On the probability of error in fuzzy discrimination problems

Abstract

The decision rule which minimizes the probability of error, in the discrimination problem, is the Bayes decision rule which assigns x to the class with the highest a posteriori probability. This rule leads to a partial probability of error which is given by P(e)(x) = 1-max p(C(i)/x) for each x is-an-element-of X. Prior to observing X, the probability of error associated with X is defined as P(e) = E(X)[P(e)(x)]. Tanaka, Okuda and Asai formulated the discrimination problem with fuzzy classes and fuzzy information using the probability of fuzzy events and derived a bound for the average error probability, when the decision in the classifier is made according to the fuzzified Bayes method. The aim is to obtain bounds for the average error probability in terms of (alpha,beta)-information energy, when the decision in the classifier is made according to the fuzzified Bayes method.