本文選題：模糊數(shù)商空間 + 中點函數(shù)��； 參考：《南京師范大學》2017年碩士論文

【摘要】：模糊數(shù)理論是模糊分析學的重要組成部分.由對稱模糊數(shù)引入的等價關系確定的模糊數(shù)商空間受到許多學者的關注.本文主要研究模糊數(shù)商空間F/(?)的代數(shù)性質、收斂結構,以及函數(shù)列的一致收斂等問題.主要內容有以下三個方面:一、首先給出模糊數(shù)等價類加法的具體表示,研究等價類加法與中點函數(shù)以及Mares核之間的關系.證明了模糊數(shù)商空間F/(?)和所有(0,1]上左連續(xù),0點右連續(xù)的有界變差函數(shù)全體V[0,1]之間同構,并指出(F/(?),+,.)是實數(shù)域上的線性空間.二、研究模糊數(shù)商空間F/(?)中在度量dsup意義下序列收斂的一些性質.并和F/(?)意義下的收斂對比,證明了F/(?)意義下的收斂強于dsup意義下的收斂.模糊數(shù)商空間(F/(?),+)關于上述兩種收斂均成為拓撲群.且(F/(?),dsup)為線性度量空間.給出了模糊數(shù)商空間中序列水平收斂的概念,得到了模糊數(shù)商空間中序列水平收斂的一個充要條件.三、在度量dsup意義下,給出在[a,b]→F/(?)上的函數(shù)列一致收斂的定義,證明了模糊數(shù)商空間中一致收斂函數(shù)列的極限函數(shù)保連續(xù)性和�？煞e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.
【學位授予單位】：南京師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O159

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相關期刊論文 前1條

1 方錦暄;關于Fuzzy拓撲群[J];科學通報;1984年11期

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本文編號：2066987