Fuzzy Implications Based On The Powers Of Pseudo-continuous Uninorms

Fuzzy implication functions are particularly important in fuzzy logic,and they have become the cornerstone of fuzzy control and approximate reasoning and have also been used in many other fields.According to demands,the researchers con-structed many fuzzy implications by different methods and different operators,and each fuzzy implication family will satisfy several common properties.But a special property is not common to fuzzy implication functions,but this prop-erty is closely related to approximate reasoning.Studies have shown that fuzzy implication functions based on powers of continuous triangular have this spe-cial property.According to the dual relationship between the triangular norms and the triangular conorms,the implication function based on the power of the continuous triangular conorms can also be obtained with this special property.Although triangular normms and triangular conorms mode have important,appli-cations in fuzzy set theory and application,there are gaps between triangular norms and triangular conorms,which leads them to have huge defects in describ-ing information aggregation,and uninorms which is thehe promotion of triangular norms and triangular conorms can make up for this deficiency.Under this back-ground and foundation,this paper constructs the fuzzy implica.tion based on the power of pseudo-continuous uninorms,and this U-power implication satisfies this special property.The main work is divided into the following four parts:Chapter 1 introduces the research background and significance of this paper and briefly describes the main work of this paper.Chapter 2 is preliminary knowledge.It mainly reviews the related concepts and properties of triangular norms,triangular conorms,uninorms and pseudo-continuous uninorms,fuzzy implication.Chapter 3 is based on the power of pseudo-continuou uninorms to construct a new fuzzy implication-U-power implication,and gives the structure of different U-power implications corresponding to different pseudo-continuous uninorms.Chapter 4 gives the properties of U-power implication,and mainly draws the following conclusions:(1)U-power implpication satisfies power invariance,that is,the invariance with respect to linguistic modifiers modeled through powers of uninorm which keep the true value of fuzzy conditional invariant:(2)U-power implication satisfies(OP)propert.ies,(IP)properties but it does not satisfy(NP),(EP)and(LIT)properties corresponding to any trigonometric mode T;(3)The expression of the fuzzy negation of U-power implication is related to the structure of the uninorms;(4)If IU sa.tisfies the(C.P(N))property,then N is strictly decreasing.If N is continuous and has fixed points,then,if we know the idempotent element of the basic triangular T of U,we can get,the idempotent element of the basic triangular conorms of U;(5)U-power implication satisfies T-transitvity,that is,there is some t-norm T such that IU satisfy the following in equation:T(IU((x,y),IU(y,z))?IL,(x,z),(?)x,y,z ?[0,1].The innovations of this paper can be summarized as:(1)A new type of fuzzy implication is constructed by means of pseudo-continuous uninorms.This new fuzzy implication satisfies a property closely related to ap-proximation reasoning,and studies some other related properties;(2)The(CP(N))properties of U-power implication are studied and some con-ditions for satisfying the properties of(CP(N))are given.