Based On The Fuzzy Implication Of Abel Semigroups And The Partitioning Of Semi-zero Modes On 2 Uniform Modes

This paper mainly introduces two new fuzzy implications and discusses the distributivity for the semi-nullnorms over 2-uninorms,which includes three specific core elements.Given that the promotion of a generalization of addtive generator of triangular norms which was put forward by Y.Y.Ou and the generation method of R-impl;ication,the first core content of this essay is to use a strictly decreasing function f whose range belongs to Abel semigroup to generate a new fuzzy implication being called Mf-implication.However,we introduce the second core content that is M-implication which is the ordinal sum of a family of Mf-implications according to the definition of ordinal sum implications.Moreover,we also discuss some basic properties of these two fuzzy implications which have been proved to be two new types of fuzzy implication indeed.They are indeed different from the known(S.N)-,R-,Yager' s f-implication and M-implication proposed by Y.Su.Besides,in view of a 2-uninorm covering a uninorm and a semi-uninorm and a semi-uninorm being generation of uninorms by omitting commutativity and as sociativity,the third core content of this thesis discusses the distributivity for semi-nullnorms over 2-uninorm and presents the necessary and sufficient conditions which determines the distributivity for semi-nullnorms has the continuously underlying operators over 2-uninorms.