Fuzzy Logic and Approximate Reasoning

Abstract

Two of the most exemplary capabilities of the human mind are the capability of using perceptions (human knowledge) in purposeful ways and the capability of approximating perceptions by statements in natural language. Understanding these capabilities and emulating them by linguistic approximation is the crux of our thesis. There has been a rapid growth in the number and variety of applications of fuzzy logic. In a narrow sense, fuzzy logic is a logical system which is an extension of multivalued logic and is intended to serve as logic of approximate reasoning. But in a wider sense, fuzzy logic is more or less synonymous with the theory of fuzzy sets. In classical logic the propositional value of a statement is either true (1) or false (0) but in lukasiewicz logic we gave value as a truthfulness to a certain proposition between [0, 1]. As a generalization of many valued logic, fuzzy logic was established in order to deal with those fuzzy propositions and to underlie approximate reasoning. We have calculated the fuzzy truth values and compare the results of different operations (conjunction, disjunction etc) with the approach to Baldwin's (1979) and with the help of modus ponens law (If p → q and p then q .).There are many chemical reactions that are very sensitive and a little change in temperature and particle size can create serious problems. We have developed the idea of approximate reasoning and fuzzy logic to find the approximate value of reaction rate with the given conditions by means of the extended modus ponens law. The methodology is very simple and can be applied to several other chemical reactions in the similar way by connecting AND and OR operations. The result Q can be found by the fuzzy relation equation Q = P o R where "o" is the max-min composition of P and R operation. Result Q for the certain situation is in the form of fuzzy set, in which we choose the value with maximum membership degree.iv