Fuzzy bases and the fuzzy dimension of fuzzy vector spaces∗
نویسندگان
چکیده
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, μ) is a fuzzy set β on E. The cardinality of a fuzzy basis β is called the fuzzy dimension of (E, μ). 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 Ẽ1 and Ẽ2 are two fuzzy vector spaces, then dim(Ẽ1 + Ẽ2) + dim(Ẽ1 ∩ Ẽ2) = dim(Ẽ1) + dim(Ẽ2) and dim(k̃erf) + dim(ĩmf) = dim(Ẽ) hold without any restricted conditions. AMS subject classifications: 03E72, 08A72
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