模糊数学中积分不等式以及分配方程的研究
发布时间：2018-09-12 07:46
【摘要】：1965年L.A.Zadeh给出了模糊集的概念,随着模糊集理论的不断研究和深入,越来越多的学者研究模糊积分不等式.而且积分不等式在处理实际问题中起到了重要作用,我们也在此基础上研究了几类积分不等式以及聚合算子的分配方程.本文二三章主要研究了模糊积分不等式,第四章研究了 semi-t-operator关于semi-nullnorms的分配方程.全文共分为五个章节,各章节内容如下:第2章研究了 Hermite-Hadamard类型的积分不等式以及Sandaor类型的积分不等式.首先利用r-凸函数和Sugeno积分的性质对经典的Sandor类型的不等式进行模糊化处理,得到其模糊积分不等式.这里通过对r和被积函数f三种不同取值的讨论,得到了不同类型的Sandor型模糊积分不等式;其次将被积函数推广到Orlicz-凸函数,进而利用其性质将经典的Hermite-Hadamard型不等式进行模糊化处理,这里同样对被积函数进行了三种讨论.第3章研究了Barnes-Godunova-Levin型和Lyapunov型不等式,第一部分将经典的Lyapunov型不等式推广到区间值伪积分,包含两种类型,第一类是将Lyapunov型不等式推广到基于区间值测度的伪积分;第二类是将Lyapunov型不等式推广到基于有界的区间值函数的伪积分.第二部分研究了 Barnes-Godunova-Levin型不等式,首先利用伪积分的定义和性质对Barnes-Godunova-Levin型不等式进行推广,其次对测度进行处理,通过对测度的区间化,给出区间值测度定义,进而将Barnes-Godunova-Levin型不等式推广到区间值测度的区间值伪积分.第4章研究了 semi-t-operator关于semi-nullnorms的分配方程.第5章首先给出了本文的结论和展望.
[Abstract]:L.A.Zadeh gave the concept of fuzzy set in 1965. With the continuous research and deepening of fuzzy set theory, more and more scholars studied fuzzy integral inequality. Moreover, integral inequality plays an important role in dealing with practical problems. On this basis, we also study several kinds of integral inequalities and the distribution equations of aggregation operators. In chapter 2 and 3, the fuzzy integral inequality is studied. In the fourth chapter, semi-t-operator 's distribution equation about semi-nullnorms is studied. The whole paper is divided into five chapters. The contents of each chapter are as follows: chapter 2 studies the integral inequality of Hermite-Hadamard type and the integral inequality of Sandaor type. Firstly, by using the properties of r-convex function and Sugeno integral, the classical Sandor type inequality is fuzzy treated, and its fuzzy integral inequality is obtained. In this paper, three different values of r and f are discussed, and different types of fuzzy integral inequalities of Sandor type are obtained. Secondly, the integrable function is generalized to Orlicz- convex function. Furthermore, the classical Hermite-Hadamard type inequality is fuzzied by its properties. Three kinds of integrable functions are also discussed in this paper. In chapter 3, Barnes-Godunova-Levin type and Lyapunov type inequality are studied. In the first part, the classical Lyapunov type inequality is generalized to interval valued pseudo integral, which includes two types. The first kind is to extend Lyapunov type inequality to pseudo integral based on interval valued measure. The second is the extension of Lyapunov type inequality to pseudo integral based on bounded interval valued function. In the second part, we study the Barnes-Godunova-Levin type inequality. Firstly, we generalize the Barnes-Godunova-Levin type inequality by using the definition and property of pseudo integral. Secondly, we deal with the measure and give the definition of interval valued measure by means of interval measure. Then the Barnes-Godunova-Levin type inequality is extended to the interval valued pseudo integral of interval valued measure. In chapter 4, semi-t-operator 's partition equation about semi-nullnorms is studied. Chapter 5 first gives the conclusion and prospect of this paper.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178;O159
本文编号：2238364
[Abstract]:L.A.Zadeh gave the concept of fuzzy set in 1965. With the continuous research and deepening of fuzzy set theory, more and more scholars studied fuzzy integral inequality. Moreover, integral inequality plays an important role in dealing with practical problems. On this basis, we also study several kinds of integral inequalities and the distribution equations of aggregation operators. In chapter 2 and 3, the fuzzy integral inequality is studied. In the fourth chapter, semi-t-operator 's distribution equation about semi-nullnorms is studied. The whole paper is divided into five chapters. The contents of each chapter are as follows: chapter 2 studies the integral inequality of Hermite-Hadamard type and the integral inequality of Sandaor type. Firstly, by using the properties of r-convex function and Sugeno integral, the classical Sandor type inequality is fuzzy treated, and its fuzzy integral inequality is obtained. In this paper, three different values of r and f are discussed, and different types of fuzzy integral inequalities of Sandor type are obtained. Secondly, the integrable function is generalized to Orlicz- convex function. Furthermore, the classical Hermite-Hadamard type inequality is fuzzied by its properties. Three kinds of integrable functions are also discussed in this paper. In chapter 3, Barnes-Godunova-Levin type and Lyapunov type inequality are studied. In the first part, the classical Lyapunov type inequality is generalized to interval valued pseudo integral, which includes two types. The first kind is to extend Lyapunov type inequality to pseudo integral based on interval valued measure. The second is the extension of Lyapunov type inequality to pseudo integral based on bounded interval valued function. In the second part, we study the Barnes-Godunova-Levin type inequality. Firstly, we generalize the Barnes-Godunova-Levin type inequality by using the definition and property of pseudo integral. Secondly, we deal with the measure and give the definition of interval valued measure by means of interval measure. Then the Barnes-Godunova-Levin type inequality is extended to the interval valued pseudo integral of interval valued measure. In chapter 4, semi-t-operator 's partition equation about semi-nullnorms is studied. Chapter 5 first gives the conclusion and prospect of this paper.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178;O159
【参考文献】
相关期刊论文 前2条
1 杨秀丽;宋晓秋;卢威;;基于模糊积分的Sandor型不等式（英文）[J];南京大学学报(数学半年刊);2015年02期
2 宋晓秋;关于(T)Fuzzy积分的讨论[J];中国矿业大学学报;1992年01期
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