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.
Highlights
The notion of a hypergroup was introduced by Marty in 1934 [1]
The concept of a fuzzy subset of a nonempty set was introduced by Zadeh in 1965 [7] as a function from a nonempty set X into the unit real interval I = [0, 1]
We study the algebraic nature of fuzzy hypervector spaces under transformation
Summary
The notion of a hypergroup was introduced by Marty in 1934 [1]. Since many researchers have worked on hyperalgebraic structures and developed this theory (for more see [2–4]). In 1990, Tallini introduced the notion of hypervector spaces (see [5, 6]) and studied basic properties of them. In [11], the first author introduced and studied the notion of fuzzy hypervector space over valued fields. The paper provides the suitable tools to define and study the properties of fuzzy hypervector spaces, as a generalization of fuzzy vector spaces, and can be considered as an application of fuzzy sets to hyperstructure theory. In this regard, we study the algebraic nature of fuzzy hypervector spaces under transformation. A fuzzy quotient hyperspace is defined and it is shown that each fuzzy sub-hyperspace of Vμ has a correspondence in a natural way to a fuzzy sub-hyperspaces of V
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
