In fuzzy set theory, classical bivalent sets are usually called crisp sets. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics. [4] A fuzzy set is a pair where is a set (often required to be non-empty) and a membership function.

2013年2月4日 · In the fuzzy set theory, the value of and element is determined via the membership of the element to a fuzzy set—resulting in a value between zero and one (and not just zero or one). Some basic concepts of fuzzy sets are as follows.

Fuzzy set theory is an extension of classical set theory where elements have degree of membership. In real world, there exist much fuzzy knowledge (i.e. vague, uncertain inexact etc). Human thinking and reasoning (analysis, interpretation) frequently involved fuzzy information. Human can give satisfactory answers, which are probably true.

Fuzzy sets can be considered as an extension and gross oversimplification of classical sets. It can be best understood in the context of set membership. Basically it allows partial membership which means that it contain elements that have varying degrees of membership in the set.

Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed between theory and practice.

2019年6月22日 · The first volume contains the basic theory of fuzzy sets and some areas of application. It is intended to provide extensive coverage of the theoretical and applicational approaches to fuzzy sets. Sophisticated formalisms have not been included.

Fuzzy Set Theory was formalized by Professor Lofti Zadeh at the University of California in 1965. He proposed a paradigm shift that first gained acceptance in the Far East and its successful application has ensured its adoption around the world.

2022年1月24日 · Fuzzy set is a set having degrees of membership between 1 and 0. Fuzzy sets are represented with tilde character (~). For example, Number of cars following traffic signals at a particular time out of all cars present will have membership value between [0,1].

2010年5月1日 · In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques.

2011年10月21日 · Fuzzy set is a mathematical model of vague qualitative or quantitative data, frequently generated by means of the natural language. The model is based on the generalization of the classical concepts of set and its characteristic function. The concept of a fuzzy set was published in 1965 by Lotfi A. Zadeh (see also Zadeh 1965).