Afrika Matematika

, Volume 29, Issue 1–2, pp 97–114 | Cite as

Rough approximations in non-commutative residuated lattices

  • Mahmood Bakhshi
  • Mahdi Izanlou


Based on Pawlak’s rough set theory, we study and investigate the roughness in non-commutative residuated lattices, which are generalizations of non-commutative fuzzy structures such as MV-algebras and BL-algebras. We give many theorems and examples to describe the rough approximations. Also, to investigate the properties of roughness of subsets (and of course filters) more closely, we consider some different kinds of filters such as Boolean filters and prime filters. Especially, we prove that with respect to some certain filters, the obtained approximations form a Boolean algebra or a pseudo MTL-algebra.


Algebras of fuzzy logics Residuated lattice Boolean algebra Rough approximation 

Mathematics Subject Classification

03G25 08A72 



The authors would like to express their sincere thanks to the referees for their valuable suggestions and comments.


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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BojnordBojnordIran

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