Research On Integrals Inequalities And Distributivity Equation In Fuzzy Mathematics

In 1965,L.A.Zadeh gave the concept of fuzzy set,With the continuous research and deepening of fuzzy set theory,With the development of it,more and more scholars have studied the fuzzy integral inequality.And the integral inequality has played an important role in dealing with practical problems,Furthermore,We also study several kinds of integral inequalities and the distribution equations with aggregate operator.In Chapter 2 and Chapter 3,we mainly study the fuzzy integral inequalities,we study the distribution equation of semi-t-operator with semi-nullnorms in Chapter 4.This paper is constituted by 5 Chapter as follows:In Chapter 2,we study the integral inequality of Hermite-Hadamard and Sandaor types.Firstly,we use the properties of r-convex function and Sugeno integral to fuzzify the classical Sandor type inequality so as to obtain its fuzzified integral inequality.Here we draw different types of Sandor type fuzzy integral inequalities based on three different r and the integrand f.Secondly,we extend the integrand to Orlicz-convex function whose properties are used to fuzzify the classical Hermite-Hadamard type inequality.And we also discuss the integrand f under three circumstances.In Chapter 3,we study the inequalities of Barnes-Godunova-Levin and Lyapunov types.In the first part,we extend the classic Lyapunov type inequality to pseudo-integrals with respect to two interval-valued measures.One defined by pseudo-integrals of interval-valued measure,the other one obtained from pseudo-integrals of bounded interval-valued functions.In the second part,we study the Barnes-Godunova-Levin type inequalities.First we extend the inequalities using the definition and properties of pseudo-integral.Then with the transformation into interval values,we give the defi-nition of interval-valued measure,which extends the Barnes-Godunova-Levin type in-equalities to interval-valued pseudo-integrals of interval-valued measure.In Chapter 4,we investigate the solution of distributivity between semi-nullnorms over semi-t-operations.In Chapter 5,the conclusions and prospects of this paper are summarized.