Fuzzy Hyperideals Research Articles

RETRACTED: Ordered semihyperrings characterized in terms of multipolar fuzzy hyperideals

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219433.

Fuzzy Almost Hyperideals and Fuzzy Almost Quasi-Hyperideals in Semihypergroups

Studying fuzzy hyperideals is necessary for comprehending semihypergroups. The idea of fuzzy hyperideals is expanded upon by several concepts. The notion of almost fuzzy hyperideals is one of them. In this article, we first define the notions of fuzzy almost hyperideals and fuzzy almost quasi-hyperideals in semihypergroups. We investigate the fundamental characteristics of fuzzy almost hyperideals and fuzzy quasi-hyperideals. Additionally, we establish the connection between fuzzy (resp., quasi-) hyperideals and almost (resp., quasi-) hyperideals.

Multipolar Fuzzy Hyperideals in Ordered Semihypergroups

An multi-polar fuzzy set is a robust mathematical model to examine multipolar, multiattribute, and multi-index data. The multi-polar fuzzy sets was created as a useful mechanism to portray uncertainty in multiattribute decision making. In this article, we consider the theoretical applications of multi-polar fuzzy sets. We present the notion of multi-polar fuzzy sets in ordered semihypergroups and define multi-polar fuzzy hyperideals (bi-hyperideals, quasi hyperideals) in an ordered semihypergroup. Relations between multi-polar fuzzy hyperideals, multi-polar fuzzy bi-hyperideals and multi-polar fuzzy quasi hyperideals are discussed.

Complex Fuzzy Krasner Hyperrings

There exist different kinds of hyperrings. If the addition [Formula: see text] is a hyperoperation and the multiplication ⋅ is an ordinary operation, then we can consider an additive hyperring. A special case of this type is the Krasner hyperring. In this paper, we apply the concept of complex fuzzy sets to Krasner hyperrings, define their complex fuzzy hyperideals and identify their properties.

On δ-Primary Fuzzy Hyperideals of Commutative Semihyperrings

On δ-Primary Fuzzy Hyperideals of Commutative Semihyperrings

Characterizations of regularities in ordered semihypergroups in terms of some generalized union soft hyperideals

A soft set of \(E\) over \(U\) is a mapping from \(E\) to the set of all subsets of \(U\). There are many studies that apply the concept of soft sets to investigate the properties of some algebraic structures. The notions of \((M, N)\)-union soft left (resp., right) hyperideals in ordered semihypergroups were introduced by Farooq, Khalaf, and Khan. These concepts are generalizations of uni-soft left and right hyperideals. Ordered semihypergroups can be characterized by many mathematical concepts, such as their hyperideals, fuzzy hyperideals, and soft hyperideals. In this paper, we apply the notions of \((M, N)\)-union soft left (resp., right) hyperideals to characterize some regularities of ordered semihypergroups: regular, weakly regular, and intra-regular ordered semihypergroups.

Bipolar fuzzy hyperideals in regular and intra-regular semihypergroups

Bipolar fuzzy hyperideals in regular and intra-regular semihypergroups

A novel investigation on fuzzy hyperideals in ordered $$*$$-semihypergroups

In this paper, we study the ordered $$*$$ -semihypergroups in terms of fuzzy subsets in detail and define a unary operation $$\star $$ on the set of all the fuzzy subsets of an ordered $$*$$ -semihypergroup. To begin with, we define and study the fuzzy hyperideals of an ordered $$*$$ -semihypergroup. In particular, we investigate the properties of fuzzy hyperideals generated by ordered fuzzy points of an ordered $$*$$ -semihypergroup. Furthermore, we introduce the concepts of prime, weakly prime and semiprime fuzzy hyperideals of ordered $$*$$ -semihypergroups. Especially, the relationships among these three types of fuzzy hyperideals are established. In the sequel, we give some characterizations of intra-regular ordered $$*$$ -semihypergroups and semisimple ordered $$*$$ -semihypergroups in terms of fuzzy hyperideals. Especially, we prove that an ordered $$*$$ -semihypergroup S is semisimple if and only if every fuzzy hyperideal of S can be expressed as the intersection of all weakly prime fuzzy hyperideals of S containing it.

On interval valued intuitionistic fuzzy hyperideals of ordered semihypergroups

We introduce the notion of interval valued intuitionistic fuzzy hyperideals, bi-hyperideals and quasi-hyperideals of an ordered semihypergroup. We characterize an interval valued intuitionistic fuzzy hyperideal of an ordered semihypergroup in terms of its level subset. Moreover, we show that interval valued intuitionistic fuzzy bi-hyperideals and quasi-hyperideals coincide only in a particular class of ordered semihypergroups. Finally, we show that every interval valued intuitionistic fuzzy quasi-hyperideal is the intersection of an interval valued intuitionistic fuzzy left hyperideal and an interval valued intuitionistic fuzzy right hyperideal.

Hypercongruences in fuzzy AG-hypergroupoids

We introduce the notion of fuzzy Abel-Grassmann’s hypergroupoid, hypercongruence, fuzzy hypercongruence, fuzzy strong hypercongruence, compatible relations in an Abel-Grassmann’s hypergroupoid. This paper is aimed to study fuzzy hyperideals, smallest fuzzy hyperideals, fuzzy equivalence relations, fuzzy compatible fuzzy strong compatible, fuzzy hypercongruences, fuzzy strong hypercongruences, fuzzy regular, fuzzy strong regular relations and fuzzy hypercongruences in Abel-Grassmann’s hypergroupoids. Characterizations of hypercongruences, their corresponding quotient structure, homomorphisms and an important theorem on embedding Abel-Grassmann’s hypergroupoids by means of fuzzy sets. We show that each hypergroupoid is embedded into a poe-hypergroupoid of all fuzzy subsets of an Abel-Grassmann’s hypergroupoid.

A short note on some of the fuzzy rough hyper-ideals in semihyper-groups

A short note on some of the fuzzy rough hyper-ideals in semihyper-groups

Study of Γ-hyperrings by fuzzy hyperideals with respect to a t-norm

Abstract In this paper, we study the Γ-hyperrings via T-fuzzy hyperideals. By means of the use of a triangular norm T, we define, characterize and study the T-fuzzy left and right hyperideals, T-fuzzy quasi-hyperideal and bi-hyperideal in Γ-hyperrings and some related properties are investigated. Regular Γ-hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal. We also introduce the T-(λ, µ)-fuzzy bi-hyperideals in Γ-hyperrings and investigate some of their properties.

A study of (α, β)-complex fuzzy hyperideals in non-associative hyperrings

A study of (α, β)-complex fuzzy hyperideals in non-associative hyperrings

On generalized fuzzy hyperideals in ordered LA-semihypergroups

In this paper, we study the hyperideals of ordered LA-semihypergroups in terms of $$(\overline{\in },\overline{\in }\vee \overline{q_{k}})$$-fuzzy sets which is a new generalization of fuzzy hyperideals. We study the relation between different $$(\overline{\in },\overline{\in }\vee \overline{q_{k}})$$ -fuzzy hyperideals in regular ordered LA-semihypergroups. Finally the upper parts of the $$(\overline{\in },\overline{\in }\vee \overline{q_{k}})$$-fuzzy LA-subsemihypergroup (resp., left hyperideal, right hyperideal, hyperideal, interior hyperideal, bi-hyperideal) is defined and some related results are provided.

Fuzzy set approach to hyperideal theory of po-ternary semihypergroups

The aim of this paper is to apply fuzzy sets in hyperstructure theory. We initiate fuzzy hyperideals over po-ternary semihypergroups and explore some related properties. We introduce the concept of po-fuzzy point in po-ternary semihypergroups. Moreover, we give a number of characterizations for regular po-ternary semihypergroups by using the concept of fuzzy hyperideals.

On Fuzzy Ordered Hyperideals in Ordered Semihyperrings

In this paper, we introduce the concept of fuzzy ordered hyperideals of ordered semihyperrings, which is a generalization of the concept of fuzzy hyperideals of semihyperrings to ordered semihyperring theory, and we investigate its related properties. We show that every fuzzy ordered quasi-hyperideal is a fuzzy ordered bi-hyperideal, and, in a regular ordered semihyperring, fuzzy ordered quasi-hyperideal and fuzzy ordered bi-hyperideal coincide.

Regular and strongly regular relations on soft hyperrings

Soft set theory, introduced by Molodtsov, has been considered as an effective mathematical tool for modeling uncertainties, and soft hyperrings can be regarded as a generalization of soft rings. The motivation for such an investigation is to generalize the concept of quotient soft hyperrings and isomorphism theorems. Also, we consider when the fuzzy hyperideals of a soft hyperring are normal, then the equivalence relations defined by J. Wang et. al. on soft hyperrings are strongly regular. Moreover, the quotient soft hyperrings determined by this equivalence relation are soft rings.

Bipolar Fuzzy Soft Hyperideals and Homomorphism of Gamma-Hypersemigroups

In this paper, we introduce the concept of bipolar fuzzy soft gamma hyperideals in gamma hyper semigroups. We define bipolar fuzzy soft hyper ideals, bi-ideals and interior ideals of gamma hyper semigroups and discuss some properties.

On fuzzy subsets in $$\Gamma $$ Γ -semihypergroup through left operator semihypergroup

In this paper, some fundamental relationships of a \(\Gamma \)-semihypergroup and its operator semihypergroup in terms of fuzzy subsets, fuzzy hyperideals and fuzzy hyperideal extension are obtained. Using these in obtaining some characterization theorems of \(\Gamma \)-semihypergroups in terms of fuzzy subsets, we highlight the effectiveness of operator semihypergroups in the study of \(\Gamma \)-semihypergroups in terms of fuzzy subsets.

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

The concept of (∈,∈∨qk)-fuzzy hyperideal of an ordered LA-semihypergroup is introduced by the ordered fuzzy points, and related properties are investigated. We study the relations between different (∈,∈∨qk)-fuzzy hyperideal of an ordered LA-semihypergroup. Furthermore, we study some results on homomorphisms of (∈,∈∨qk)-fuzzy hyperideals.