Fuzzy bases and the fuzzy dimension of fuzzy vector spaces

被引：3
|
作者：
Shi, Fu-Gui [1 ]
Huang, Chun-E [2 ]
机构：
[1] Beijing Inst Technol, Dept Math, Sch Sci, Beijing 100081, Peoples R China
[2] Tsinghua Univ, Dept Thermal Engn, Beijing 100081, Peoples R China
来源：
MATHEMATICAL COMMUNICATIONS | 2010年 / 15卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Fuzzy vector space; fuzzy basis; fuzzy dimension; SET;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, new definitions of a fuzzy basis and a fuzzy dimension for a fuzzy vector space are presented. A fuzzy basis for a fuzzy vector space (E, mu) is a fuzzy set beta on E. The cardinality of a fuzzy basis beta is called the fuzzy dimension of (E, mu). The fuzzy dimension of a finite dimensional fuzzy vector space is a fuzzy natural number. For a fuzzy vector space, any two fuzzy bases have the same cardinality. If (E) over tilde (1) and (E) over tilde (2) are two fuzzy vector spaces, then dim ((E) over tilde (1) + (E) over tilde (2)) + dim ((E) over tilde (1) boolean AND (E) over tilde (2)) = dim((E) over tilde (1)) + dim((E) over tilde (2)) and dim((ker) over tildef) + dim((im) over tildef) = dim((E) over tilde) hold without any restricted conditions
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页码：303 / 310
页数：8
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