Another Way Of Constructing Fuzzy Implications And Distributive Equation On The Overlap Or Grouping Functions

According to the diversity of practical application,it is necessary to construct different fuzzy implication.Based on theory of ordinal sum of semigroups,starting from a given class of fuzzy implications,we introduce a method to construct new ordinal sum of fuzzy implications and characterize the necessary and sufficient conditions for the ordinal sum of fuzzy implications to become fuzzy implications.It shows that it extends and unifies the ways of constructing of several current ordinal sums of fuzzy implications.At the end,we discuss some their properties.(And the rusults of this part was submitted to Science and Technology Journal of Shandong University).And then,we aim to study the distributive equation between the overlapping functionO with additive generator pair(?,?)and the uninormUrespectively,and the distributive equation between the grouping function with additive generator pair(?,?)and the uninormUrespectively.Finally,we deduce that the aggregate function A satisfies the necessary and sufficient conditions of the distributive equation on the overlap function O with additive generator pair(?,?)and the grouping function G with additive generator pair(?,?).