Fuzzy Systems Modeling: An Introduction

Background

Conventional system modeling techniques suggest constructing a model described by a set of differential or difference equations. This approach is effective only when the underlying system is mathematically well-defined and precisely expressible. They often fail to handle uncertain, vague or ill-defined physical systems, and yet most real-world problems do not obey such precise, idealized, and subjective mathematical rules. According to the incompatibility principle (Zadeh, 1973), as the complexity of a system increases, human’s ability to make precise and significant statements about its behaviors decreases, until a threshold is reached beyond which precision and significance become impossible. Under this principle, Zadeh (1973) proposed a modeling method of human thinking with fuzzy numbers rather than crisp numbers, which had eventually led to the development of various fuzzy modeling techniques later on.