The Distributive And Conditional Distributive Of Several Types Of Aggregation Operators

In recent years,aggregation operators have captured a great number of at-tentions of researchers,since their valuable role in many fields,such as decision-making theory,fuzzy logic,fuzzy implication,economics and so on.In general,we will choose different types aggregation operators by the interests and demands.In this paper,first of all,we study the distributivity between uni-nullnorms and semi-nullnorms.And we acquire the necessary or sufficient conditions and the solutions of the distributivity equation are not more than one.But,we also find that if the semi-nullnorm is distributive over the any aggregation operator,it will make the aggregation operator become idempotent.Next,we investigate the conditional distributivity of T-uninorms and S-uninorms over uninorms with the continuous operators and acquire the necessary and sufficient conditions.Meanwhile,accord-ing to the results what we get,uninorms with the continuous underlying operators will degrade into uninorms G?umin or G?umax but not vice versa.This is be-cause G?umin or G?umax simplifies the structure of the uninorms,in particular,it simplifies the structure of the border of the uninorms.