On Fuzzy Reasoning Schemes

摘要

In this work we provide a short survey of the most frequently used fuzzy reasoning schemes. The paper is organized as follows: in the first section we introduce the basic notations and definitions needed for fuzzy inference systems; in the second section we explain how the GMP works under Mamdani, Larsen and G odel implications, furthermore we discuss the properties of compositional rule of inference with several fuzzy implications; and in the third section we describe Tsukamoto's, Sugeno's and the simplified fuzzy inference mechanisms in multi-input-single-output fuzzy systems. 1 FUZZY SETS AND LOGIC The use of fuzzy logic and fuzzy reasoning methods are becoming more and more popular in intelligent information systems [30, 31], especially in hyperknowledge support systems [6, 7, 8]; knowledge formation processes in knowledge-based systems [26]; active decision support systems [1, 3, 4, 5, 27]; medical support systems [9, 11, 12, 13, 14, 15, 18, 23]; robotics [16]; financial analysis [2]; control [19, 20, 28, 29] and pattern recognition [22]. Fuzzy sets were introduced by Zadeh [32] as a means of representing and manipulating data that was not precise, but rather fuzzy. # appeared in: C. Carlsson ed., The State of the Art of Information Systems in 2007, TUCS General Publications, No. 16, Turku Centre for Computer Science, Abo, [ISBN 952-12-0492-3], 1999 85-112. 1 Definition 1.1 Let X be a nonempty set. A fuzzy set A in X is characterized by its membership function A : # [0, 1] and A (x) is interpreted as the degree of membership of element x in fuzzy set A for each x # X . Frequently we will write simply A(x) instead of A (x). The family of all fuzzy (sub)sets in X is denoted by F(X). The degree to which the statement "x is A" is true is defined as A(x) -...