模糊数级数收敛性的度量刻画
发布时间：2018-09-12 06:14
【摘要】：本文主要研究模糊数级数收敛性的度量刻画问题.由以下部分组成:第一章介绍了本文的研究意义和背景以及国内外研究现状.第二章介绍了与本文有关的预备知识.第三章与第四章是本文的主要内容.讨论了模糊数级数在不同度量下的收敛是否可转化为研究其余项是否收敛到零模糊数的问题,结果表明关于大部分度量的收敛都等价于余项收敛到零,模糊数级数是否水平收敛也等价于余项收敛到零模糊数.通过反例说明模糊数级数部分和依endograph度量′收敛与其余项收敛到0不等价.证明了收敛的模糊数级数的极限也是模糊数,通过反例说明模糊数序列与模糊数级数不能相互转化.证明了模糊数级数关于sendograph度量,endograph度量,上确界度量,skorokhod度量,d_p度量以及支集收敛是互相等价的.将模糊数序列分解为区间数序列和正规点为0的单峰模糊数序列之和.在这种分解下,模糊数级数sum from n=1 to ∞(u_n)收敛等价于sum from n=1 to ∞(a_n)收敛且sum from n=1 to ∞(v_n)收敛.讨论这种分解下等式两边的模糊数序列关于同一度量的收敛关系.通过反例说明在sendograph度量,endograph度量,上确界度量下,等式两边模糊数序列收敛是不等价的;证明了度量ρ与上确界度量不等价.讨论了正规点为0的单峰模糊数空间的拓扑性质.通过这种分解导出一个新的度量d_～.讨论模糊数序列依度量d_～收敛与依度量d收敛的关系,结论:模糊数序列依上确界度量d_∞收敛等价于模糊数序列u_n依度量(d_∞)_～收敛。
[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，
本文编号：2238147
[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，
本文编号：2238147
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