Fuzzy Sets and Their Application to Pattern Classification and Clustering Analysis

Abstract

This chapter provides an overview of a conceptual framework for pattern classification and cluster analysis based on the theory of fuzzy sets. There is a connection between the theory of fuzzy sets and pattern classification. The development of the theory of Fuzzy drew much of its initial inspiration from problems relating to pattern classification, especially the analysis of proximity relations and the separation of subsets of Rn by hyperplanes. However, in a more fundamental way, the intimate connection between the theory of fuzzy sets and pattern classification rests on the fact that most real-world classes are fuzzy in nature, in the sense that the transition from membership to nonmembership in such classes is gradual rather than abrupt. Most of the practical problems in pattern classification do not lend themselves to a precise mathematical formulation, with the consequence that the less precise methods based on the linguistic approach prove to be better matched to the imprecision that is intrinsic in such problems.