Introduction

Abstract

The twenty five years of research in fuzzy sets following the celebrated paper “Fuzzy Sets” by L. A. Zadeh (1965) has revealed the power of this theory as a tool for modeling human information processing. Various attempts have been made to establish mathematical theories that are based on fuzzy sets instead of ordinary sets. Means for understanding human behavior in terms of distribution in metric spaces have been provided, and applications to various fields of information processing have been discussed. Some major applications of fuzzy sets are fuzzy control, artificial intelligence, and fuzzy databases. In these applications, subjective human judgments or expressions in natural language must be interpreted in terms of numbers or distributions in a space of measurements. Fuzzy sets provide an appropriate framework for the mathematical modeling of such systems. Although the subject of this monograph differs somewhat from these major applications, the reasons why fuzzy sets are useful in the subjects described here, are about the same.