Constructing general overlap and grouping functions via multiplicative generators

Abstract

General overlap and grouping functions have been proposed by De Miguel et al. as a generalization of overlap and grouping functions respectively. In this paper, we continue to investigate the two functions by their multiplicative generator pairs. First, we introduce the concept of multiplicative generator pairs for general overlap functions and obtain some construction of general overlap functions by them. Then we introduce the notion of general pseudo-automorphism and obtain two construction methods of general overlap functions by general pseudo-automorphism and multiplicative generator pairs. Finally, we give the definition of multiplicative generator pairs for general grouping functions and show some related results by the duality of general overlap and grouping functions.