Rough approximations in non-commutative residuated lattices
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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.
KeywordsAlgebras of fuzzy logics Residuated lattice Boolean algebra Rough approximation
Mathematics Subject Classification03G25 08A72
The authors would like to express their sincere thanks to the referees for their valuable suggestions and comments.
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