Fuzzy analogy based reasoning and classification of fuzzy analogies

Abstract

Conventional research on analogical reasoning (AR, for short) theory has not yet addressed the management of fuzzy matching between two different predicates, though human beings essentially utilize fuzzy matching when they infer analogically. On the other hand, fuzzy logic has been successfully applied to deductive and inductive reasoning to make them more flexible. Although the goal of both fuzzy logic and AR is to achieve more flexible human-like reasoning, there have been few applications of fuzzy logic to analogical reasoning. In this paper, fuzzy-analogy based reasoning (F-ABR), an extension of ABR, is proposed. In ABR, an analogy represents clear partial agreements between two knowledge areas, each of which is described as a set of predicates. In F-ABR, a knowledge area is a set of fuzzy predicates and a fuzzy analogy means fuzzy partial agreements between two knowledge areas. Using fuzzy logic, F-ABR can infer in a way that is more flexible and human-like than conventional ABR. This paper discusses three topics: first, a fuzzy matching method between two fuzzy predicate symbols is described. A fuzzy analogy contains a set of pairs composed of a predicate symbol and a similarity degree, and three methods for calculating the similarity degree are also described. Second, methods for classifying and ordering fuzzy analogies, based mainly on similarity degrees, are introduced. These methods are necessary when selecting a single fuzzy analogy to use in the reasoning process. Finally, the features of each type of fuzzy analogy are analyzed in order to show that many kinds of flexible reasoning can be achieved by selecting a fuzzy analogy.