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两个基本定理在模糊数度量空间的推广
  • ISSN号：1001-7011
  • 期刊名称：《黑龙江大学自然科学学报》
  • 时间：0
  • 分类：O177.3[理学—数学;理学—基础数学]
  • 作者机构：[1]哈尔滨工业大学数学系,哈尔滨150001
  • 相关基金：国家自然科学基金资助项目（10571035）
作者： 吴从炘[1], 李洪亮[1]
关键词： 模糊数, 确界度量, 单调收敛定理, fuzzy number, supremum metric, monotone convergence theorem
中文摘要：

基于模糊数及模糊数度量空间的研究，引入连续模糊数的概念，并给出了模糊数空间中的单调有界序列收敛的一个充分条件：对任意的自然数n,un是模糊数,{un}n=1是模糊数空间中单调减有下界的序列,下确界u是连续模糊数,如果满足lim ua^＋/n→∞（O）=limlim/x→O n→∞un^＋（x）,那么un收敛，并且lim/x→∞D（un,u）=0.在给出一个序列极限换序的引理后，得到了闭区间套定理在模糊数空间中的推广，这个定理的表述和经典的数学分析中的表述基本上完全一致。

英文摘要：

Based on studies of fuzzy number and the fuzzy number space with supremum metric, the definition of continuous fuzzy numbers is given. And a sufficient condition which a monotone bounded sequence in fuzzy number space is convergence is obtained： un is fuzzy number for any nature number,{un}n=1 is nonincreasing bounded sequence in fuzzy number space, let u be the infimum of {un}n=1, u is continuous fuzzy number, then un is conver-gent and lim/n→∞D（un, u） =O. By showing a lemma about changing order of limits of sequence, the extension of nested theorem of closed intervals is obtained in fuzzy number space, it is very similar to the nested theorem in real number space.

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期刊信息
  • 《黑龙江大学自然科学学报》
  • 北大核心期刊（2011版）
  • 主管单位:黑龙江省教育厅
  • 主办单位:黑龙江大学
  • 主编：霍丽华
  • 地址：哈尔滨市学府路74号
  • 邮编：150080
  • 邮箱：hdxb@vip.sohu.com
  • 电话：0451-86608818
  • 国际标准刊号：ISSN：1001-7011
  • 国内统一刊号：ISSN：23-1181/N
  • 邮发代号:14-114
  • 获奖情况:
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  • 被引量:4204