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An index for ranking fuzzy numbers by belief feature. (English) Zbl 1187.90161

Summary: The aim of this paper is to explore the belief feature in ranking fuzzy algorithms, because it is a characteristic of great importance in fuzzy membership functions. Currently, many algorithms adopt the concept of \(\alpha\)-cuts to solve the ranking of fuzzy numbers. The calculating procedures have been largely simplified. However, these algorithms do not take belief into account, so their fuzzy ranking theories cannot fully demonstrate the character of fuzzy membership functions. In this paper, the information provided by \(\alpha\)-cuts is discussed from the viewpoint of belief. At the same time, the \(\alpha\)-cuts fuzzy operation and the belief feature are integrated to investigate the fuzzy ranking algorithms. Therefore, the algorithm presented in this paper can fully show the membership and characteristics of the original fuzzy function.

MSC:

90B50 Management decision making, including multiple objectives
03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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