On The Conditional Distributivity For Uni-nullnorms Over Uninorms

Aggregation operators play a very important role in fuzzy sets and fuzzy logic theory.Note that nullnorms,uninorms,uni-nullnorms,null-uninorms and2-uninorm are all special aggregation operators,and from the structural point of view,it is found that these operators are constructed from triangular-norms and triangular conorms through a method similar to the order and sum.In particular,the concept of uni-nullnorm is derived by combining uninorm and nullnorm not simply pieced together,but by making them share a basic triangular conorm(or triangular norm).In recent years,the distributivity and conditional distributivity of two aggregate operators have become a research focus and achieved a lot of results.But it is worth noting that there are few researchs on the conditional distributivity of aggregate operators on uninorms with the continuous underlying operators,so This article is mainly devoted to dealing with the conditional distributivity of a uni-nullnorm over a uninorm with the continuous underlying operators and also gives the full characterization of all pairs(,)satisfying this property.Moreover,this paper extends the previous research since the focus is now on a much wider class of uninorms.