Approximate Reasoning in the Knowledge-Based Dynamic Fuzzy Sets

Abstract

Intan and Mukaidono discussed that knowledge plays an important role in determining the membership function of a given fuzzy set by introducing a concept, called Knowledge-based Fuzzy Sets (KFS) in 2002. Here, the membership degree of an element given a fuzzy set is subjectively determined by the knowledge. Every knowledge may have each different membership degree of the element given the fuzzy set. In 1988, Wang et al. extended the concept of fuzzy set, called Dynamic Fuzzy Sets (DFS) by considering that the membership degree of an element given a fuzzy set might be dynamically changeable over the time. Both generalized concepts, KFS and DFS, were hybridized by Intan et al. to be a Knowledge-based Dynamic Fuzzy Set (KDFS). As usually happened in the real-world application, the KDFS showed that a membership function of a given fuzzy set subjectively determined by a certain knowledge may be dynamically changeable over time. Moreover, the concept of fuzzy granularity was discussed dealing with the KDFS. Related to the concept of fuzzy granularity in KDFS, this paper discusses the concept of approximate reasoning of KDFS in representing fuzzy production rules as generally applied in the fuzzy expert system.