Fuzzy hypervector spaces based on fuzzy singletons

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 μ of a hypervector space V and finally we characterize it in terms of linear independence in the usual sense. © 2011 Elsevier Ltd. All rights reserved.