Fuzzy Hyperideals Research Articles

On Fuzzy Ordered LA-Semihypergroups

We introduce the notion of fuzzy ordered LA-semihypergroups and provide different examples. We also discuss some results related with fuzzy left and right hyperideals.

Characterizations of Hyperrings by Fuzzy Hyperideals with Respect to A [formula omitted]-norm

In this paper, we inquire further into the properties on some kind fuzzy hyperideals and we study the 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 hyperrings and some related properties are investigated. Regular hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal.

A study on (i-v) prime fuzzy hyperideal of semihypergroups

In this paper, our main objective is to introduce and investigate the interval-valued (in short, (i-v)) prime fuzzy hyperideal in semihypergroups in detail. We notice that every (i-v) semiprime fuzzy hyperideal may not be an (i-v) prime fuzzy hyperideal and we produce a counter example to illustrate this result. Moreover, we define (i-v) fuzzy hyper radical of an (i-v) fuzzy hyperideal of a semihypergroup. Finally, we study some interesting properties regarding this radical.

A note on the lattice of fuzzy hyperideals of a hyperring

Many studies have investigated lattices of fuzzy algebraic systems. One of them belongs to Borzooei et al. (Soft Comput 12:739–749, 2008) who found some properties of lattices of fuzzy algebraic structures. In this study, we solve the problem of finding necessary and sufficient conditions for distributivity and modularity of lattice of fuzzy hyperideals of a hyperring which was one of the open problems in Borzooei’s paper.

Fuzzy Hyperideals of Left Almost Semihypergroups

This paper explores the foundations of fuzzy left (resp. right) hyperideals of left almost semihypergroups (briefly, LA-semihypergroups). We investigate the properties of fuzzy left hyperideals and fuzzy right hyperideals in regular and intra-regular LA-semihypergroups. We also characterize regular and intra-regular LA-semihypergroups in terms of fuzzy hyperideals.

Characterizations of semisimple ordered semihypergroups in terms of fuzzy hyperideals

In this paper, the concept of ordered fuzzy points of ordered semihypergroups is introduced. By using this new concept, we define and study the fuzzy left, right and two-sided 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, semiprime, weakly prime and weakly semiprime fuzzy hyperideals of ordered semihyper- groups and establish the relationship between the four classes of fuzzy hyperideals. Finally, we give some characterizations of 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.

Classes of fuzzy hyperideals

In this paper we study fuzzy hyperideals of a fuzzy hyperring, we define and analyze two particular kinds of fuzzy hyperideals, which extend similar notions of ring context, namely prime fuzzy hyperideals and maximal fuzzy hyperideals. Moreover, we study the hyperideal transfer through a fuzzy hyperring homomorphism, particularly for prime fuzzy hyperideals and for maximal fuzzy hyperideals.

Fuzzy ordered Krasner hyperrings

An ordered Krasner hyperring is a Krasner hyperring (R, +, ·) besides a partial order relation ≤ that satisfies the monotone conditions. In this paper, we introduce the concept of fuzzy hyperideals, fuzzy quasi-hyperideals and fuzzy bi-hyperideals of an ordered Krasner hyperring and we present some examples in this respect. We give the main theorems which characterize the hyperideals, quasi-hyperideals and bi-hyperideals in terms of fuzzy hyperideals, fuzzy quasi-hyperideals and fuzzy bi-hyperideas, respectively.

Hyperfilters and fuzzy hyperfilters of ordered semihypergroups

In this paper, we introduce the concept of hyperfilters of an ordered semihypergroup, and present some examples in this respect. Furthermore, we define and discuss the fuzzy hyperfilters of ordered semihypergroups. We also introduce the concept of completely prime fuzzy hyperideals of an ordered semihypergroup S, and establish the relation of fuzzy hyperfilters and completely prime fuzzy hyperideals of S. In particular, we prove that a fuzzy subset f of S is a fuzzy hyperfilter of S if and only if the complement fof f is a completely prime fuzzy hyperideal of S. As an application of the results of this paper, the corresponding results in ordinary semihypergroups can be also obtained by moderate modification.

Semihypergroups characterized by (∈ γ, ∈ γ ∨ qδ)-fuzzy hyperideals

In this paper, we generalize the concept of (∈, ∈∨ qk)-fuzzy hyperideals of a semihypergroup H and we define (∈γ , ∈γ ∨qδ)-fuzzy subsemihypergroup, (∈γ , ∈γ ∨qδ)-fuzzy left (right) hyperideal, (∈γ , ∈γ ∨qδ)-fuzzy hyperideal, (∈γ , ∈γ ∨qδ)-fuzzy interior hyperideal, (∈γ , ∈γ ∨qδ)-fuzzy quasihyperideal, (∈γ , ∈γ ∨qδ)-fuzzy bi-hyperideal and (∈γ , ∈γ ∨qδ)-fuzzy generalized bi-hyperideal of a semihypergroup H and study some basic properties. Also we characterize regular and intra-regular semihypergroups using these notions.

N-Dimensional fuzzy hyperideals in semihyperrings

In this article we introduce the notion of \(n\)-dimensional fuzzy sets, fuzzy hyperideals and fuzzy prime hyperideals in semihyperrings with identity. We also discuss some basic properties of \(n\)-dimensional fuzzy prime hyperideals and characterize the \(n\)-dimensional fuzzy prime hyperideals. We also investigate the topology on \(n\)-dimensional fuzzy hyperideals and fuzzy prime hyperideals.

On some interval-valued fuzzy hyperideals of semihypergroups

We first introduce the notion of some interval-valued fuzzy hyperideals of a semihypergroup and present some important structural results. Then we find some inter-relations between interval-valued fuzzy hyperideals and obtain some characterizations of regular semihypergroups, intra-regular semihypergroups by using interval-valued fuzzy hyperideals of semihypergroups.

Some Generalized Forms of Fuzzy Interval Valued Hyperideals in a Hyperring

Some generalized forms of the hyperideals of a hyperring in the paper of Zhan et al. (2008) will be given. As a generalization of the interval valued(α,β)-fuzzy hyperideals of a hyperring withα,β∈{∈,q,∈∧q,∈∨q}andα≠∈∧q, the notion of generalized interval valued(α,β)-fuzzy hyperideals of a hyperring is also introduced. Special attention is concentrated on the interval valued(∈γ~,∈γ~∨qδ~)-fuzzy hyperideals. As a consequence, some characterizations theorems of interval valued(∈γ~,∈γ~∨qδ~)-fuzzy hyperideals will be provided.

On generalized intuitionistic fuzzy subhyperalgebras of Boolean hyperalgebras

This paper deals with a special class of hyperalgebra, called Boolean hyperalgebra, which is redefined in it. We introduce the concepts of generalized intuitionistic fuzzy subhyperalgebras and generalized intuitionistic fuzzy hyperideals of Boolean hyperalgebras. A necessary and sufficient condition for an intuitionistic fuzzy subset of the Boolean hyperalgebra to be a generalized intuitionistic fuzzy subhyperalgebra (hyperideal) is proved. Images and inverse-images of generalized intuitionistic fuzzy subhyperalgebra (hyperideal) under Boolean hyperalgebra homomorphism are studied. MSC: 03E72, 08A72.

Characterizations of Semihyperrings by Their (∈γ,∈γ∨qδ)-Fuzzy Hyperideals

The concepts of (∈γ,∈γ∨qδ)-fuzzy bi-hyperideals and (∈γ,∈γ∨qδ)-fuzzy quasi-hyperideals of a semihyperring are introduced, and some related properties of such (∈γ,∈γ∨qδ)-fuzzy hyperideals are investigated. In particular, the notions of hyperregular semihyperrings and left duo semihyperrings are given, and their characterizations in terms of hyperideals and (∈γ,∈γ∨qδ)-fuzzy hyperideals are studied.

An Algebra of Fuzzy (<i>m</i>, <i>n</i>)-Semihyperrings

We propose a new class of algebraic structure named as (m, n)-semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (m, n)-semihyperring, etc. and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (m, n)-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (m, n)-semihyperrings and the relationship between fuzzy (m, n)-semihyperrings and the usual (m, n)-semihyper-rings.

Rough Fuzzy Hyperideals in Ternary Semihypergroups

The relations between rough sets and algebraic systems have been already considered by many mathematicians, and rough sets have been studied in various kinds of algebraic systems. This paper concerns a relationship between rough sets and ternary semihypergroups. We introduce the notion of rough hyperideals and rough bi-hyperideals in ternary semihypergroups. We also study fuzzy, rough, and rough fuzzy ternary subsemihypergroups (left hyperideals, right hyperideals, lateral hyperideals, hyperideals, and bi-hyperideals) of ternary semihypergroups.

SEMISIMPLE SEMIHYPERGROUPS IN TERMS OF HYPERIDEALS AND FUZZY HYPERIDEALS

In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

On interval valued (α,β)—fuzzy hyperideals of hyperlattices

By using the concept of quasi-coincidence of interval valued fuzzy set, the notion of interval valued fuzzy hyperideal of hyperlattices is introduced. Also some related properties are studied. In particular, the interval valued ( α,β ) – fuzzy hyperideals in a hyperlattice will be investigated. Finally, the concept of implication-based interval valued (∈,∈⊔q) – fuzzy hyperideal and its basic properties in logical view is considered.

A fuzzy view of $$\Upgamma$$ -hyperrings

In this paper, by means of a kind of new idea, we consider the ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$ -hyperrings. The notion of ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$ -hyperrings is provided and some related properties are investigated. A kind of quotient $$\Upgamma$$ -hyperring of a $$\Upgamma$$ -hyperring by an ( ∈ , ∈ ∨ q)-fuzzy hyperideal is presented and the relationships among ( ∈ , ∈ ∨ q)-fuzzy hyperideals, quotient $$\Upgamma$$ -hyperrings and homomorphisms are explored. Several homomorphism theorems in the framework of fuzzy setting are provided.