Hyperfilters and fuzzy hyperfilters of ordered semihypergroups

Tang, Jian; Davvaz, Bijan; Luo, Yanfeng

doi:10.3233/ifs-151571

Cited by 35 publications

(27 citation statements)

References 9 publications

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“…Here, if A, B ∈ P * (S), then we say that A ≤ B if for every a ∈ A there exists b ∈ B such that a ≤ b. Clearly, every ordered semigroup can be regarded as an ordered semihypergroup, see [26]. By a subsemihypergroup of an ordered semihypergroup S we mean a nonempty subset…”

Section: Preliminaries and Some Notationsmentioning

confidence: 99%

“…We give the covering relation "≺" and the gure of S as follows: Then (S, •, ≤) is an ordered semihypergroup (see [26]). Let ρ , ρ be equivalence relations on S de ned as follows: …”

Section: Preliminaries and Some Notationsmentioning

confidence: 99%

“…Then (S, •, ≤) is an ordered semihypergroup (see [26]). Let ρ be a weak pseudoorder on S de ned as follows:…”

Section: We Can Easily Verify That ρ Is a Weak Pseudoorder On S But mentioning

confidence: 99%

“…Also see [2]. The work on ordered semihypergroup theory can be found in [24][25][26][27]. It is worth pointing out that Davvaz et al [25] introduced the concept of a pseudoorder on an ordered semihypergroup, and extended some results in [16] on ordered semigroups to ordered semihypergroups.…”

Section: Introductionmentioning

confidence: 99%

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A further study on ordered regular equivalence relations in ordered semihypergroups

et al. 2018

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Abstract:In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208-217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.

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Section: Preliminaries and Some Notationsmentioning

confidence: 99%

“…We give the covering relation "≺" and the gure of S as follows: Then (S, •, ≤) is an ordered semihypergroup (see [26]). Let ρ , ρ be equivalence relations on S de ned as follows: …”

Section: Preliminaries and Some Notationsmentioning

confidence: 99%

“…Then (S, •, ≤) is an ordered semihypergroup (see [26]). Let ρ be a weak pseudoorder on S de ned as follows:…”

Section: We Can Easily Verify That ρ Is a Weak Pseudoorder On S But mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A further study on ordered regular equivalence relations in ordered semihypergroups

et al. 2018

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“…The concept of ordering hypergroups was introduced by Chvalina [31] as a special class of hypergroups. Many authors studied various aspects of ordered semihypergroups, for instance, Davvaz, et al, [32], Gu and Tang [33], Heidari and Davvaz [23], Tang, et al [34], and many others. Explicit study of ordered semihypergroups seems to have begun with Heidari and Davvaz [23] in 2011.…”

Section: Introductionmentioning

confidence: 99%

C-Γ-hyperideal Theory in Ordered Γ-semihypergroups

Davvaz

Omidi

2017

J. Math. Fund. Sci.

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Abstract. Our purpose in this article is to characterize the properties of C-Γ-hyperideals in ordered Γ-semihypergroups. As an application of the results of this paper, the corresponding results of ordered semihypergroups can also be obtained by moderate modification. Keywords: C--hyperideal;-hyperideal, ordered -semihypergroup; regular; semihypergroup; IntroductionThe formal study of semigroups began in the early 20th century. As a generalization of semigroups, the notion of a Γ-semigroup was first introduced by Sen Algebraic hyperstructures are a suitable generalization of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of hyperstructure was first introduced by Marty [15] at the eighth Congress of Scandinavian Mathematicians in 1934. Since then, several books have been published on this topic, for example see [16][17][18][19]. Ameri and Hoskova [20] studied the fuzzy continuous polygroup as a fuzzy

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Study on Green’s relations in ordered semihypergroups

Tang

Davvaz

2020

Soft Comput

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Hyperfilters and fuzzy hyperfilters of ordered semihypergroups

Cited by 35 publications

References 9 publications

A further study on ordered regular equivalence relations in ordered semihypergroups

A further study on ordered regular equivalence relations in ordered semihypergroups

C-Γ-hyperideal Theory in Ordered Γ-semihypergroups

Study on Green’s relations in ordered semihypergroups

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