模糊数商空间的有关研究

发布时间：2018-06-25 18:01

本文选题：模糊数商空间 + 中点函数　；参考：《南京师范大学》2017年硕士论文

【摘要】：模糊数理论是模糊分析学的重要组成部分.由对称模糊数引入的等价关系确定的模糊数商空间受到许多学者的关注.本文主要研究模糊数商空间F/(?)的代数性质、收敛结构,以及函数列的一致收敛等问题.主要内容有以下三个方面:一、首先给出模糊数等价类加法的具体表示,研究等价类加法与中点函数以及Mares核之间的关系.证明了模糊数商空间F/(?)和所有(0,1]上左连续,0点右连续的有界变差函数全体V[0,1]之间同构,并指出(F/(?),+,.)是实数域上的线性空间.二、研究模糊数商空间F/(?)中在度量dsup意义下序列收敛的一些性质.并和F/(?)意义下的收敛对比,证明了F/(?)意义下的收敛强于dsup意义下的收敛.模糊数商空间(F/(?),+)关于上述两种收敛均成为拓扑群.且(F/(?),dsup)为线性度量空间.给出了模糊数商空间中序列水平收敛的概念,得到了模糊数商空间中序列水平收敛的一个充要条件.三、在度量dsup意义下,给出在[a,b]→F/(?)上的函数列一致收敛的定义,证明了模糊数商空间中一致收敛函数列的极限函数保连续性和保可积性.
[Abstract]:Fuzzy number theory is an important part of fuzzy analysis. The fuzzy number quotient space determined by the equivalent relation of symmetric fuzzy numbers has been paid much attention by many scholars. In this paper, the fuzzy number quotient space F / (?) Some problems such as algebraic properties, convergence structure and uniform convergence of function sequences are discussed. The main contents are as follows: firstly, the concrete representation of the equivalence class addition of fuzzy numbers is given, and the relationship between the equivalence class addition and the midpoint function and the Mares kernel is studied. It is proved that the fuzzy number quotient space F / (?) Isomorphism with all bounded variation functions V [0 ~ 1] on (0 ~ 1), and points out (F / (?) Is a linear space on a real number field. Secondly, the fuzzy number quotient space F / (?) Some properties of sequence convergence in the sense of metric dsup. And F/ (?) It is proved that F / (?) The convergence in the sense of dsup is stronger than that in the sense of dsup. Fuzzy number quotient space (F / (?),) on the above two convergences are topological groups. And (F / (?) dsup) is a linear metric space. In this paper, the concept of sequence horizontal convergence in fuzzy quotient space is given, and a sufficient and necessary condition for sequence horizontal convergence in fuzzy quotient space is obtained. Third, in the sense of measuring dsup, we give the results of [AGB] F / (?) In this paper, we prove the continuity and integrability of limit functions of uniformly convergent function sequences in fuzzy quotient spaces.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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