Analysis of specificity of fuzzy sets

A comprehensive model for evaluating specificity of fuzzy sets is presented. It is designed in terms of possibility values, independent of the domain of discourse. For a discrete distribution two measures are defined. One is exponential, and the other is logarithmic. The exponential measure is derived from a few intuitively plausible properties of specificity, and the logarithmic measure is dual to nonspecificity in Dempster-Shafer theory. Specificity measures for arbitrary measurable sets are defined as domains of discourse. They can be discrete, finite, or infinite, or, as a measurable set X, have μ(X)<∞ or μ(X)=∞. The framework for measurable domains is built directly, through an extensive use of a technique borrowed from inequalities of mathematical physics. It consists of rearranging a measurable function according to a prespecified pattern