Interval-Valued Primary Fuzzy Ideal of Non-commutative Semigroup

Sarkar, Pranab; Kar, S.

doi:10.1007/s40819-017-0336-2

Cited by 2 publications

(1 citation statement)

References 19 publications

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“…In [23], Abdullah et al initiated the notion of interval‐valued intuitionistic fuzzy left (right, two sided)

normalΓ

‐hyperideal (IVIF‐ left [right, two sided]

normalΓ

‐hyperideal), interval‐valued intuitionistic fuzzy bi‐

normalΓ

‐hyperideal (IVIF‐bi‐

normalΓ

‐hyperideal), and interval‐valued intuitionistic fuzzy

(1, 2) - normalΓ

‐hyperideal (IVIF‐

(1, 2) - normalΓ

‐hyperideal) in

normalΓ

‐semihypergroups. In 2017, Sarkar and Kar 24 have studied the

(i - v)

left (right) primary fuzzy ideals [

(i - v)

L(R) PFIs] in semigroups. In 2020, Yiarayong 25 applied the theory of interval‐valued fuzzy soft sets (IVFSSs) to semigroups and introduced the notion of interval‐valued fuzzy soft sets (IVFSSs), which is a generalization of fuzzy soft sets (FSSs).…”

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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“…In [23], Abdullah et al initiated the notion of interval‐valued intuitionistic fuzzy left (right, two sided)

normalΓ

‐hyperideal (IVIF‐ left [right, two sided]

normalΓ

‐hyperideal), interval‐valued intuitionistic fuzzy bi‐

normalΓ

‐hyperideal (IVIF‐bi‐

normalΓ

‐hyperideal), and interval‐valued intuitionistic fuzzy

(1, 2) - normalΓ

‐hyperideal (IVIF‐

(1, 2) - normalΓ

‐hyperideal) in

normalΓ

‐semihypergroups. In 2017, Sarkar and Kar 24 have studied the

(i - v)

left (right) primary fuzzy ideals [

(i - v)

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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On Prime Hesitant Fuzzy Ideals in Semigroups

Yiarayong

2022

Handbook of Research on Advances and Applications of Fuzzy Sets and Logic

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Theory of hesitant fuzzy sets is an important tool in algebraic systems, fuzzy sets theory, partially ordered sets, data mining, etc. The aim of this chapter is to apply prime hesitant fuzzy ideal for dealing with several kinds of theories in semigroups. The concepts of prime hesitant fuzzy, weakly prime hesitant fuzzy, completely prime hesitant fuzzy, and weakly completely prime hesitant fuzzy ideals on semigroups have been introduced. The authors deduce some fascinating properties and characterizations for these hesitant fuzzy ideals. Finally, they obtain sufficient conditions of a prime hesitant fuzzy (weakly prime hesitant fuzzy) in order to rephrase a completely prime hesitant fuzzy (weakly completely prime hesitant fuzzy) ideal in a semigroup.

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Interval-Valued Primary Fuzzy Ideal of Non-commutative Semigroup

Cited by 2 publications

References 19 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

On Prime Hesitant Fuzzy Ideals in Semigroups

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