Rough approximations in non-commutative residuated lattices

被引：0

作者：

Bakhshi M. ^{[1
]}

Izanlou M. ^{[1
]}

机构：

[1] Department of Mathematics, University of Bojnord, P. O. Box 1339, Bojnord

来源：

Afrika Matematika | 2018年 / 29卷 / 1-2期

关键词：

Algebras of fuzzy logics; Boolean algebra; Residuated lattice; Rough approximation;

D O I：

10.1007/s13370-017-0529-1

中图分类号：

学科分类号：

摘要：

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. © 2017, African Mathematical Union and Springer-Verlag GmbH Deutschland.

引用

页码：97 / 114

页数：17

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