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.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
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)
关键词
模糊数
确界度量
单调收敛定理
fuzzy number
supremum metric
monotone convergence theorem
