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Rough filters based on residuated lattices

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Abstract

The paper is devoted to introduce the notion of rough sets within the context of residuated lattices. By considering the notion of a residuated lattice, we concern a relationship between rough sets theory and residuated lattices theory. We shall introduce the notion of rough subalgebra (resp. filter) with respect to a filter of a residuated lattice, which is an extended notion of subalgebra (resp. filter) in a residuated lattice and investigate some of their properties.

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Acknowledgements

The authors are highly grateful to referees for their valuable comments and suggestions which were helpful in improving this paper.

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Authors and Affiliations

  1. Department of Mathematics, Persian Gulf University, Bushehr, Iran

    Saeed Rasouli

  2. Department of Mathematics, Yazd University, Yazd, Iran

    Bijan Davvaz

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  1. Saeed Rasouli
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  2. Bijan Davvaz
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Correspondence to Bijan Davvaz.

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Rasouli, S., Davvaz, B. Rough filters based on residuated lattices. Knowl Inf Syst 58, 399–424 (2019). https://doi.org/10.1007/s10115-018-1219-5

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