Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making
Two important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2373762 |
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| author | Yuchu Qin Xiaolan Cui Meifa Huang Yanru Zhong Zhemin Tang Peizhi Shi |
| author_facet | Yuchu Qin Xiaolan Cui Meifa Huang Yanru Zhong Zhemin Tang Peizhi Shi |
| author_sort | Yuchu Qin |
| collection | DOAJ |
| description | Two important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is aggregation operator (AO). To date, nearly ten AOs of LIVIFNs have been presented. Each AO has its own features and can work well in its specific context. But there is not yet an AO of LIVIFNs that can offer desirable generality and flexibility in aggregating attribute values and capturing attribute interrelationships and concurrently reduce the influence of unreasonable attribute values. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operator and its weighted form, which have such capabilities, are presented in this paper. Firstly, the generalised expressions of the AOs are established by a combination of the Muirhead mean operator and the power average operator under the Archimedean T-norm and T-conorm operations of LIVIFNs. Then the properties of the AOs are explored and proved, their specific expressions are constructed, and the special cases of the specific expressions are discussed. After that, a new method for solving the MAGDM problems based on LIVIFNs is designed on the basis of the weighted AO. Finally, the designed method is illustrated via a practical example, and the presented AOs are evaluated via experiments and comparisons. |
| format | Article |
| id | doaj-art-f50fa6130dd64ff6adfaa17f46648f0d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f50fa6130dd64ff6adfaa17f46648f0d2025-02-03T01:20:27ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/23737622373762Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-MakingYuchu Qin0Xiaolan Cui1Meifa Huang2Yanru Zhong3Zhemin Tang4Peizhi Shi5School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, ChinaSchool of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, ChinaGuangxi Key Laboratory of Intelligent Processing of Computer Images and Graphic, Guilin University of Electronic Technology, Guilin 541004, ChinaSchool of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, ChinaSchool of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UKTwo important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is aggregation operator (AO). To date, nearly ten AOs of LIVIFNs have been presented. Each AO has its own features and can work well in its specific context. But there is not yet an AO of LIVIFNs that can offer desirable generality and flexibility in aggregating attribute values and capturing attribute interrelationships and concurrently reduce the influence of unreasonable attribute values. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operator and its weighted form, which have such capabilities, are presented in this paper. Firstly, the generalised expressions of the AOs are established by a combination of the Muirhead mean operator and the power average operator under the Archimedean T-norm and T-conorm operations of LIVIFNs. Then the properties of the AOs are explored and proved, their specific expressions are constructed, and the special cases of the specific expressions are discussed. After that, a new method for solving the MAGDM problems based on LIVIFNs is designed on the basis of the weighted AO. Finally, the designed method is illustrated via a practical example, and the presented AOs are evaluated via experiments and comparisons.http://dx.doi.org/10.1155/2020/2373762 |
| spellingShingle | Yuchu Qin Xiaolan Cui Meifa Huang Yanru Zhong Zhemin Tang Peizhi Shi Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making Complexity |
| title | Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making |
| title_full | Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making |
| title_fullStr | Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making |
| title_full_unstemmed | Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making |
| title_short | Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making |
| title_sort | linguistic interval valued intuitionistic fuzzy archimedean power muirhead mean operators for multiattribute group decision making |
| url | http://dx.doi.org/10.1155/2020/2373762 |
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