Fuzzy Hypergroup Research Articles

Construction of Fuzzy Hyper BCI-Algebras Using Fuzzy Hypergroupoid

In this paper, by considering the notion of fuzzy hyperoperation, we define the concept of fuzzy hyper [Formula: see text]-algebras as a generalization of [Formula: see text]-algebras and study related properties. Moreover, we introduce the notions of fuzzy hyper [Formula: see text]-ideal and weak (strong) fuzzy hyper [Formula: see text]-ideal, and then examine the relations among them. Finally, we investigate the relation between fuzzy hyper [Formula: see text]-algebras with fuzzy hypersemigroup, fuzzy hypergroup and hyper [Formula: see text]-algebras.

On $\alpha$-solvable fundamental groups

We introduce a specific kind of equivalence relation ${xi^*}_n^{alpha}$ on a fuzzy hypergroup S such that the quotient $S/ {xi^*}_n^{alpha}$, the set of all equivalence classes, is an $alpha$-solvable group. This helps us to introduce the $alpha$-solvable fundamental relation $xi^{*alpha}$. In particular, we obtain an equivalent condition with transitivity of $xi^alpha$.

Weak injectivity in the category of normal fuzzy hypergroups

Based on injectivity, we introduce some definitions in the category NFHG of normal fuzzy hypergroups. And we show that a complete normal fuzzy hypergroup is a weakly injective object in NFHG. Also we investigate weak injectivity in the comma category NFHG/K.

COMPLEX FUZZY HYPERGROUPS BASED ON COMPLEX FUZZY SPACES

The aim of this study is to define and elaborate the concept of a complex fuzzy hypergroup, which is based on the concept of a complex fuzzy space.

EXTENDED THEORETICAL CONCEPT OF COMPLEX FUZZY SETS BY COMPLEX FUZZY SOFT HYPERGROUP, COMPLEX FUZZY SOFT HYPERRING

In this paper, we develop the initial theory of complex fuzzy soft hypergroup by introducing the novel concept of complex fuzzy soft hypergroup, complex fuzzy soft hyperring. Consequently, a major part of this work is dedicated to extend the theory of complex fuzzy soft set, complex fuzzy hypergroup. Complex fuzzy soft quasihypergroup, complex fuzzy soft semihypergroup and complex fuzzy soft subhypergroup also discussed in this paper.

Approximations in hypergroups and fuzzy hypergroups

The first part of this paper represents a continuation of the study of approximations in a hypergroup. We analyse the lower and upper approximations of a subset in a hypergroup, with respect to some operators, particularly the completeness operator. In the last part, we introduce and analyse the lower and upper approximation of a subset in a fuzzy hypergroup.

Fuzzy hypergroups based on fuzzy relations

Based on fuzzy reasoning in fuzzy logic, this paper studies a fuzzy hyperoperation and a fuzzy hypergroupoid associated with a fuzzy relation. A sufficient and necessary condition for such a fuzzy hypergroupoid being a fuzzy hypergroup is given, and the properties of the fuzzy hypergroups associated with fuzzy relations are investigated. Furthermore, the definition of normal fuzzy hypergroups is put forward and it is shown that the category NFHG of normal fuzzy hypergroups satisfies all the axioms of topos except for the subobject classifier axiom.

Fuzzy hypersemigroups

We introduce the notions of fuzzy hypersemigroup, fuzzy hypergroup, fuzzy hyperideal, homomorphism, hyper congruence, fuzzy homomorphism, fuzzy hypercongruence. The purpose of this note is the study of some characterization of fuzzy hypersemigroup, fuzzy hyperideal of a fuzzy hypersemigroup and homomorphism and hypercongruence on a hypersemigroup.