文献类型：期刊文献

英文题名：ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES

作者：Huang, C. E.[1];Shi, F. G.[2]

第一作者：黄春娥

通讯作者：Huang, CE[1]

机构：[1]Beijing Union Univ, Biochem Engn Coll, Beijing 100023, Peoples R China;[2]Beijing Inst Technol, Sch Sci, Dept Math, Beijing 100081, Peoples R China

第一机构：北京联合大学生物化学工程学院

通讯机构：[1]corresponding author), Beijing Union Univ, Biochem Engn Coll, Beijing 100023, Peoples R China.|[1141726]北京联合大学生物化学工程学院;[11417]北京联合大学;

年份：2012

卷号：9

期号：4

起止页码：141-150

外文期刊名：IRANIAN JOURNAL OF FUZZY SYSTEMS

收录：;Scopus(收录号：2-s2.0-84907328450);WOS:【SCI-EXPANDED(收录号:WOS:000314000800010)】；

语种：英文

外文关键词：Fuzzy vector space; Fuzzy basis; Fuzzy dimension; Direct sum

摘要：In this paper, firstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases defined by Shi and Huang, is equivalent to the family of its bases defined by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however, the converse is not true. Finally, fuzzy dimension of direct sum is considered, for a finite number of fuzzy vector spaces and it is proved that fuzzy dimension of their direct sum is equal to the sum of fuzzy dimensions of fuzzy vector spaces.