The role of properties of the membership function in construction of fuzzy sets ranking

Abstract

The paper presents a several new definitions of concepts regarding the properties of fuzzy sets in the aspect of their use in decision support processes. These are concepts such as the image and counter – image of the fuzzy set, the proper fuzzy set, the fuzzy support and the ranking of fuzzy set. These concepts can be important in construction decision support algorithms. Particularly a lot of space was devoted to the study of the properties of membership function of the fuzzy set as a result of operations on fuzzy sets. Two additional postulates were formulated that should be fulfilled by the membership function product of fuzzy sets in decision making.