Basic theory and algorithms for fuzzy sets and logic

Abstract

Fuzzy sets were first introduced by Zadeh as a method of handling 'real-world' classes of objects. Ambiguities abound in these real-world sets, examples given by Zadeh include the 'class of all real numbers which are much greater than 1, and the 'class of tall men'. Examples of these ambiguous sets are easily found in the process control field, where operators may talk about 'very high temperatures' or a 'slight increase in flowrate'. Conventional set theory is clearly inadequate to handle these ambiguous concepts since set members either do, or do not, belong to a set. For example, consider the set 'tall men' a man who is seven feet tall will clearly belong to the set and one who is four feet tall will not, but what about someone who measures five feet ten inches? Zadeh's solution to this problem was to create the fuzzy set, in which members could have a continuous range of membership ranging from zero, or not belonging, to one indicating definite belonging.