A Characterization of Linearly Compensated Hybrid Connectives Used in Fuzzy Classifications

The study of linearly compensated hybrid connectives H = λC +(1−λ)C̄, where C is a t-norm and C̄ represents the dual connective of C, to define aggregation operators for fuzzy classifications is a key point not only in fuzzy sets theory but also in learning processes. Although these operators are not associative, the fact that they can be decomposed into associative functions easily gives rise to n-ary aggregation functions by straightforward iteration. Among the most commonly used t-norms are those of Frank’s family, which are simultaneously t-norms and copulas. The purpose of this paper is to give a characterization of the hybrid connective H , via the properties of the connective C. Necessary and sufficient conditions of H that define C as a copula are given. The characterized hybrid connectives H are used to compute the global adequacy degree of an object in a class from marginal adequacy degrees in a learning system.