Modularity conditions between overlap (grouping) function and uni-nullnorm or null-uninorm

摘要

Overlap and grouping functions as two kinds of special continuous, commutative aggregation functions have wide applications in image processing and classification. Modularity conditions between the class of overlap (grouping) functions satisfying O(1,e)=e (G(0,e)=e) and special classes of uninorms, and those of another special class of overlap (grouping) functions over nullnorms have been studied in [49]. In this paper we extend these results to any overlap (grouping) function. Moreover, we study the modularity conditions between overlap (grouping) functions and uni-nullnorms (null-uninorms), which are the generalization of uninorms (nullnorms).