Convex fuzzy cones of hypervector spaces

Abstract

In this paper we introduce and study convex fuzzy cones of hypervector spaces (or for short hyperspaces) as a generalization of vector spaces as well as for fuzzy vector spaces. A new characterization of fuzzy subhyperspaces is presented as a decomposition of special subhyperspaces. Also, convex cones spanned by non-empty subsets of hypervector spaces (over the real number field) are given. One use fuzzy convex cones, to obtain the generated fuzzy subhyperspaces by fuzzy subsets, that is for a given convex fuzzy cone $\mu$ on real hypervector space $V$, one fined the smallest fuzzy subhyperspace of $V$ containing $\mu$ and the largest fuzzy subhyperspace of $V$ contained in $\mu$.