On Distributive Laws of Uninorms Over Overlap and Grouping Functions

Overlap and grouping functions, as two new classes of special binary aggregation functions, have been investigated by several authors for applications in image processing, decision making, classification, and fuzzy community detection problems. On the other hand, after studied the distributive law between two operations, the distributive laws among particular binary aggregation functions become an interesting and natural research area. In this paper, we continue to discuss this topic for uninorms and overlap and grouping functions. First, we give some basic properties for the distributive law of uninorms over overlap functions. Second, we study this distributive law when the uninorms belong to one of the usual classes the family of idempotent uninorms, representable uninorms or uninorms continuous on Finally, we investigate the distributive law of uninorms over grouping functions by an analogous way.