Fuzzy Hypervector Spaces

Abstract

The aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. Certain conditions are obtained under which a given fuzzy hypervector space can or cannot be realized as a union of two fuzzy hypervector spaces such that none is contained in the other. The construction of a fuzzy hypervector space generated by a given fuzzy subset of a hypervector space is given. The set of all fuzzy cosets of a fuzzy hypervector space is shown to be a hypervector space. Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained.

Generalized fuzzy subhyperspaces based on fuzzy points

“…Similarly fuzzy algebraic hyperstructures were investigated in many branches ( [8]). Ameri [1] introduced fuzzy subhyperspaces of hypervector spaces in the sense of Scafatti-Tallini [18]. Fuzzy subhyperspaces were studied more in [2], [3] and [13].…”

Soft Hypervector Space and Fuzzy Soft Hypervector Space

“…As a generalization of hypervector spaces, the fuzzy hypervector spaces are studied by Ameri and et. (see [3,4]). Jun et al [8] discussed the applications of fuzzy soft set in BCK/BCI-algebras.…”

On (∈,∈∨qk)-Fuzzy Hyperideals in Ordered LA-Semihypergroups

“…There are several authors who applied the concept of fuzzy sets to algebraic hyperstructures. Ameri and others studied fuzzy sets in hypervector spaces [25], Γ-hyperrings [26], and polygroups [27]. Corsini et al [28] studied semisipmle semihypergroups in terms of hyperideals and fuzzy hyperideals.…”