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      저자 : Faisal Yousafzai (검색결과 4 건)
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        ON (m, n)-IDEALS OF AN ORDERED ABEL-GRASSMANN GROUPOID

        YOUSAFZAI, FAISAL,KHAN, ASAD,IAMPAN, AIYARED The Kangwon-Kyungki Mathematical Society 2015 한국수학논문집 Vol.23 No.3

        In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

      • KCI등재

        (∈, ∈ ∨q<sub>k</sub>)-FUZZY IDEALS IN LEFT REGULAR ORDERED $\mathcal{LA}$-SEMIGROUPS

        Yousafzai, Faisal,Khan, Asghar,Khan, Waqar,Aziz, Tariq The Honam Mathematical Society 2013 호남수학학술지 Vol.35 No.4

        We generalize the idea of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered semi-group and give the concept of (${\in}$, ${\in}{\vee}q_k$)-fuzzy ordered $\mathcal{LA}$-semigroup. We show that (${\in}$, ${\in}{\vee}q_k$)-fuzzy left (right, two-sided) ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy (generalized) bi-ideals, (${\in}$, ${\in}{\vee}q_k$)-fuzzy interior ideals and (${\in}$, ${\in}{\vee}q_k$)-fuzzy (1, 2)-ideals need not to be coincide in an ordered $\mathcal{LA}$-semigroup but on the other hand, we prove that all these (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideals coincide in a left regular class of an ordered $\mathcal{LA}$-semigroup. Further we investigate some useful conditions for an ordered $\mathcal{LA}$-semigroup to become a left regular ordered $\mathcal{LA}$-semigroup and characterize a left regular ordered $\mathcal{LA}$-semigroup in terms of (${\in}$, ${\in}{\vee}q_k$)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (${\in}$, ${\in}{\vee}q_k$)-fuzzy ideal theory by using the notions of duo and (${\in}{\vee}q_k$)-fuzzy duo.

      • KCI등재

        (∈, ∈ Vqk)-FUZZY IDEALS IN LEFT REGULAR ORDERED LA-SEMIGROUPS

        Faisal Yousafzai,Waqar Khan,Tariq Aziz,Asghar Khan 호남수학회 2013 호남수학학술지 Vol.35 No.4

        We generalize the idea of (2; 2 _qk)-fuzzy ordered semi-group and give the concept of (2; 2 _qk)-fuzzy ordered LA-semigroup. We show that (2; 2 _qk)-fuzzy left (right, two-sided) ideals, (2;2_qk)-fuzzy (generalized) bi-ideals, (2; 2 _qk)-fuzzy interior idealsand (2; 2 _qk)-fuzzy (1; 2)-ideals need not to be coincide in an or-dered LA-semigroup but on the other hand, we prove that all these(2;2 _qk)-fuzzy ideals coincide in a left regular class of an orderedLA-semigroup. Further we investigate some useful conditions foran ordered LA-semigroup to become a left regular ordered LA-semigroup and characterize a left regular ordered LA-semigroupin terms of (2; 2 _qk)-fuzzy one-sided ideals. Finally we connectan ideal theory with an (2; 2 _qk)-fuzzy ideal theory by using thenotions of duo and (2;2 _qk)-fuzzy duo.

      • KCI등재

        (∈, ∈ Vqk)-FUZZY IDEALS IN LEFT REGULAR ORDERED ιA-SEMIGROUPS

        ( Faisal Yousafzai ),( Asghar Khan ),( Waqar Khan ),( Tariq Aziz ) 호남수학회 2013 호남수학학술지 Vol.35 No.4

        We generalize the idea of (E, E Vqk)-fuzzy ordered semi-group and give the concept of (E, E Vqk)~fuzzy ordered ŁA-semigroup. We show that (E, E Vqk)-fuzzy left (right, two-sided] ideals, (E, E Vqk)-fuzzy (generalized) hi-ideals, (E, E Vqk)-fuzzy interior ideals and (E, E vqk)-fuzzy (1, 2)-ideals need not to be coincide in an or-dered ŁA-semigroup but on the other hand, we prove that all these (E, E Vqk)-fuzzy ideals coincide in a left regular class of an ordered .cA-semigroup. Further we investigate some useful conditions for an ordered ŁA-semigroup to become a left regular ordered ŁA-semigroup and characterize a left regular ordered L:A-sernigroup in terms of (E, E Vqk)-fuzzy one-sided ideals. Finally we connect an ideal theory with an (E, E vqk)-fuzzy ideal theory by using the notions of duo and (E, E vqk)-fuzzy duo.

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