An overview of fuzzy quantifiers. (II). Reasoning and applications

Although intervalvalued quantifiers are only a special case of general quantifiers, some specific properties and results arise from them, and the authors suggest another approach to interence with fuzzy quantifiers.

Abstract

In the second part of the overview, reasoning with fuzzily defined quantifiers and applications are presented. Possibility based reasoning is summarized in detail. The widely used quantifier extension principle and various reasoning schemas derived from it are discussed. Some disadvantages of the quantifier extension principle are pointed out. Although intervalvalued quantifiers are only a special case of general quantifiers, some specific properties and results arise from them. Furthermore, they suggest another approach to interence with fuzzy quantifiers. Reasoning with quantification and several kinds of qualification is introduced. This kind of reasoning requires a seamless synthesis of probability theory, possibility theory, fuzzy logic and belief theory. At last, the applications of fuzzily defined quantifiers in decision making and fuzzy database systems are introduced.