NEW RESULTS ON ADDITIVE GENERATOR PAIRS OF OVERLAP AND GROUPING FUNCTIONS

Abstract

In this article, we deeply reveal the relationship between functions θ and ϑ in an overlap function additively generated by an additive generator pair (θ,ϑ), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions θ and ϑ. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions.