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Regular and intra-regular semirings in terms of bipolar fuzzy ideals

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Abstract

Using the concept of belongingness and quasi-coincidence of a bipolar fuzzy point with a bipolar fuzzy set, the concepts of \((\alpha ,\beta )\)-bipolar fuzzy subsemiring, \((\alpha ,\beta )\)-bipolar fuzzy ideal and \((\alpha ,\beta )\)-bipolar fuzzy bi-ideal in semiring are introduced. We emphasized more on \((\in ,\in \vee q)\)-bipolar fuzzy ideals and \((\in ,\in \vee q)\)-bipolar fuzzy bi-ideals. Characterizations of regular and intra-regular semirings by using \((\in ,\in \vee q)\)-bipolar fuzzy ideals and \((\in ,\in \vee q)\)-bipolar fuzzy bi-ideals are presented.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam university, Islamabad, Pakistan

    Muhammad Shabir & Saba Liaquat

  2. Department of Mathematics, University of Gujrat, Gujrat, Pakistan

    Shahida Bashir

Authors
  1. Muhammad Shabir
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  2. Saba Liaquat
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  3. Shahida Bashir
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Correspondence to Saba Liaquat.

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Communicated by Anibal Tavares de Azevedo.

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Shabir, M., Liaquat, S. & Bashir, S. Regular and intra-regular semirings in terms of bipolar fuzzy ideals. Comp. Appl. Math. 38, 197 (2019). https://doi.org/10.1007/s40314-019-0974-6

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  • DOI: https://doi.org/10.1007/s40314-019-0974-6

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