Knowledge and Information Systems

, Volume 58, Issue 2, pp 399–424 | Cite as

Rough filters based on residuated lattices

  • Saeed Rasouli
  • Bijan DavvazEmail author
Regular Paper


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.


Rough set Lower approximation Upper approximation Residuated lattice Subalgebra Filter 



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


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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsPersian Gulf UniversityBushehrIran
  2. 2.Department of MathematicsYazd UniversityYazdIran

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