• 제목/요약/키워드: fuzzy left (resp. right) simple ordered $\Gamma$-semigroups

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INTUITIONISTIC FUZZY IDEALS IN ORDERED SEMIGROUPS

  • Khan, Asghar;Khan, Madad;Hussain, Saqib
    • Journal of applied mathematics & informatics
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    • 제28권1_2호
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    • pp.311-324
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    • 2010
  • We prove that a regular ordered semigroup S is left simple if and only if every intuitionistic fuzzy left ideal of S is a constant function. We also show that an ordered semigroup S is left (resp. right) regular if and only if for every intuitionistic fuzzy left(resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ for every $a\;{\in}\;S$. Further, we characterize some semilattices of ordered semigroups in terms of intuitionistic fuzzy left(resp. right) ideals. In this respect, we prove that an ordered semigroup S is a semilattice of left (resp. right) simple semigroups if and only if for every intuitionistic fuzzy left (resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ and $\mu_A(ab)\;=\;\mu_A(ba)$, $\gamma_A(ab)\;=\;\gamma_A(ba)$ for all a, $b\;{\in}\;S$.

FUZZY INTERIOR $\Gamma$-IDEALS IN ORDERED $\Gamma$-SEMIGROUPS

  • Khan, Asghar;Mahmood, Tariq;Ali, M. Irfan
    • Journal of applied mathematics & informatics
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    • 제28권5_6호
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    • pp.1217-1225
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    • 2010
  • In this paper we define fuzzy interior $\Gamma$-ideals in ordered $\Gamma$-semigroups. We prove that in regular(resp. intra-regular) ordered $\Gamma$-semigroups the concepts of fuzzy interior $\Gamma$-ideals and fuzzy $\Gamma$-ideals coincide. We prove that an ordered $\Gamma$-semigroup is fuzzy simple if and only if every fuzzy interior $\Gamma$-ideal is a constant function. We characterize intra-regular ordered $\Gamma$-semigroups in terms of interior (resp. fuzzy interior) $\Gamma$-ideals.

GENERALIZED BIPOLAR FUZZY INTERIOR IDEALS IN ORDERED SEMIGROUPS

  • Ibrar, Muhammad;Khan, Asghar;Abbas, Fatima
    • 호남수학학술지
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    • 제41권2호
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    • pp.285-300
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    • 2019
  • This research focuses on the characterization of an ordered semigroups (OS) in the frame work of generalized bipolar fuzzy interior ideals (BFII). Different classes namely regular, intra-regular, simple and semi-simple ordered semigroups were characterized in term of $({\alpha},{\beta})$-BFII (resp $({\alpha},{\beta})$-bipolar fuzzy ideals (BFI)). It has been proved that the notion of $({\in},{\in}{\gamma}q)$-BFII and $({\in},{\in}{\gamma}q)$-BFI overlap in semi-simple, regular and intra-regular ordered semigroups. The upper and lower part of $({\in},{\in}{\gamma}q)$-BFII are discussed.