Concepts and Issues

Fuzzy Sets

Fuzzy sets were introduced by Zadeh [351] in 1965 to represent/manipulate data and information possessing nonstatistical uncertainties. It was specifically designed to mathematically represent uncertainty and vagueness and to provide formalized tools for dealing with the imprecision intrinsic to many problems. Fuzzy sets serve as a means of representing and manipulating data that was not precise, but rather fuzzy. Some of the essential characteristics of fuzzy logic relate to the following [356]: (i) In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning; (ii) In fuzzy logic, everything is a matter of degree; (iii) In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables; (iv) Inference is viewed as a process of propagation of elastic constraints; and (v) Any logical system can be fuzzified. There are two main characteristics of fuzzy systems that give them better performance for specific applications: (i) Fuzzy systems are suitable for uncertain or approximate reasoning, especially for systems with mathematical models that are difficult to derive; and (ii) Fuzzy logic allows decision making with estimated values under incomplete or uncertain information.