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Modified Soft-rough Modules and their Approximations
Srinivasan Vijayabalaji, Shanmugam Kalaiselvan, Natesan Thillaigovindan and Bijan Davvaz
This paper introduces the idea of pull back and push out on soft module homomorphism. Exact sequence on soft modules are also studied. Rough module approximations and related results are investigated. Hybrid structures of soft modules and rough modules namely softrough modules (respectively modified soft-rough modules) over soft-rough rings (respectively modified soft-rough rings) are introduced and an interesting result that every modified soft-rough module of modified soft-rough ring is a soft-rough module of soft-rough ring, but not viceversa is established. The paper is completed with the illustration of a decision making problem in modified soft-rough module environment.
Keywords: SR-rings, SR-module, MSR-ring, MSR-module, soft modules homomorphism, exact sequence of soft modules