【摘要】：1965年L.A.Zadeh給出了模糊集的概念,隨著模糊集理論的不斷研究和深入,越來越多的學者研究模糊積分不等式.而且積分不等式在處理實際問題中起到了重要作用,我們也在此基礎上研究了幾類積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積分不等式,第四章研究了 semi-t-operator關于semi-nullnorms的分配方程.全文共分為五個章節(jié),各章節(jié)內(nèi)容如下:第2章研究了 Hermite-Hadamard類型的積分不等式以及Sandaor類型的積分不等式.首先利用r-凸函數(shù)和Sugeno積分的性質(zhì)對經(jīng)典的Sandor類型的不等式進行模糊化處理,得到其模糊積分不等式.這里通過對r和被積函數(shù)f三種不同取值的討論,得到了不同類型的Sandor型模糊積分不等式;其次將被積函數(shù)推廣到Orlicz-凸函數(shù),進而利用其性質(zhì)將經(jīng)典的Hermite-Hadamard型不等式進行模糊化處理,這里同樣對被積函數(shù)進行了三種討論.第3章研究了Barnes-Godunova-Levin型和Lyapunov型不等式,第一部分將經(jīng)典的Lyapunov型不等式推廣到區(qū)間值偽積分,包含兩種類型,第一類是將Lyapunov型不等式推廣到基于區(qū)間值測度的偽積分;第二類是將Lyapunov型不等式推廣到基于有界的區(qū)間值函數(shù)的偽積分.第二部分研究了 Barnes-Godunova-Levin型不等式,首先利用偽積分的定義和性質(zhì)對Barnes-Godunova-Levin型不等式進行推廣,其次對測度進行處理,通過對測度的區(qū)間化,給出區(qū)間值測度定義,進而將Barnes-Godunova-Levin型不等式推廣到區(qū)間值測度的區(qū)間值偽積分.第4章研究了 semi-t-operator關于semi-nullnorms的分配方程.第5章首先給出了本文的結論和展望.
[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.
【學位授予單位】：中國礦業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O178;O159

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本文編號：2238364