Fakhry Asad Agusfrianto, Fitriani, Yudi Mahatma
The notion of a rough set is an extension of set theory. The notion of set theory such as intersection and union can be applied in rough sets. The properties of the rough set in detail were introduced by Pawlak in 1982. The construction of notions in algebraic structures is motivated by set theory. This is also done in rough sets so that a notion called rough algebraic structures is obtained. Some concepts of rough algebraic structures that have been constructed include rough groups, rough rings, and rough modules. Furthermore, in multilinear algebra, we know the concept (R, S) - bimodules. Motivated by the relationship of the concept of the rough sets with algebraic structures, this paper aims to provide a definition (R, S) -bimodules in rough algebra, namely by replacing the R and S rings with the rough rings R1 and S1. Furthermore, we will give some examples of (R1, S1) -rough bimodules and it will also be shown that some of the properties (R1, S1) -bimodules still apply in (R1, S1) -rough bimodules. On the other hand, we will also give the definition of rough bisubmodules and the homomorphism of rough bimodules. © 2024 Author(s).
Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, Jl. Rawamangun Muka, RT.11/RW.14, Rawamangun, Pulo Gadung, Jakarta Timur, Jakarta, 13220, Indonesia; Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, Jl. Prof. Dr. Sumantri Brojonegoro No. 1, Lampung, Bandar Lampung, 35145, Indonesia
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