Fuzzy bases and the fuzzy dimension of fuzzy vector spaces

Abstract

In this paper, new deflnitions of a fuzzy basis and a fuzzy dimension for a fuzzy vector space are presented. A fuzzy basis for a fuzzy vector space (E;) is a fuzzy set fl on E. The cardinality of a fuzzy basis fl is called the fuzzy dimension of (E;). The fuzzy dimension of a flnite dimensional fuzzy vector space is a fuzzy natural number. For a fuzzy vector space, any two fuzzy bases have the same cardinality. If e E1 and e E2 are two fuzzy vector spaces, then dim( e E1 + e