On generalized fuzzy ideals of ordered $$\mathcal {AG}$$ AG -groupoids

Yousafzai, Faisal; Yaqoob, Naveed; Zeb, Anwar

doi:10.1007/s13042-014-0305-6

Cited by 9 publications

(8 citation statements)

References 20 publications

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“…Lemma 2.4. [18] Let A and B be any subsets of an ordered AG-groupoid S, where r ∈ (γ, 1] and γ, δ ∈ [0, 1], then:…”

Section: Preliminariesmentioning

confidence: 99%

“…Theorem 2.6. [18] A fuzzy subset f of an ordered AG-groupoid S is called an (∈ γ , ∈ γ ∨q δ )-fuzzy left (right) ideal of S if for all a, b ∈ S and γ, δ ∈ [0, 1], the following conditions hold:…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 2.7. [18] Let f be a fuzzy subset of an ordered AG-groupoid S and γ, δ ∈ [0, 1], then f is an (∈ γ , ∈ γ ∨q δ )-fuzzy left (right) ideal of S if and only if f satisfies the following conditions.…”

Section: Preliminariesmentioning

confidence: 99%

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On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups

Khalaf

Yousafzai

Zia

2022

bspm

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An ordered AG-groupoid can be referred to as a non-associativeordered semigroup, as the main di¤erence between an ordered semigroup and anordered AG-groupoid is the switching of an associative law. In this paper, wedene the smallest left (right) ideals in an ordered AG-groupoid and use them tocharacterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with itssemilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the conceptof an ordered A*G**-groupoid and investigate its structural properties by usingthe generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts willverify the existing characterizations and will help in achieving more generalizedresults in future works.

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“…Lemma 2.4. [18] Let A and B be any subsets of an ordered AG-groupoid S, where r ∈ (γ, 1] and γ, δ ∈ [0, 1], then:…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups

Khalaf

Yousafzai

Zia

2022

bspm

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“…In 2015, Khan et al [24] defined (0, 2)-ideals and (1, 2)-ideals of an ordered LAsemigroups and proved that the ordered LA-semigroup S is 0-(0, 2)-bisimple if and only if S is right 0-simple. In 2016, Yousafzai et al [51] introduced the notion of (∈ γ , ∈ γ ∨q δ )fuzzy (left, right, bi-) ideals of an ordered LA-semigroup and characterized intra-regular ordered LA-semigroups in terms of these generalized fuzzy ideals. In 2017, Yiarayong [42] have also studied prime, semiprime, quasi-prime and quasi-semiprime ideals of ordered LAsemigroups.…”

Section: Introductionmentioning

confidence: 99%

On generalizations of quasi-prime ideals of an ordered left almost semigroups

Yiarayong

2021

Afr. Mat.

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The purposes of this paper are to introduce generalizations of quasi-prime ideals to the context of $$\phi $$ ϕ -quasi-prime ideals. Let $$\phi : {\mathcal {I}}(S) \rightarrow {\mathcal {I}}(S) \cup \left\{ \emptyset \right\} $$ ϕ : I ( S ) → I ( S ) ∪ ∅ be a function where $$ {\mathcal {I}}(S)$$ I ( S ) is the set of all left ideals of an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S. A proper left ideal A of an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S is called a $$\phi $$ ϕ -quasi-prime ideal, if for each $$a, b\in S$$ a , b ∈ S with $$ab \in A - \phi (A)$$ a b ∈ A - ϕ ( A ) , then $$a \in A$$ a ∈ A or $$b\in A$$ b ∈ A . Some characterizations of quasi-prime and $$\phi $$ ϕ -quasi-prime ideals are obtained. Moreover, we investigate relationships between weakly quasi-prime, almost quasi-prime, $$\omega $$ ω -quasi-prime, m-quasi-prime and $$\phi $$ ϕ -quasi-prime ideals of ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroups. Finally, we obtain necessary and sufficient conditions of $$\phi $$ ϕ -quasi-prime ideal in order to be a quasi-prime ideal.

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“…Ameri and Nozeri [5] initiated fuzzy hyperalgebras and introduced some important results. In [20], Yousafzai et al defined generalized fuzzy ideals of ordered AG-groupoids. Khan and Muhammad introduced the notion of ð2; 2 _qÞ-intuitionistic fuzzy ideals of soft semigroups [9].…”

Section: Introductionmentioning

confidence: 99%