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Generalized fuzzy rough sets based on (β, δ)-fuzzy similarity relation and their application to emergency management

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Abstract

In literature the researchers employ the idea of fuzzy similarity relation to find the fuzzy rough approximations. To our knowledge, nowadays, there does not exist any research methodology for fuzzy rough set model based on \(\left( \beta ,\delta \right)\)-fuzzy similarity relations where \(\beta \in \left[ 0,0.5\right) ,\) and \(\delta \in \left( 0.5,1\right] .\) So, in order to accommodate this research space, this paper aims to extend the notion of Pawlak’s rough sets to the so-called \(\alpha\)-fuzzified rough sets based on \(\left( \beta ,\delta \right)\)-fuzzy similarity relations. Moreover, the approximation defined based on \(\alpha\)-fuzzified rough sets using \(\left( \beta ,\delta \right)\)-fuzzy similarity relations play a key role between \(\left( \beta ,\delta \right)\)-fuzzy similarity relation and crisp set. Furthermore, the approximation defined based on \(\alpha\)-similarity rough sets using \(\left( \beta ,\delta \right)\)-fuzzy similarity relations are useful in different uncertainties. Then we put forward the notion of generalized fuzzy rough set by the combination of fuzzy implication \(\mathcal {I}\) and t-norm \(\mathcal {T}\) called \(\left( \mathcal {I},\mathcal {T }\right)\)-fuzzy rough sets based on \(\left( \beta ,\delta \right)\)-fuzzy similarity relation and investigate their various properties for the development of this study. Presently a characterization is available for R -implications obtained from left continuous quasi-overlap functions denoted by \(\mathcal {I}_{O}\). We establish the \(\left( \mathcal {I}_{O},O\right)\) -fuzzy rough set model obtained from quasi-overlap functions, especially for the connections between \(\left( \beta ,\delta \right)\)-fuzzy similarity relations and the new fuzzy rough approximation operators. We further described two algorithms to manipulate the unpredictability problems based on \(\left( \mathcal {I}_{O},O\right)\)-fuzzy rough set using \(\left( \beta ,\delta \right)\)-fuzzy similarity relation. Finally, we discuss the applications of the proposed techniques for finding the most suitable conditional attribute for emergency plans among the given ones and present the comparison analysis of the proposed techniques with other existing models.

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Acknowledgements

The research of Noor Rehman was partially supported by the Higher Education Commission of Pakistan through project NRPU 15942. The authors also would like to express appreciation to the anonymous reviewers and editors for their very helpful comments that improved the paper.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, Bacha Khan University, Charsadda, Khyber Pakhtunkhwa, Pakistan

    Noor Rehman

  2. Department of Mathematics & Statistics, Riphah International University, Islamabad, Pakistan

    Abbas Ali

  3. Department of Mathematical Engineering, Polytechnic University of Tirana, 1001, Tirana, Albania

    Kostaq Hila

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  1. Noor Rehman
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  2. Abbas Ali
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  3. Kostaq Hila
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Correspondence to Kostaq Hila.

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Rehman, N., Ali, A. & Hila, K. Generalized fuzzy rough sets based on (β, δ)-fuzzy similarity relation and their application to emergency management. J Ambient Intell Human Comput 14, 4127–4155 (2023). https://doi.org/10.1007/s12652-022-04478-5

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