期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 26, 期 1, 页码 193-202出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2016.2646749
关键词
Fuzzy preference relations (FPRs); interval valued; intuitionistic; isomorphic multiplicative transitivity; priority vector
资金
- National Natural Science Foundation of China [71571166, 71501135]
- Zhejiang Provincial Natural Science Foundation of China [LY15G010003]
- Zhejiang Provincial Philosophy and Social Science Foundation-Zhijiang Young Talent of Social Science [16ZJQN046YB]
- China Postdoctoral Science Foundation [2016T90863]
- Scientific Research Foundation for Excellent Young Scholars at Sichuan University [2016SCU04A23]
Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation, while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multicriteria decision making (MCDM). This paper aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM. To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations. It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's extension principle. The use of the multiplicative transitivity isomorphism is twofold: 1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and 2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively. Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak transitivity, max-max transitivity, and center-division transitivity. A multiplicative consistency-based multiobjective programming (MOP) model is investigated to derive the priority vector from an IFPR. This model has the advantage of not losing information, as the priority vector representation coincides with that of the input information, which was not the case with the existing methods, where crisp priority vectors were derived as a consequence of the modeling transitivity just for the intuitionistic membership function and not for the intuitionistic nonmembership function. Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model.
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