On the Knowledge-based Dynamic Fuzzy Sets

Abstract

In 1965, Zadeh [1] introduced fuzzy set as a generalization of crisp set by considering membership degrees of elements. That membership degree is represented gradually as a real number in an interval [0, 1]. Wang et al. [2] generalized the concept of fuzzy set, called dynamic fuzzy sets (DFS). In the DFS, each membership degree of an element is given by a membership function dealing with time variable. Thus, the membership degree of an element in a given dynamic fuzzy set might dynamically change according to the time’s variable. In 2002, Intan and Mukaidono [3] proposed an extended concept of fuzzy set, called knowledge-based fuzzy sets (KFS). In the KFS, the membership degree of an element given a fuzzy set is subjectively determined by a single knowledge. The membership degree of an element with respect to a given fuzzy set may be different provided by different knowledge of persons. This paper combines both concepts, DFS and KFS, called knowledge-based dynamic fuzzy sets (KDFS), by realizing that membership function of a given fuzzy set provided by a certain knowledge may be dynamically changed over time. Three kinds of summary fuzzy sets are proposed and discussed. Some basic operations of KDFS are defined. Their properties are verified and examined.