On multiplicative generators of overlap and grouping functions

Overlap and grouping functions have been proposed by Bustince et al.. In this paper, we continue investigating the two functions by their multiplicative generator pairs. At first, we introduce the concept of multiplicative generator pair for overlap functions. And then, we investigate the migrativity, homogeneity, idempotency, Archimedean and cancellation properties for the overlap functions obtained by such multiplicative generator pairs. Finally, we give the definition of multiplicative generator pair for grouping functions and show some related results by the duality of overlap and grouping functions.