Interval valued (α, β)-fuzzy bi-ideals of semigroups

Hedayati, H.

doi:10.1134/s1995080211020077

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…The concept of an interval‐valued fuzzy left (right, two‐sided, interior, bi‐) ideal [IVF‐left (right, two‐sided, interior, bi‐) ideal] in a semigroup was introduced by Narayanan and Manikantan 14 in 2006, as a generalization of the notion of fuzzy left (right, two‐sided, interior, bi‐) ideals. In 2011, Hedayati 15 defined the interval‐valued

(α, β)

‐fuzzy bi‐ideals [IV‐

(α, β)

‐F‐bi‐ideal] of semigroups, and investigated some elementary properties. In 2013, Kar et al, 16 has studied the interval‐valued fuzzy ideals (IVFIs) and interval‐valued fuzzy points (IVFPs) in semigroups.…”

Section: Introductionmentioning

confidence: 99%

A new approach of bipolar valued fuzzy set theory applied on semigroups

Yiarayong

2021

Int J Intell Syst

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In this paper, we generalize the concept of interval‐valued bipolar fuzzy sets (IVBFSs) and define interval‐valued bipolar fuzzy subsemigroups (IVBF‐subsemigroup) and interval‐valued bipolar fuzzy left (right, two‐sided) ideals (IVBF‐left [right, two‐sided] ideals) over semigroups, which is a generalization of the concept of an bipolar valued fuzzy set (BVFS) in a semigroup. The purpose of this paper is to deal with the algebraic structure of semigroups by applying IVBFS theory. We give characterizations of different classes of (intra‐regular, left [right] regular, regular, semisimple) semigroups by the properties of their IVBF‐ideals. We also characterize these classes in terms of IVBF‐left ideals, IVBF‐right ideals, and IVBF‐two‐sided ideals. In this respect, we prove that a semigroup is regular if and only if for every IVBF‐right ideal true A ˜ = )( true μ A P ˜ , true μ A N ˜ and every IVBF‐left ideal true B ˜ = )( true μ B P ˜ , true μ B N ˜ over S , we have true A ˜ ∩ true B ˜ = true A ˜ ⊙ true B ˜ . Further, we characterize intra‐regular and regular semigroups and prove that a semigroup is intra‐regular and regular if and only if for every IVBF‐left ideal true A ˜ = )( true μ A P ˜ , true μ A N ˜ and every IVBF‐right ideal true B ˜ = )( true μ B P ˜ , true μ B N ˜ over S we have true A ˜ ∩ true B ˜ 0.25em ≼ 0.25em true A ˜ ⊙ true B ˜ .

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(α, β)

‐fuzzy bi‐ideals [IV‐

(α, β)

Section: Introductionmentioning

confidence: 99%

A new approach of bipolar valued fuzzy set theory applied on semigroups

Yiarayong

2021

Int J Intell Syst

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“…In 2008, Shabir and Khan introduced the concept of interval valued fuzzy ideals generated by interval valued fuzzy subset in ordered semigroup. Recently, H. Hedayati initiated interval valued (α,β)-fuzzy bi-ideals of semigroups and obtained some fundamental results [26,34]. J. Ahsan et al introduced the concept of fuzzy semiring in his paper [3].…”

Section: Introductionmentioning

confidence: 99%

Interval valued (α, β)-intuitionistic fuzzy ideals in hemirings

Abdullah

Aslam

Hedayati

2014

Journal of Intelligent &Amp; Fuzzy Systems

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In this paper, we introduced the concept interval valued intuitionistic fuzzy point. We combine the concept of an interval valued intutionistic fuzzy set with interval valued intuitionistic fuzzy point, to introduce the notion of an (α, β)-intuitionistic fuzzy sub-hemiring (left, right, two sided) ideal of hemirings, where α, β are any two of {∈, q, ∈ ∨q, ∈ ∧q} with α / = ∈ ∧q. Moreover, we define prime (semiprime) interval valued (α, β)-intuitionistic fuzzy ideals of hemirings and investigate some different properties of these ideals.

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Rough bipolar fuzzy ideals in semigroups

Malik

Shabir

Al-shami

et al. 2023

Complex Intell. Syst.

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Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, the bipolar FS (BFS) theory can tackle the uncertainty and the bipolarity of the data in different circumstances. This article aims to introduce the idea of rough bipolar fuzzy ideals in semigroup (SG), which is a generalization of the concept of rough BFSs (RBFSs) in an SG. We also investigate the roughness in the bipolar fuzzy subsemigroup (BF-SSG) with the help of congruence relation (cng-R) defined on the SG and studied some relevant structural properties. Moreover, the idea is extended to the rough bipolar fuzzy left ideal, rough bipolar fuzzy right ideal, rough bipolar fuzzy two-sided ideal, rough bipolar fuzzy interior ideal, and rough bipolar fuzzy bi-ideal in SGs. Further, it is seen that cng-Rs and complete cng-Rs play vital roles in the construction of rough approximations of bipolar fuzzy ideals. Consequently, their associated properties are explored by using cng-Rs and complete cng-Rs.

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Interval valued (α, β)-fuzzy bi-ideals of semigroups

Cited by 4 publications

References 8 publications

A new approach of bipolar valued fuzzy set theory applied on semigroups

A new approach of bipolar valued fuzzy set theory applied on semigroups

Interval valued (α, β)-intuitionistic fuzzy ideals in hemirings

Rough bipolar fuzzy ideals in semigroups

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