Pattern classification through fuzzy likelihood

This paper introduces a novel way to compute the membership function of a fuzzy set approximating the distribution of some observed data starting with their histogram. This membership function is in turn used to obtain a posteriori probability through a suitable version of the Bayesian formula. The ordering imposed by an overtaking relation between fuzzy numbers translates immediately into a dominance of the a posteriori probability of a class over another for a given observed value. In this way a crisp classification is eventually obtained.