【摘要】：本文主要研究模糊數(shù)級數(shù)收斂性的度量刻畫問題.由以下部分組成:第一章介紹了本文的研究意義和背景以及國內外研究現(xiàn)狀.第二章介紹了與本文有關的預備知識.第三章與第四章是本文的主要內容.討論了模糊數(shù)級數(shù)在不同度量下的收斂是否可轉化為研究其余項是否收斂到零模糊數(shù)的問題,結果表明關于大部分度量的收斂都等價于余項收斂到零,模糊數(shù)級數(shù)是否水平收斂也等價于余項收斂到零模糊數(shù).通過反例說明模糊數(shù)級數(shù)部分和依endograph度量′收斂與其余項收斂到0不等價.證明了收斂的模糊數(shù)級數(shù)的極限也是模糊數(shù),通過反例說明模糊數(shù)序列與模糊數(shù)級數(shù)不能相互轉化.證明了模糊數(shù)級數(shù)關于sendograph度量,endograph度量,上確界度量,skorokhod度量,d_p度量以及支集收斂是互相等價的.將模糊數(shù)序列分解為區(qū)間數(shù)序列和正規(guī)點為0的單峰模糊數(shù)序列之和.在這種分解下,模糊數(shù)級數(shù)sum from n=1 to ∞(u_n)收斂等價于sum from n=1 to ∞(a_n)收斂且sum from n=1 to ∞(v_n)收斂.討論這種分解下等式兩邊的模糊數(shù)序列關于同一度量的收斂關系.通過反例說明在sendograph度量,endograph度量,上確界度量下,等式兩邊模糊數(shù)序列收斂是不等價的;證明了度量ρ與上確界度量不等價.討論了正規(guī)點為0的單峰模糊數(shù)空間的拓撲性質.通過這種分解導出一個新的度量d_～.討論模糊數(shù)序列依度量d_～收斂與依度量d收斂的關系,結論:模糊數(shù)序列依上確界度量d_∞收斂等價于模糊數(shù)序列u_n依度量(d_∞)_～收斂。
[Abstract]:In this paper, we study the metric characterization of the convergence of fuzzy series. It is composed of the following parts: the first chapter introduces the significance and background of this paper and the current research situation at home and abroad. The second chapter introduces the preparatory knowledge related to this paper. The third and fourth chapters are the main contents of this paper. This paper discusses whether the convergence of fuzzy number series under different metrics can be transformed into studying whether the rest of the items converge to zero fuzzy numbers. The results show that the convergence of most of the measures is equivalent to the convergence of the remainder to zero. Whether the series of fuzzy numbers converges horizontally is equivalent to the convergence of the remainder to zero fuzzy numbers. It is shown by a counterexample that the convergence of the partial sum of the series of fuzzy numbers according to the endograph metric is not equivalent to the convergence of the other terms to zero. It is proved that the limit of convergent series of fuzzy numbers is also fuzzy number, and it is proved by counterexample that the sequence of fuzzy numbers and the series of fuzzy numbers cannot be transformed mutually. It is proved that the series of fuzzy numbers are equivalent to each other in terms of the sendograph metric and the upper bound metric Skorokhod metric d _ p metric and the convergence of the branch set. The fuzzy number sequence is decomposed into the sum of interval number sequence and unimodal fuzzy number sequence with normal point 0. Under this decomposition, the convergence of the fuzzy number series sum from nn 1 to 鈭，

本文編號：2238147