Original scientific paper

Fuzzy bases and the fuzzy dimension of fuzzy vector spaces

Fu-Gui Shi orcid.org/0000-0001-8090-3872 ; Department of Mathematics, School of Science,Beijing Institute of Technology, Beijing, P. R. China
Chun-E Huang ; Department of Thermal Engineering, Tsinghua University, Beijing, P. R. China

Abstract

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 $\widetilde{E}_1$
and $\widetilde{E}_2$ are two fuzzy vector spaces, then
$\dim(\widetilde{E}_1+\widetilde{E}_2)+\dim(\widetilde{E}_1\cap
\widetilde{E}_2)=\dim(\widetilde{E}_1) +\dim(\widetilde{E}_2)$ and
$\dim({\widetilde{\rm{ker }}f})+\dim({\widetilde{\rm{im
}}f})=\dim(\widetilde{E})$ hold without any restricted conditions.
\end{abstract}

Keywords

Fuzzy vector space; fuzzy basis; fuzzy dimension

Hrčak ID:

61798

URI

https://hrcak.srce.hr/61798

Publication date:

8.12.2010.

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