Characterizations of ordered $h$-regular semirings by ordered $h$-ideals

Anjum, Rukhshanda; Ullah, Saad; Chu, Yu‐Ming; Munir, Mohammad; Kausar, Nasreen; Kadry, Seifedine

doi:10.3934/math.2020370

Cited by 5 publications

(5 citation statements)

References 10 publications

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“…In 2019, Shabir et al [39] used (α, β)−bipolar fuzzy ideals and (α, β)−bipolar fuzzy bi-ideals for the characterizations of the regular and intraregular semiring. Recently, Anjum et al [27] studied ordered h-ideals in regular semiring. Here, we have extended the study in [39] for (α, β)−h-BFSHs and (α, β)−h-BFIs of hemirings.…”

Section: Innovative Contributionmentioning

confidence: 99%

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A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

Bashir

Al-Kenani

Mazhar

et al. 2022

Mathematical Problems in Engineering

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This paper provides a generalized form of ideals, that is, h-ideals of hemirings with the combination of a bipolar fuzzy set (BFS). The BFS is an extension of the fuzzy set (FS), which deals with complex and vague problems in both positive and negative aspects. The basic purpose of this paper is to introduce the idea of α , β − bipolar fuzzy h-subhemirings (h-BFSHs), α , β − bipolar fuzzy h-ideals (h-BFIs), and α , β − bipolar fuzzy h-bi-ideals (h-BFbIs) in hemirings by applying the definitions of belongingness ∈ and quasicoincidence q of the bipolar fuzzy point. We will also focus on upper and lower parts of the h-product of bipolar fuzzy subsets (BFSSs) of hemirings. In the end, we have characterized the h-hemiregular and h-intrahemiregular hemirings in terms of the ∈ , ∈ ∨ q − h-BFIs and ∈ , ∈ ∨ q − h-BFbIs.

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Section: Innovative Contributionmentioning

confidence: 99%

“…Another more restricted class of ideals which is h-ideals has been given in hemirings by Iizuka [25]. However, in an additively commutative semiring, ideals of a semiring coincide with "ideals" of a ring, provided that the semiring is a hemiring [26,27]. For more applications of h-ideals, see [28,29].…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

Bashir

Al-Kenani

Mazhar

et al. 2022

Mathematical Problems in Engineering

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“…The notions of (m, n)-bi-hyperideals and Prime (m, n)-bi-hyperideals were established and inter-related properties were considered by Omidi and Davvaz [7]. The characterization of ordered h-regular semirings was considered by Anjum et al [8]. In [9], Patchakhieo and Pibaljommee characterized ordered k-regular semirings using ordered k-ideals.…”

Section: Introductionmentioning

confidence: 99%

“…Omidi and Davvaz [7] considered the concepts of (m, n)-bi-hyperideals and Prime (m, n)-bi-hyperideals and established interrelated features. Anjum et al [8] proposed characterizing ordered h-regular semirings. By using ordered k-ideals, Patchakhieo and Pibaljommee described ordered k-regular semirings in [9].…”

Section: Introductionmentioning

confidence: 99%

A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings

Muhiuddin

Abughazalah

Mahboob³

et al. 2023

Axioms

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In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is established. We prove that (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are fuzzy bi-ideals but that the converse is not true, and an example is provided to support this proof. A condition is given under which fuzzy bi-ideals of ordered semirings coincide with (∈,∈∨(κ*,qκ))-fuzzy bi-ideals. An equivalent condition and certain correspondences between bi-ideals and (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are presented. Moreover, the (κ*,κ)-lower part of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is described and depicted in terms of several classes of ordered semirings. Furthermore, it is shown that the ordered semiring is bi-simple if and only if it is (∈,∈∨(κ*,qκ))-fuzzy bi-simple.

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“…Several authors have studied fuzzy h-ideals and fuzzy k -ideals in semirings [10,11]. In [12], Shabir and Anjum have examined the fuzzy right k-ideals by using the characterizations of right k-ideals in hemirings.…”

Section: Introductionmentioning

confidence: 99%

Some Studies in Hemirings by the Falling Fuzzy $k$ -Ideals

Anjum

Sarfraz

Kausar

et al. 2021

Journal of Function Spaces

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In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy k -ideals and falling fuzzy k -ideals in hemirings. In particular, we shall establish different characterizations of k -hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy k -ideals.

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Characterizations of ordered $h$-regular semirings by ordered $h$-ideals

Cited by 5 publications

References 10 publications

A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings

Some Studies in Hemirings by the Falling Fuzzy $k$ -Ideals

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Characterizations of ordered $h$-regular semirings by ordered $h$-ideals

Cited by 5 publications

References 10 publications

A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals

A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings

Some Studies in Hemirings by the Falling Fuzzy k -Ideals

Contact Info

Product

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Some Studies in Hemirings by the Falling Fuzzy $k$ -Ideals