Triangular norm‐based cuts and possibility characteristics of triangular intuitionistic fuzzy numbers for decision making |
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Authors: | Zhi‐Hong Yi Hong‐Quan Li |
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Affiliation: | 1. College of Business, Hunan Normal University Changsha, People's Republic of China;2. College of Mathematics and Computer Science, Hunan Normal University, Changsha, People's Republic of China;3. College of Modern Economics and Management, Jiangxi University of Finance and Economics, Nanchang, People's Republic of China |
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Abstract: | Triangular intuitionistic fuzzy numbers (TIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, triangular norm (t‐norm) based cuts of TIFNs are developed to synthesize the membership and nonmembership functions in describing the cut sets, then the possibility characteristics of TIFNs, i.e., the possibility mean, the possibility variance, and the possibility mean‐standard deviation ratio, are given. Thereby, on the ground of the possibility mean‐standard deviation ratio, a ranking method of TIFNs is introduced. With these elements, an approach to multiple attributes decision making (MADM) is proposed and illustrated by a numerical example. It is shown that the approach to MADM comprehensively considers both the membership and nonmembership functions and can lead to objective and reasonable results. |
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Keywords: | triangular intuitionistic fuzzy numbers t‐norms t‐norm‐based cuts multiple attribute decision making |
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