Parameterized fuzzy operators in fuzzy decision making

Abstract

The basic operations of fuzzy sets, such as negation, intersection, and union, usually are computed by applying the one-complement, minimum, and maximum operators to the membership functions of fuzzy sets. However, different decision agents may have different perceptions for these fuzzy operations. In this article, the concept of parameterized fuzzy operators will be introduced. A parameter α will be used to represent the degree of softness. The variance of α captures the differences of decision agents' subjective attitudes and characteristics, which result in their differing perceptions. The defined parameterized fuzzy operators also should satisfy the axiomatic requirements for the traditional fuzzy operators. A learning algorithm will be proposed to obtain the parameter α given a set of training data for each agent. In this article, the proposed parameterized fuzzy operators will be used in individual decision-making problems. An example is given to show the concept and application of the parameterized fuzzy operators. © 2003 Wiley Periodicals, Inc.