Fuzzy multiple criteria decision-making via an inverse function-based total utility approach
This work presents ranking alternatives under fuzzy multiple criteria decision making (MCDM) via an inverse function-based total utility approach, where ratings of alternatives versus qualitative criteria as well as importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. Membership functions of the final fuzzy values of alternatives can be developed; some of their properties are investigated and proved. The right utility is obtained from the inverse function of right membership function of the final fuzzy value and the inverse function of maximizing set, while the left utility is obtained from the inverse function of left membership function of the final fuzzy value and the inverse function of minimizing set. Total utility is the sum of the right and left utilities. A larger total utility indicates that the corresponding alternative is more favorable. The ranking of fuzzy numbers can be clearly formulated to increase the applicability of the suggested fuzzy MCDM model. A numerical example demonstrates the feasibility of the proposed method, and some comparisons are provided to reveal robustness and advantages of the proposed method.
KeywordsRanking Fuzzy number Fuzzy MCDM Inverse function Total utility
The authors would like to thank the two anonymous referees, Prof. Genovese and Prof. Bruno for providing very helpful comments and suggestions. Their insights and comments led to a better presentation of the ideas expressed in this paper. This work was supported in part by Ministry of Science and Technology of the Republic of China, Taiwan, under Grant MOST 105-2410-H-218-002.
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Conflict of interest
The author declares that he has no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.