id sid eid entity type iajs-3596 1 1 417 CARDINAL iajs-3596 1 2 2025 CARDINAL iajs-3596 2 1 al-haitham ORG iajs-3596 2 2 university of baghdad ORG iajs-3596 3 1 4.0 CARDINAL iajs-3596 3 2 h. hasan1 PERSON iajs-3596 3 3 iden h. al kanani2 PERSON iajs-3596 4 1 university of technology-iraq ORG iajs-3596 5 1 2department TIME iajs-3596 5 2 baghdad GPE iajs-3596 5 3 baghdad GPE iajs-3596 5 4 iraq GPE iajs-3596 7 1 12 CARDINAL iajs-3596 7 2 june 2023 PERSON iajs-3596 7 3 27 CARDINAL iajs-3596 7 4 20 january 2025 DATE iajs-3596 9 1 linear programming ORG iajs-3596 12 1 generalized heptagonal ORG iajs-3596 15 1 1 CARDINAL iajs-3596 16 1 the linear fractional programming problem ORG iajs-3596 16 2 healthcare ORG iajs-3596 17 1 1,2 CARDINAL iajs-3596 18 1 a https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.30526/38.1.3501 https://orcid.org/0000-0001-9289-0909 mailto:israa.h.hasn@uotechnology.edu.iq https://orcid.org/0000-0002-6492-8196 mailto:idanha_math@csw.uobaghdad.edu.iq TIME iajs-3596 19 1 2025 CARDINAL iajs-3596 19 2 38 CARDINAL iajs-3596 19 3 1 CARDINAL iajs-3596 19 4 418 CARDINAL iajs-3596 19 5 seven CARDINAL iajs-3596 22 1 3-5 CARDINAL iajs-3596 22 2 nonnormal NORP iajs-3596 24 1 t. GPE iajs-3596 24 2 6 CARDINAL iajs-3596 25 1 alharbi PRODUCT iajs-3596 25 2 m.g. GPE iajs-3596 25 3 khalifa PERSON iajs-3596 25 4 h.a. GPE iajs-3596 27 1 mitlif ORG iajs-3596 27 2 r.j. PERSON iajs-3596 27 3 9,10 ORG iajs-3596 28 1 first ORDINAL iajs-3596 29 1 gupta GPE iajs-3596 29 2 gupta GPE iajs-3596 29 3 g.(11 GPE iajs-3596 31 1 12-18 CARDINAL iajs-3596 32 1 first ORDINAL iajs-3596 32 2 linear ORG iajs-3596 34 1 eight CARDINAL iajs-3596 35 1 section 2 LAW iajs-3596 36 1 section 3 LAW iajs-3596 36 2 𝜎-cut NORP iajs-3596 37 1 section 4 LAW iajs-3596 38 1 section 5 LAW iajs-3596 39 1 section 6 LAW iajs-3596 39 2 section 7 LAW iajs-3596 39 3 section 8 LAW iajs-3596 40 1 ihjpas PERSON iajs-3596 41 1 2025 CARDINAL iajs-3596 41 2 38 CARDINAL iajs-3596 41 3 1 CARDINAL iajs-3596 41 4 419 2 CARDINAL iajs-3596 42 1 2.1 CARDINAL iajs-3596 42 2 19 CARDINAL iajs-3596 44 1 0 CARDINAL iajs-3596 44 2 1 CARDINAL iajs-3596 45 1 2.2 CARDINAL iajs-3596 45 2 β€’ CARDINAL iajs-3596 45 3 at least one CARDINAL iajs-3596 46 1 1. CARDINAL iajs-3596 46 2 β€’ CARDINAL iajs-3596 46 3 β€’ CARDINAL iajs-3596 47 1 β„΄π‘₯1 CARDINAL iajs-3596 47 2 ∈ ORG iajs-3596 48 1 0 CARDINAL iajs-3596 48 2 1 CARDINAL iajs-3596 49 1 2.3 CARDINAL iajs-3596 49 2 seven CARDINAL iajs-3596 49 3 0 CARDINAL iajs-3596 49 4 1 CARDINAL iajs-3596 52 1 one CARDINAL iajs-3596 54 1 seven CARDINAL iajs-3596 55 1 .propose ORG iajs-3596 55 2 generalized heptagonal membership function ORG iajs-3596 57 1 β„³π’œπ»πΈ ORG iajs-3596 58 1 π’œπ»πΈ ORG iajs-3596 58 2 𝛼1 ≀ 𝛼2 ≀ 𝛼3 ≀ QUANTITY iajs-3596 60 1 0 CARDINAL iajs-3596 60 2 ≀ 1 CARDINAL iajs-3596 61 1 2025 CARDINAL iajs-3596 61 2 38 CARDINAL iajs-3596 61 3 1 CARDINAL iajs-3596 61 4 420 CARDINAL iajs-3596 61 5 β„³π’œπ»πΈ ORG iajs-3596 61 6 0 CARDINAL iajs-3596 62 1 1/3 CARDINAL iajs-3596 63 1 1/3 CARDINAL iajs-3596 65 1 1/3 CARDINAL iajs-3596 66 1 1/3 CARDINAL iajs-3596 66 2 βˆ’ 𝛼5 PERSON iajs-3596 66 3 1/3 CARDINAL iajs-3596 66 4 βˆ’ 𝛼6 GPE iajs-3596 67 1 1/3 CARDINAL iajs-3596 67 2 0 𝛼6 ≀ MONEY iajs-3596 67 3 3.1 CARDINAL iajs-3596 69 1 𝛼1 + β„΄3 CARDINAL iajs-3596 70 1 0 CARDINAL iajs-3596 70 2 β„΄3 CARDINAL iajs-3596 70 3 ∈ ORG iajs-3596 70 4 β„΄3 CARDINAL iajs-3596 70 5 β„΄3 CARDINAL iajs-3596 70 6 β„΄3 CARDINAL iajs-3596 70 7 βˆ’ 𝛼5 PERSON iajs-3596 70 8 ∈ ORG iajs-3596 70 9 1 CARDINAL iajs-3596 71 1 0 CARDINAL iajs-3596 73 1 1 CARDINAL iajs-3596 73 2 0 CARDINAL iajs-3596 75 1 β„΄3βˆ’π‘˜1 π‘˜2βˆ’π‘˜1 PERSON iajs-3596 75 2 βˆ’ 𝛼5 PERSON iajs-3596 75 3 ∈ ORG iajs-3596 75 4 β„΄3βˆ’π‘˜2 DATE iajs-3596 75 5 ∈ ORG iajs-3596 76 1 2025 CARDINAL iajs-3596 76 2 38 CARDINAL iajs-3596 76 3 1 CARDINAL iajs-3596 76 4 421 3.2 CARDINAL iajs-3596 78 1 1 2 CARDINAL iajs-3596 79 1 π‘–π‘›π‘“π‘–π’œπ»πΈπ‘ƒπ“Έ Μƒ ORG iajs-3596 79 2 0 CARDINAL iajs-3596 80 1 1,2,3 CARDINAL iajs-3596 81 1 + 2 DATE iajs-3596 81 2 1 CARDINAL iajs-3596 81 3 2 CARDINAL iajs-3596 81 4 2 CARDINAL iajs-3596 81 5 3 CARDINAL iajs-3596 81 6 β„œ(π’œπ»πΈ ORG iajs-3596 81 7 1 2 βˆ— QUANTITY iajs-3596 81 8 𝐹1+ CARDINAL iajs-3596 81 9 1 CARDINAL iajs-3596 81 10 𝐹1 CARDINAL iajs-3596 81 11 β„΄3 CARDINAL iajs-3596 82 1 1 CARDINAL iajs-3596 83 1 𝐹1 CARDINAL iajs-3596 84 1 1 4 DATE iajs-3596 84 2 π‘˜1 3(𝛼2 CARDINAL iajs-3596 85 1 2 CARDINAL iajs-3596 85 2 𝐹2 CARDINAL iajs-3596 85 3 β„΄3 CARDINAL iajs-3596 87 1 β„΄3 CARDINAL iajs-3596 87 2 βˆ’ 𝛼5 PERSON iajs-3596 87 3 3 4 DATE iajs-3596 88 1 ++ π‘˜1 2π‘˜2 4 DATE iajs-3596 89 1 βˆ’ 𝛼2+𝛼5 βˆ’ 𝛼6)βˆ’π‘˜1(𝛼3+𝛼5 ORG iajs-3596 90 1 3 4 DATE iajs-3596 91 1 3 CARDINAL iajs-3596 91 2 𝐹3 CARDINAL iajs-3596 92 1 β„΄3 CARDINAL iajs-3596 94 1 β„΄3 CARDINAL iajs-3596 96 1 3 4 DATE iajs-3596 97 1 2πœ” 4 DATE iajs-3596 97 2 2𝛼4 CARDINAL iajs-3596 97 3 2 4 DATE iajs-3596 97 4 2𝛼4 CARDINAL iajs-3596 98 1 4 CARDINAL iajs-3596 99 1 4 CARDINAL iajs-3596 99 2 2 CARDINAL iajs-3596 99 3 3 CARDINAL iajs-3596 99 4 4 CARDINAL iajs-3596 100 1 1 CARDINAL iajs-3596 100 2 𝕽(𝓐𝑯𝑬 LOC iajs-3596 100 3 1 8 DATE iajs-3596 101 1 2π‘˜1 CARDINAL iajs-3596 104 1 2πœ”(2𝛼4 CARDINAL iajs-3596 104 2 2𝛼4 CARDINAL iajs-3596 105 1 8𝛼4 + 4π‘Ž6 DATE iajs-3596 108 1 two CARDINAL iajs-3596 108 2 π’œπ»πΈ ORG iajs-3596 109 1 𝑏1 NORP iajs-3596 109 2 𝑏2 GPE iajs-3596 109 3 10 CARDINAL iajs-3596 109 4 β€’ CARDINAL iajs-3596 109 5 π’œπ»πΈ ORG iajs-3596 109 6 𝑏2 GPE iajs-3596 109 7 β€’ CARDINAL iajs-3596 109 8 π’œπ»πΈ ORG iajs-3596 109 9 βŠ–β„¬π»πΈ ORG iajs-3596 109 10 βˆ’ 𝑏2 PERSON iajs-3596 109 11 βˆ’ 𝑏1;min(π‘˜1 ORG iajs-3596 109 12 β€’ CARDINAL iajs-3596 109 13 π’œπ»πΈ ORG iajs-3596 109 14 𝑏2 GPE iajs-3596 109 15 ihjpas PERSON iajs-3596 110 1 2025 CARDINAL iajs-3596 110 2 38 CARDINAL iajs-3596 110 3 1 CARDINAL iajs-3596 112 1 ℷ𝛼2 ORG iajs-3596 113 1 0 5 CARDINAL iajs-3596 113 2 9),(20 CARDINAL iajs-3596 114 1 ∈ ORG iajs-3596 115 1 1 ≀ QUANTITY iajs-3596 115 2 1 ≀ QUANTITY iajs-3596 115 3 6 CARDINAL iajs-3596 117 1 1 CARDINAL iajs-3596 117 2 21,22 DATE iajs-3596 118 1 2 CARDINAL iajs-3596 118 2 1 CARDINAL iajs-3596 118 3 2 DATE iajs-3596 119 1 3 CARDINAL iajs-3596 119 2 1 CARDINAL iajs-3596 120 1 1 CARDINAL iajs-3596 121 1 1 CARDINAL iajs-3596 121 2 2 CARDINAL iajs-3596 121 3 1 CARDINAL iajs-3596 121 4 2 CARDINAL iajs-3596 121 5 1 CARDINAL iajs-3596 121 6 2 CARDINAL iajs-3596 121 7 11 CARDINAL iajs-3596 121 8 12 CARDINAL iajs-3596 121 9 1𝑛 CARDINAL iajs-3596 122 1 1 CARDINAL iajs-3596 122 2 21 CARDINAL iajs-3596 122 3 22 CARDINAL iajs-3596 122 4 2𝑛 CARDINAL iajs-3596 122 5 2 CARDINAL iajs-3596 122 6 4 CARDINAL iajs-3596 123 1 5 CARDINAL iajs-3596 123 2 𝕽(π‘‘β„Žπ‘’ DATE iajs-3596 124 1 6 CARDINAL iajs-3596 125 1 7 CARDINAL iajs-3596 126 1 8 CARDINAL iajs-3596 127 1 7 CARDINAL iajs-3596 127 2 23 CARDINAL iajs-3596 127 3 π‘€π‘Žπ‘₯ GPE iajs-3596 127 4 4Μƒ CARDINAL iajs-3596 127 5 1+6Μƒ CARDINAL iajs-3596 127 6 2βˆ’2Μƒ 6Μƒ DATE iajs-3596 127 7 2+3Μƒ CARDINAL iajs-3596 128 1 2025 CARDINAL iajs-3596 128 2 38 CARDINAL iajs-3596 128 3 1 CARDINAL iajs-3596 128 4 423 𝑠. QUANTITY iajs-3596 128 5 1+3Μƒ CARDINAL iajs-3596 128 6 2 ≀ 5Μƒ PERCENT iajs-3596 128 7 1+ CARDINAL iajs-3596 128 8 2 ≀ 2Μƒ CARDINAL iajs-3596 128 9 1 CARDINAL iajs-3596 128 10 2 CARDINAL iajs-3596 128 11 0 CARDINAL iajs-3596 128 12 1 CARDINAL iajs-3596 128 13 0,2,4,6,8,10,12;πœ”2)⨂ CARDINAL iajs-3596 128 14 1 CARDINAL iajs-3596 128 15 2 ≀ MONEY iajs-3596 128 16 βˆ’4,βˆ’2,0,2,4,6,8;πœ”2)⨂ ORG iajs-3596 128 17 1⨁(βˆ’5,βˆ’3,βˆ’1,1,3,5,7;πœ”2)⨂ CARDINAL iajs-3596 128 18 2 ≀ CARDINAL iajs-3596 128 19 1 CARDINAL iajs-3596 128 20 2 CARDINAL iajs-3596 128 21 0 CARDINAL iajs-3596 129 1 first ORDINAL iajs-3596 130 1 π‘€π‘Žπ‘₯ PERSON iajs-3596 130 2 π‘€π‘Žπ‘₯ PERSON iajs-3596 130 3 1 CARDINAL iajs-3596 130 4 0,2,4,6,8,10,12;πœ”2)⨂ CARDINAL iajs-3596 130 5 π‘€π‘Žπ‘₯ GPE iajs-3596 130 6 1 CARDINAL iajs-3596 132 1 2 ⨁(βˆ’4,βˆ’2,0,2,4,6,8 QUANTITY iajs-3596 132 2 π‘€π‘Žπ‘₯ πœ”β€² PERSON iajs-3596 132 3 π‘€π‘Žπ‘₯ GPE iajs-3596 132 4 π‘€π‘Žπ‘₯ GPE iajs-3596 132 5 2 CARDINAL iajs-3596 132 6 0,2,4,6,8,10,12 ORG iajs-3596 132 7 1 CARDINAL iajs-3596 132 8 2 CARDINAL iajs-3596 132 9 π‘€π‘Žπ‘₯ πœ”β€² PERSON iajs-3596 132 10 2⨁(βˆ’7,βˆ’3,1,5,9,13,17;min CARDINAL iajs-3596 132 11 2 ≀ MONEY iajs-3596 132 12 βˆ’4,βˆ’2,0,2,4,6,8;πœ”2)⨂ ORG iajs-3596 132 13 1⨁(βˆ’5,βˆ’3 CARDINAL iajs-3596 132 14 2 ≀ CARDINAL iajs-3596 132 15 1 CARDINAL iajs-3596 132 16 2 CARDINAL iajs-3596 132 17 0 CARDINAL iajs-3596 132 18 second ORDINAL iajs-3596 132 19 π‘€π‘Žπ‘₯ GPE iajs-3596 132 20 2⨁(βˆ’7,βˆ’3,1,5,9,13,17;min CARDINAL iajs-3596 132 21 ihjpas PERSON iajs-3596 133 1 2025 CARDINAL iajs-3596 133 2 38 CARDINAL iajs-3596 133 3 1 CARDINAL iajs-3596 133 4 424 CARDINAL iajs-3596 133 5 1⨁(βˆ’3,βˆ’1,1,3,5,7,9 CARDINAL iajs-3596 133 6 2⨁1̃⨂ CARDINAL iajs-3596 133 7 1⨁ ≀ MONEY iajs-3596 133 8 βˆ’4,βˆ’2,0,2,4,6,8;πœ”2)⨂ ORG iajs-3596 133 9 1⨁(βˆ’5,βˆ’3 CARDINAL iajs-3596 133 10 2⨁1̃⨂ CARDINAL iajs-3596 133 11 2 ≀ CARDINAL iajs-3596 133 12 1 CARDINAL iajs-3596 133 13 2 CARDINAL iajs-3596 133 14 1 CARDINAL iajs-3596 133 15 2 CARDINAL iajs-3596 133 16 0Μƒ CARDINAL iajs-3596 133 17 1 CARDINAL iajs-3596 133 18 first ORDINAL iajs-3596 133 19 2 CARDINAL iajs-3596 133 20 2 CARDINAL iajs-3596 133 21 π‘¨πŸŽ CARDINAL iajs-3596 133 22 βˆ’2,2,6,10 ORG iajs-3596 133 23 1 CARDINAL iajs-3596 133 24 βˆ’15,βˆ’11,βˆ’7 ORG iajs-3596 133 25 1 CARDINAL iajs-3596 133 26 5,9,13,17 CARDINAL iajs-3596 133 27 1 CARDINAL iajs-3596 133 28 1 CARDINAL iajs-3596 133 29 1,3,5,7 CARDINAL iajs-3596 133 30 1 CARDINAL iajs-3596 133 31 3,5,7,9 DATE iajs-3596 133 32 1 CARDINAL iajs-3596 133 33 1Μƒ;1 CARDINAL iajs-3596 133 34 5,7,9,11 CARDINAL iajs-3596 134 1 1 CARDINAL iajs-3596 134 2 5/3 CARDINAL iajs-3596 134 3 π‘¨πŸ ORG iajs-3596 134 4 2,4,6,8 CARDINAL iajs-3596 134 5 1 CARDINAL iajs-3596 134 6 1,3,5,7 CARDINAL iajs-3596 134 7 1 CARDINAL iajs-3596 134 8 1Μƒ;1 CARDINAL iajs-3596 134 9 2,4,6,8 CARDINAL iajs-3596 134 10 1 CARDINAL iajs-3596 134 11 2/1 CARDINAL iajs-3596 134 12 β€²ΜƒβŠ– ORG iajs-3596 134 13 β€²ΜƒβŠ– ORG iajs-3596 134 14 2 CARDINAL iajs-3596 135 1 1 CARDINAL iajs-3596 135 2 1 CARDINAL iajs-3596 135 3 β„œ(βˆ’4,βˆ’2,0,2,4,6,8 PERSON iajs-3596 135 4 1 CARDINAL iajs-3596 135 5 1 CARDINAL iajs-3596 135 6 5 3 DATE iajs-3596 135 7 2 1 CARDINAL iajs-3596 135 8 5 3 DATE iajs-3596 135 9 2 CARDINAL iajs-3596 135 10 1 CARDINAL iajs-3596 136 1 1 CARDINAL iajs-3596 139 1 1 3 CARDINAL iajs-3596 139 2 𝐴0 β€² TIME iajs-3596 140 1 3 CARDINAL iajs-3596 140 2 3 CARDINAL iajs-3596 141 1 π‘¨πŸŽ CARDINAL iajs-3596 141 2 5,11,17 CARDINAL iajs-3596 141 3 1 CARDINAL iajs-3596 141 4 6,12,18 CARDINAL iajs-3596 141 5 1 CARDINAL iajs-3596 141 6 0,0 CARDINAL iajs-3596 141 7 0 CARDINAL iajs-3596 141 8 0;1 DATE iajs-3596 141 9 βˆ’7.3 PERSON iajs-3596 141 10 βˆ’2.6,2,6.6 ORG iajs-3596 141 11 11.3,16,20.6 CARDINAL iajs-3596 141 12 1 CARDINAL iajs-3596 141 13 1,1.6,2.3 DATE iajs-3596 141 14 1 CARDINAL iajs-3596 141 15 1 CARDINAL iajs-3596 141 16 0,0 CARDINAL iajs-3596 141 17 0.3 CARDINAL iajs-3596 141 18 0 CARDINAL iajs-3596 141 19 0 CARDINAL iajs-3596 141 20 1 CARDINAL iajs-3596 141 21 2.3,3,3.6 CARDINAL iajs-3596 141 22 1 CARDINAL iajs-3596 141 23 βˆ’6.3 GPE iajs-3596 141 24 4.3,7,9.6 CARDINAL iajs-3596 141 25 1 CARDINAL iajs-3596 141 26 2.7,5.3,8 CARDINAL iajs-3596 141 27 1 CARDINAL iajs-3596 141 28 0 DATE iajs-3596 141 29 0 CARDINAL iajs-3596 141 30 1 CARDINAL iajs-3596 141 31 0,0 CARDINAL iajs-3596 141 32 1 CARDINAL iajs-3596 141 33 1 CARDINAL iajs-3596 141 34 3,5.6,8.3 CARDINAL iajs-3596 141 35 1 CARDINAL iajs-3596 141 36 1 CARDINAL iajs-3596 141 37 4 CARDINAL iajs-3596 141 38 ihjpas PERSON iajs-3596 142 1 2025 CARDINAL iajs-3596 142 2 38 CARDINAL iajs-3596 142 3 1 CARDINAL iajs-3596 142 4 425 CARDINAL iajs-3596 142 5 4 CARDINAL iajs-3596 143 1 βˆ’7.6 ORG iajs-3596 143 2 0 DATE iajs-3596 143 3 6.5,15.2,22.7 DATE iajs-3596 143 4 1 CARDINAL iajs-3596 143 5 βˆ’7.5 ORG iajs-3596 143 6 0 DATE iajs-3596 143 7 22.8 CARDINAL iajs-3596 143 8 1 CARDINAL iajs-3596 143 9 βˆ’14.9 DATE iajs-3596 143 10 βˆ’7.6 GPE iajs-3596 143 11 βˆ’0.3,6.9 PERSON iajs-3596 143 12 14.3,21.6,28.9 DATE iajs-3596 143 13 1 CARDINAL iajs-3596 143 14 βˆ’2.4 ORG iajs-3596 143 15 1.2,2.3,3.5 CARDINAL iajs-3596 143 16 1 CARDINAL iajs-3596 143 17 2.1,3.3,4.6 CARDINAL iajs-3596 143 18 1 CARDINAL iajs-3596 143 19 1 CARDINAL iajs-3596 143 20 0,0 CARDINAL iajs-3596 143 21 0.06 CARDINAL iajs-3596 143 22 1 CARDINAL iajs-3596 143 23 βˆ’0.2 PERSON iajs-3596 143 24 0 CARDINAL iajs-3596 143 25 1 CARDINAL iajs-3596 143 26 βˆ’1.9 PERSON iajs-3596 143 27 2.7,4,5.1 CARDINAL iajs-3596 143 28 1 CARDINAL iajs-3596 143 29 βˆ’2.1 ORG iajs-3596 143 30 βˆ’0.6 GPE iajs-3596 143 31 1 CARDINAL iajs-3596 143 32 2.5 CARDINAL iajs-3596 143 33 4.2,5.7 CARDINAL iajs-3596 143 34 1 CARDINAL iajs-3596 143 35 βˆ’3.1 GPE iajs-3596 143 36 1 CARDINAL iajs-3596 143 37 βˆ’0.2,0,0 ORG iajs-3596 143 38 0 CARDINAL iajs-3596 143 39 1 CARDINAL iajs-3596 143 40 0,0 CARDINAL iajs-3596 143 41 0.6 CARDINAL iajs-3596 143 42 1 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