Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making
Linear Diophantine uncertain linguistic set (LDULS) is a modified variety of the fuzzy set (FS) to manage problematic and inconsistent information in actual life troubles. LDULS covers the grade of truth, grade of falsity, and their reference parameters with the uncertain linguistic term (ULT) with...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/4168124 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560619429036032 |
|---|---|
| author | Tahir Mahmood Izatmand Zeeshan Ali Kifayat Ullah Qaisar Khan Ahmed Alsanad Mogeeb A. A. Mosleh |
| author_facet | Tahir Mahmood Izatmand Zeeshan Ali Kifayat Ullah Qaisar Khan Ahmed Alsanad Mogeeb A. A. Mosleh |
| author_sort | Tahir Mahmood |
| collection | DOAJ |
| description | Linear Diophantine uncertain linguistic set (LDULS) is a modified variety of the fuzzy set (FS) to manage problematic and inconsistent information in actual life troubles. LDULS covers the grade of truth, grade of falsity, and their reference parameters with the uncertain linguistic term (ULT) with a rule 0≤αAMGuAMGx+βANGvAMGx≤1, where 0≤αAMG+βANG≤1. In this study, the principle of LDULS and their useful laws are elaborated. Additionally, the power Einstein (PE) aggregation operator (AO) is a conventional sort of AO utilized in innovative decision-making troubles, which is effective to aggregate the family of numerical elements. To determine the interrelationship between any numbers of arguments, we elaborate the linear Diophantine uncertain linguistic PE averaging (LDULPEA), linear Diophantine uncertain linguistic PE weighted averaging (LDULPEWA), linear Diophantine uncertain linguistic PE geometric (LDULPEG), and linear Diophantine uncertain linguistic PE weighted geometric (LDULPEWG) operators; then, we discuss their useful results. Conclusively, a decision-making methodology is utilized for the multiattribute decision-making (MADM) dilemma with elaborated information. A sensible illustration is specified to demonstrate the accessibility and rewards of the intended technique by comparison with certain prevailing techniques. The intended AOs are additional comprehensive than the prevailing ones to exploit the ambiguous and inaccurate knowledge. Numerous remaining operators are chosen as individual incidents of the suggested one. Ultimately, the supremacy and advantages of the elaborated operators are also discussed with the help of the geometrical form to show the validity and consistency of explored operators. |
| format | Article |
| id | doaj-art-bb4ce850330b4a19b13125a182fdeb7d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-bb4ce850330b4a19b13125a182fdeb7d2025-02-03T01:27:08ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/41681244168124Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision MakingTahir Mahmood0Izatmand1Zeeshan Ali2Kifayat Ullah3Qaisar Khan4Ahmed Alsanad5Mogeeb A. A. Mosleh6Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad, PakistanDepartment of Mathematics & Statistics, International Islamic University Islamabad, Islamabad, PakistanDepartment of Mathematics & Statistics, International Islamic University Islamabad, Islamabad, PakistanDepartment of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Lahore 54000, PakistanDepartment of Mathematics, University of Haripur, Haripur, PakistanSTC’s Artificial Intelligence Chair, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11451, Saudi ArabiaFaculty of Engineering and Information Technology, Taiz University, Taiz 6803, YemenLinear Diophantine uncertain linguistic set (LDULS) is a modified variety of the fuzzy set (FS) to manage problematic and inconsistent information in actual life troubles. LDULS covers the grade of truth, grade of falsity, and their reference parameters with the uncertain linguistic term (ULT) with a rule 0≤αAMGuAMGx+βANGvAMGx≤1, where 0≤αAMG+βANG≤1. In this study, the principle of LDULS and their useful laws are elaborated. Additionally, the power Einstein (PE) aggregation operator (AO) is a conventional sort of AO utilized in innovative decision-making troubles, which is effective to aggregate the family of numerical elements. To determine the interrelationship between any numbers of arguments, we elaborate the linear Diophantine uncertain linguistic PE averaging (LDULPEA), linear Diophantine uncertain linguistic PE weighted averaging (LDULPEWA), linear Diophantine uncertain linguistic PE geometric (LDULPEG), and linear Diophantine uncertain linguistic PE weighted geometric (LDULPEWG) operators; then, we discuss their useful results. Conclusively, a decision-making methodology is utilized for the multiattribute decision-making (MADM) dilemma with elaborated information. A sensible illustration is specified to demonstrate the accessibility and rewards of the intended technique by comparison with certain prevailing techniques. The intended AOs are additional comprehensive than the prevailing ones to exploit the ambiguous and inaccurate knowledge. Numerous remaining operators are chosen as individual incidents of the suggested one. Ultimately, the supremacy and advantages of the elaborated operators are also discussed with the help of the geometrical form to show the validity and consistency of explored operators.http://dx.doi.org/10.1155/2021/4168124 |
| spellingShingle | Tahir Mahmood Izatmand Zeeshan Ali Kifayat Ullah Qaisar Khan Ahmed Alsanad Mogeeb A. A. Mosleh Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making Complexity |
| title | Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making |
| title_full | Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making |
| title_fullStr | Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making |
| title_full_unstemmed | Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making |
| title_short | Linear Diophantine Uncertain Linguistic Power Einstein Aggregation Operators and Their Applications to Multiattribute Decision Making |
| title_sort | linear diophantine uncertain linguistic power einstein aggregation operators and their applications to multiattribute decision making |
| url | http://dx.doi.org/10.1155/2021/4168124 |
| work_keys_str_mv | AT tahirmahmood lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking AT izatmand lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking AT zeeshanali lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking AT kifayatullah lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking AT qaisarkhan lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking AT ahmedalsanad lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking AT mogeebaamosleh lineardiophantineuncertainlinguisticpowereinsteinaggregationoperatorsandtheirapplicationstomultiattributedecisionmaking |