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Ameri, R.; Dehghan, O.

Fuzzy hypervector spaces based on fuzzy singletons. (English) Zbl 1222.03057

Comput. Math. Appl. 61, No. 10, 2933-2943 (2011).
Summary: We introduce and study fuzzy hypervector spaces based on fuzzy singletons. In this regard, by considering the notion of fuzzy singletons, we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset. Then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset \(\mu \) of a hypervector space \(V\) and finally we characterize it in terms of linear independence in the usual sense.

Cited in 4 Documents

MSC:

03E72 Theory of fuzzy sets, etc.
15A03 Vector spaces, linear dependence, rank, lineability

Keywords:

fuzzy hypervector space; fuzzy singleton; fuzzy spanning; fuzzy freeness
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\textit{R. Ameri} and \textit{O. Dehghan}, Comput. Math. Appl. 61, No. 10, 2933--2943 (2011; Zbl 1222.03057)
Full Text: DOI

References:

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