Journal
INFORMATION SCIENCES
Volume 176, Issue 24, Pages 3658-3674Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2006.02.014
Keywords
rough sets; lower approximation; upper approximation; R-module; submodule; rough submodule
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The theory of rough sets was proposed by Pawlak in 1982. The relations between rough sets and algebraic systems have been already considered by many mathematicians. Important algebraic structures are groups, rings and modules. Rough groups and rough rings have been investigated by Biswas and Nanda, Kuroki and Wang, and Davvaz. In this paper, we consider an R-module as a universal set and we introduce the notion of rough submodule with respect to a submodule of an R-module, which is an extended notion of a subrnodule in an R-module. We also give some properties of the lower and the upper approximations in an R-module. (c) 2006 Elsevier Inc. All rights reserved.
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