两个基本定理在模糊数度量空间的推广  

The extension of two basic theorem in fuzzy number space with supremum metric

作　　者：吴从炘[1] 李洪亮[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2008年第2期141-143,148,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10571035)

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,那么un收敛,并且lim/(n→∞)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。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.

关 键 词：模糊数 确界度量 单调收敛定理 

分 类 号：O177.3[理学—数学]