Vague Soft Hypergroups and Vague Soft Hypergroup Homomorphism

We introduce and develop the initial theory of vague soft hyperalgebra by introducing the novel concept of vague soft hypergroups, vague soft subhypergroups, and vague soft hypergroup homomorphism. The properties and structural characteristics of these concepts are also studied and discussed

Homomorphism and quotient of fuzzy k-hyperideals

In [15], we introduced the notion of weak (resp. strong) fuzzy k- hyperideal. In this note we investigate the behavior of them under homomorphisms of semihyperrings. Also we define the quotient of fuzzy weak (resp. strong) k-hyperideals by a regular relation of semihyperring and obtain some results

Term Functions and Fundamental Relation of Fuzzy Hyperalgebras

We introduce and study term functions over fuzzy hyperalgebras. We start from this idea that the set of nonzero fuzzy subsets of a fuzzy hyperalgebra can be organized naturally as a universal algebra, and constructing the term functions over this algebra. We present the form of generated subfuzzy hyperalgebra of a given fuzzy hyperalgebra as a generalization of universal algebras and multialgebras. Finally, we characterize the form of the fundamental relation of a fuzzy hyperalgebra

On Intra-Regular Semihypergroups Through Intuitionistic Fuzzy Sets

The notion of intuitionistic fuzzy sets was introduced by Atanassov as ageneralization of the notion of fuzzy sets. In this paper, using Atanassov idea, wegive some properties of intuitionistic fuzzy hyperideals and intuitionistic fuzzy bihyperidealsin a semihypergroup. We use the intuitionistic fuzzy left, right, twosidedand bi-hyperideals to characterize the intra-regular semihypergroups,generalizing some known results of intra-regular semigroups

Applications of (Neutro/Anti)sophications to Semihypergroups

A hypergroup, as a generalization of the notion of a group, was introduced by F. Marty in 1934. The first book in hypergroup theory was published by Corsini. Nowadays, hypergroups have found applications to many subjects of pure and applied mathematics, for example, in geometry, topology, cryptography and coding theory, graphs and hypergraphs, probability theory, binary relations, theory of fuzzy and rough sets and automata theory, physics, and also in biological inheritance