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Roughness of a set by \((\alpha , \beta )\)-indiscernibility of Bipolar fuzzy relation

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Abstract

In this article, we introduce a new technique for roughness of a set based on \((\alpha , \beta )\)-indiscernibility, that is, objects are indiscernible up to certain degrees \(\alpha \) and \(\beta \). For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for \((\alpha , \beta )\)-bipolar fuzzified rough set.

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Authors and Affiliations

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

    Rizwan Gul & Muhammad Shabir

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  1. Rizwan Gul
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  2. Muhammad Shabir
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Correspondence to Rizwan Gul.

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Communicated by Leonardo Tomazeli Duarte.

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Gul, R., Shabir, M. Roughness of a set by \((\alpha , \beta )\)-indiscernibility of Bipolar fuzzy relation. Comp. Appl. Math. 39, 160 (2020). https://doi.org/10.1007/s40314-020-01174-y

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  • DOI: https://doi.org/10.1007/s40314-020-01174-y

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