T-overlap functions: A generalization of bivariate overlap functions by t-norms

Abstract

This paper introduces a generalization of overlap functions by extending one of the boundary conditions of its definition. More specifically, instead of requiring that “the considered function is equal to zero if and only if some of the inputs is equal to zero”, we allow the range in which some t-norm is zero. We call such generalization by a t-overlap function with respect to such t-norm. Then we analyze the main properties of t-overlap function and introduce some construction methods.