Constructions of general overlap and grouping functions on algebras of infinite-valued Łukasiewicz logic

Abstract The present paper generalizes the notion of general overlap and grouping functions from the bounded lattices to the algebras of infinite-valued Łukasiewicz logic, providing some constructive methods of these functions by means of multiplicative and additive generators. Here we first introduce the notion of general overlap and grouping functions on MV-algebras, and provide some conditions under which an MV-algebra is a multiplicative and an additive integral by using two constructions of general overlap and grouping functions, respectively. Subsequently, we introduce the concept of generators, including multiplicative and additive generators, of general overlap and grouping functions on MV-algebras, and provide the necessary and sufficient conditions of two one-place functions to be multiplicative and additive generators, respectively, discussing the relationship between multiplicative and additive generators of general overlap and grouping functions on MV-algebras.