 27 < < NOUN cana-5770 112 28 −1 −1 NOUN cana-5770 112 29 is be AUX cana-5770 112 30 fs fs ADJ cana-5770 112 31 - - NOUN cana-5770 112 32 symmetric symmetric ADJ cana-5770 112 33 . . PUNCT cana-5770 113 1 the the DET cana-5770 113 2 fs fs PROPN cana-5770 113 3 - - PUNCT cana-5770 113 4 relation relation NOUN cana-5770 113 5 < < X cana-5770 113 6 is be AUX cana-5770 113 7 fs fs ADJ cana-5770 113 8 - - ADJ cana-5770 113 9 transitive transitive ADJ cana-5770 113 10 = = NOUN cana-5770 113 11 ⇒ ⇒ NOUN cana-5770 113 12 < < X cana-5770 113 13 ◦ ◦ NOUN cana-5770 113 14 < < X cana-5770 113 15 ⊆ ⊆ X cana-5770 113 16 < < X cana-5770 113 17 which which PRON cana-5770 113 18 implies imply VERB cana-5770 113 19 ( ( PUNCT cana-5770 113 20 < < X cana-5770 113 21 ◦ ◦ NOUN cana-5770 113 22 < < X cana-5770 113 23 ) ) PUNCT cana-5770 113 24 −1 −1 NOUN cana-5770 113 25 ⊆ ⊆ NUM cana-5770 113 26 < < X cana-5770 113 27 −1 −1 NOUN cana-5770 113 28 . . PUNCT cana-5770 114 1 by by ADP cana-5770 114 2 theorem theorem VERB cana-5770 114 3 3.6 3.6 NUM cana-5770 114 4 we we PRON cana-5770 114 5 have have VERB cana-5770 114 6 < < X cana-5770 114 7 −1 −1 NOUN cana-5770 114 8 ◦ ◦ NOUN cana-5770 114 9 < < X cana-5770 114 10 −1 −1 NOUN cana-5770 114 11 ⊆ ⊆ NUM cana-5770 114 12 < < X cana-5770 114 13 −1 −1 NOUN cana-5770 114 14 hence hence ADV cana-5770 114 15 the the DET cana-5770 114 16 fs fs NOUN cana-5770 114 17 - - PUNCT cana-5770 114 18 relation relation NOUN cana-5770 114 19 < < NOUN cana-5770 114 20 −1 −1 NOUN cana-5770 114 21 is be AUX cana-5770 114 22 fs f NOUN cana-5770 114 23 - - PUNCT cana-5770 114 24 transitive transitive ADJ cana-5770 114 25 . . PUNCT cana-5770 115 1 therefore therefore ADV cana-5770 115 2 < < X cana-5770 115 3 −1 −1 NOUN cana-5770 115 4 is be AUX cana-5770 115 5 a a DET cana-5770 115 6 fs fs ADJ cana-5770 115 7 - - PUNCT cana-5770 115 8 equivalence equivalence NOUN cana-5770 115 9 relation relation NOUN cana-5770 115 10 . . PUNCT cana-5770 116 1 let let VERB cana-5770 116 2 t t NOUN cana-5770 116 3 and and CCONJ cana-5770 116 4 s s AUX cana-5770 116 5 be be AUX cana-5770 116 6 the the DET cana-5770 116 7 parameters parameter NOUN cana-5770 116 8 in in ADP cana-5770 116 9 ℘ ℘ PROPN cana-5770 116 10 such such ADJ cana-5770 116 11 that that DET cana-5770 116 12 t t PROPN cana-5770 116 13 6= 6= NUM cana-5770 116 14 s s PROPN cana-5770 116 15 , , PUNCT cana-5770 116 16 then then ADV cana-5770 116 17 for for SCONJ cana-5770 116 18 all all DET cana-5770 116 19 ε ε PROPN cana-5770 116 20 belongs belong VERB cana-5770 116 21 to to ADP cana-5770 116 22 z z PROPN cana-5770 116 23 we we PRON cana-5770 116 24 have have VERB cana-5770 116 25 , , PUNCT cana-5770 116 26 ( ( PUNCT cana-5770 116 27 < < X cana-5770 116 28 ◦ ◦ NOUN cana-5770 116 29 < < X cana-5770 116 30 ) ) PUNCT cana-5770 116 31 ts(ε ts(ε X cana-5770 116 32 ) ) PUNCT cana-5770 116 33 ≤ ≤ NOUN cana-5770 116 34 < < X cana-5770 116 35 ts(ε ts(ε X cana-5770 116 36 ) ) PUNCT cana-5770 116 37 ≤ ≤ NOUN cana-5770 117 1 < < X cana-5770 117 2 tt(ε tt(ε NOUN cana-5770 117 3 ) ) PUNCT cana-5770 117 4 = = AUX cana-5770 117 5 ⇒ ⇒ VERB cana-5770 117 6 < < X cana-5770 117 7 ◦ ◦ NOUN cana-5770 117 8 < < X cana-5770 117 9 is be AUX cana-5770 117 10 fs fs ADJ cana-5770 117 11 - - PUNCT cana-5770 117 12 reflexive reflexive ADJ cana-5770 117 13 relation relation NOUN cana-5770 117 14 . . PUNCT cana-5770 118 1 from from ADP cana-5770 118 2 theorem theorem ADJ cana-5770 118 3 3.6 3.6 NUM cana-5770 118 4 ( ( PUNCT cana-5770 118 5 < < X cana-5770 118 6 ◦ ◦ NOUN cana-5770 118 7 < < X cana-5770 118 8 ) ) PUNCT cana-5770 118 9 −1ts −1ts PROPN cana-5770 118 10 = = SYM cana-5770 118 11 ( ( PUNCT cana-5770 118 12 < < X cana-5770 118 13 −1 −1 X cana-5770 118 14 ◦ ◦ NOUN cana-5770 118 15 < < X cana-5770 118 16 −1)ts −1)ts PROPN cana-5770 118 17 = = SYM cana-5770 118 18 ( ( PUNCT cana-5770 118 19 < < X cana-5770 118 20 ◦ ◦ NOUN cana-5770 118 21 < < X cana-5770 118 22 ) ) PUNCT cana-5770 118 23 ts ts ADP cana-5770 118 24 thereby thereby ADV cana-5770 118 25 implies imply VERB cana-5770 118 26 that that SCONJ cana-5770 118 27 < < X cana-5770 118 28 ◦ ◦ NOUN cana-5770 118 29 < < X cana-5770 118 30 is be AUX cana-5770 118 31 fs f NOUN cana-5770 118 32 - - NOUN cana-5770 118 33 symmetric symmetric ADJ cana-5770 118 34 . . PUNCT cana-5770 119 1 since since SCONJ cana-5770 119 2 < < X cana-5770 119 3 is be AUX cana-5770 119 4 fs f NOUN cana-5770 119 5 - - PUNCT cana-5770 119 6 transitive transitive ADJ cana-5770 119 7 , , PUNCT cana-5770 119 8 from from ADP cana-5770 119 9 the the DET cana-5770 119 10 definition definition NOUN cana-5770 119 11 we we PRON cana-5770 119 12 have have VERB cana-5770 119 13 < < X cana-5770 119 14 2 2 NUM cana-5770 119 15 = = SYM cana-5770 119 16 < < X cana-5770 119 17 ◦ ◦ NOUN cana-5770 119 18 < < X cana-5770 119 19 which which PRON cana-5770 119 20 is be AUX cana-5770 119 21 contained contain VERB cana-5770 119 22 in in ADP cana-5770 119 23 < < X cana-5770 119 24 = = NOUN cana-5770 119 25 ⇒ ⇒ NOUN cana-5770 119 26 < < X cana-5770 119 27 2 2 NUM cana-5770 119 28 tm tm PROPN cana-5770 119 29 ( ( PUNCT cana-5770 119 30 ε ε PROPN cana-5770 119 31 ) ) PUNCT cana-5770 119 32 ≤ ≤ NOUN cana-5770 120 1 < < X cana-5770 120 2 tm tm PROPN cana-5770 120 3 ( ( PUNCT cana-5770 120 4 ε ε PROPN cana-5770 120 5 ) ) PUNCT cana-5770 120 6 and and CCONJ cana-5770 120 7 < < X cana-5770 120 8 2 2 NUM cana-5770 120 9 ms ms PROPN cana-5770 120 10 ( ( PUNCT cana-5770 120 11 ε ε PROPN cana-5770 120 12 ) ) PUNCT cana-5770 120 13 ≤ ≤ NOUN cana-5770 120 14 < < X cana-5770 120 15 ms ms X cana-5770 120 16 ( ( PUNCT cana-5770 120 17 ε ε PROPN cana-5770 120 18 ) ) PUNCT cana-5770 120 19 by by ADP cana-5770 120 20 monotonicity monotonicity NOUN cana-5770 120 21 of of ADP cana-5770 120 22 min min NOUN cana-5770 120 23 function function NOUN cana-5770 120 24 it it PRON cana-5770 120 25 follows follow VERB cana-5770 120 26 that that SCONJ cana-5770 120 27 min(<2(tm),<2(ms min(<2(tm),<2(ms PRON cana-5770 120 28 ) ) PUNCT cana-5770 120 29 ≤ ≤ NOUN cana-5770 120 30 min(