Preincavity and fuzzy decision making

Since almost all practical problems are fuzzy and approximate, fuzzy decision making becomes one of the most important practical approaches. However, the resulting problems are frequently complicated and difficult to solve. One effective way to overcome these difficulties is to explore the concavity or generalized concavity properties of the resulting problems. In this paper, we introduce and study the concept of supp-preincave and supp-prequasiincave fuzzy sets. We give characterizations for a supp-preincave fuzzy set in terms of its fuzzy hypograph, and a supp-prequasiincave fuzzy set in terms of its level sets. Furthermore, we also prove that any local maximizer of a supp-preincave fuzzy set is also a global maximizer, and that any strictly local maximizer of a supp-prequasiincave fuzzy set is also a global maximizer. Finally, some aggregation rules for supp-preincave and supp-prequasiincave fuzzy sets are given and some applications to fuzzy decision making are discussed.