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Fuzzy hypervector spaces based on fuzzy singletons. (English) Zbl 1222.03057
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.
MSC:
03E72Fuzzy set theory
15A03Vector spaces, linear dependence, rank
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References:
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