Flexible Linguistic Rules and Their Numerical Model

Abstract

This chapter introduces and makes an all-round examination of flexible linguistic rules. First, it expounds the concept and types of flexible linguistic rules; discusses the transformation and reduction of them; analyzes the truth domains and logical semantics of flexible linguistic rules; analyzes the mathematical essences and mathematical backgrounds of flexible linguistic rules; and then presents a numerical model of a flexible linguistic rule, which provides a condition for using mathematical approach to realize reasoning and computation with flexible linguistic rules. Besides, it discusses the relationship between the flexible linguistic rules and the flexible linguistic functions and correlations, and gives a query on the practice of treating a fuzzy rule as a fuzzy relation in the traditional fuzzy set theory.