Sarmin, Nor Haniza and Muhammad Khan, Faiz and Asghar Khan, Asghar Khan
(2012)
*Some new characterization of ordered semigroups in terms of (λ;θ)-fuzzy bi-ideals.*
International Journal of Algebra and Statistics, 1
(1).
pp. 22-32.
ISSN 2314-4556

Full text not available from this repository.

Official URL: https://doi.org/10.20454/ijas.2012.376

## Abstract

In this paper, we demonstrate a new concept of fuzzy bi-ideals called a \(( \lambda ,\theta ) \)-fuzzy bi-ideals of an ordered semigroup. Fuzzy ideals of type \(( \lambda ,\theta) \) are the generalization of fuzzy bi-ideals and an \(( \in ,\in\vee q) \)-fuzzy bi-ideals of an ordered semigroup. We show that \( U( \mu ,t) ( \neq \emptyset ) \) is a bi-ideal if and only if the fuzzy subset \(\mu\) is a \(( \lambda ,\theta ) \)-fuzzy i-ideal of \(S\) for all \(t\in (\lambda ,\theta ]\). Similarly, \(A\) is a bi-ideal if and only if the characteristic function \(\mu _{A}\) of \(A\) is a \(( \lambda ,\theta ) \)-fuzzy bi-ideal of \(S\). With the help of some examples, we show that \(( \lambda ,\theta ) \)-fuzzy bi-ideals (\(( \lambda ,\theta ) \)-fuzzy subsemigroups) are neither fuzzy bi-ideals (fuzzy subsemigroups ) nor \(( \in ,\in \vee q) \)-fuzzy bi-ideals (\(( \in ,\in \vee q) \)-fuzzy subsemigroups) of an ordered semigroup \(S\). Finally, the characterization of completely ordered semigroups in terms of \(( \lambda ,\theta ) \)-fuzzy bi-ideals is given.

Item Type: | Article |
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Uncontrolled Keywords: | semigroups in terms, characteristic function |

Subjects: | Q Science |

Divisions: | Science |

ID Code: | 33051 |

Deposited By: | Fazli Masari |

Deposited On: | 20 May 2014 10:08 |

Last Modified: | 28 Jan 2019 11:50 |

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