Generalized linear(convex) combination of overlap functions on bounded lattices

Abstract In the present article, the notion of the generalized linear(convex) combination of overlap functions, which extend the notion of linear(convex) combination of overlap functions on the unit interval to bounded lattices. Moreover, some algebraic and analytical properties such as associativity, idempotency, conjugacy of the generalized combination are investigated. Particularly, we prove that a generalized convex combination Ka,NO,G(x,y) of two arbitrary overlap functions under the condition G(a,N(a)) = 1 L is also an overlap function in the sense of bi-Scott continuous. Furthermore, we introduce an overlap function induced by equivalence classes in the sense of bi-Scott continuous, and discuss some basic properties related to it.