Fuzzy Sets in Pattern Recognition

Abstract

Fuzzy Set Theory is concerned with non-dichotomous structures, i.e., with situations which are not of the either-or-structure, which cannot be characterized by black-or- white, by true-or-false, by certain-or-impossible. These situations are generally considered as containing uncertainty, even though the term “uncertainty” is not defined unequivocally. Often uncertainty is considered to refer to the occurrence of events while vagueness refers to the description of events. Let us consider uncertainty with respect to occurrence first: The statement “The probability of hitting the target is.6” is certainly probabilistic in nature and could well be modelled using classical probability theory. “The chances of winning are good” will already pose some problems, because “good chances” are not well (i.e., crisply) defined. In a phrase like “It is likely that we will make a good profit” the event itself nor its occurrence are well defined. In these situations classical probabilistic models will not even be appropriate for the expression of uncertain occurrences.