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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

Sažetak

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 ${\tilde{E}}_1$
and ${\tilde{E}}_2$ are two fuzzy vector spaces, then
$\dim ({\tilde{E}}_1+{\tilde{E}}_2)+\dim ({\tilde{E}}_1\cap {\tilde{E}}_2)=\dim ({\tilde{E}}_1)+\dim ({\tilde{E}}_2)$ and
$\dim (\widetilde{\mathrm{k}\mathrm{e}\mathrm{r}}f)+\dim (\widetilde{\mathrm{i}\mathrm{m}}f)=\dim (\tilde{E})$ hold without any restricted conditions.
\end{abstract}

Ključne riječi

Fuzzy vector space; fuzzy basis; fuzzy dimension

Hrčak ID:

61798

URI

https://hrcak.srce.hr/61798

Datum izdavanja:

8.12.2010.

Posjeta: 3.085 *