Fuzzy logic: principles, applications, and perspectives

There is a longstanding tradition in science of according much more respect to theories which are quantitative, formal and precise than to those which are qualitiative, informal and approximate in nature. In recent years, however, the validity of this tradition has been called into question by the emergence of artificial intelligence as one of the fundamentally important areas of modem science and technology. More specifically, what has become increasingly obvious is that many of the basic problems relating to the conception and design of complex knowledge-based and robotic systems do not lend themselves to precise solution within the framework of classical logic and probability theory. Thus, to be able to deal with such problems we frequently have no choice but to accept solutions which are suboptimal and inexact. Furthermore, even when precise solutions can be obtained, their cost is generally much higher than that of solutions which are imprecise in nature and yet yield results which fall within the range of acceptability. Seen against this background, fuzzy logic may be viewed as an attempt at formalization of approximate reasoning, which is characteristic of the way in which humans reason in an environment of uncertainty and imprecision. In this perspective, fuzzy logic may be viewed as a generalization of both multivalued logic and probability theory. In relation to these theories, its principal constituents are: (a) a meaning-representation system referred to as test-score semantics for representing the meaning of complex facts, rules and commands expressed in a natural language; and (b) an inferential system for inference under uncertainty which is applicable to knowledge-bases that are imprecise, incomplete or lacking in reliability. In contrast to classical logical systems, the inference processes in fuzzy logic are computational rather than symbolic. Thus, in general, inference in fuzzy logic reduces to the solution of a nonlinear program. This reflects the fact that in fuzzy logic a proposition is interpreted as a constraint on a variable, with constraint propagation playing the role of chaining and aggregation. A branch of fuzzy logic which plays a particularly important role in the representation and inference from commonsense knowledge is that of dispositional logic. As its name implies, this logic deals with dispositions, that is, with propositions which are preponderantly but not necessarily always true, e.g. ,birds can fly, seat belts work, Swedes are blond, etc. A related concept is thatof a subdisposition, e.g. , overeating causes obesity, which may be interpreted as an assertion concerning the increase in a conditional probability which is implicit in the defining proposition. At this juncture, most of the practical applications of fuzzy logic involve three basic concepts: (a) the concept of a linguistic variable, that is, a variable whose values are words or sentences in a natural or synthetic language; (b) the concept of a canonical form, which expresses a proposition as an elastic constraint on a focal variable; and (c) the concept of interpolative reasoning, which provides a means of filling in the gaps in knowledge from which an answer to a query is to be derived. These concepts serve as a basis for the description of qualitative dependencies between two or more variables through a system of fuzzy if-then rules in which the antecedents and consequents are expressed in a canonical form involving linguistic variables. The role played by fuzzy if-then rules in the applications of fuzzy logic is explained and illustrated by examples. Recent advances in fuzzy logic are analyzed and their potential applications are discussed.