| Summary: | The approximation of soft set is presented in modified soft rough (MSR) approximation space in this paper, i.e., approximation of an information system with respect to another information one. Besides, the concept of rough soft set is introduced in a modified soft rough approximation space. Various properties are studied like subset, union, intersection on rough soft set with some propositions presented on rough soft set. Moreover, the measure of roughness of soft set is defined in MSR-approximation space and the order relation is introduced on soft set. Furthermore, lattice theory is studied in the MSR-approximation space under a modified rough soft environment. Finally, some realistic examples are considered to usefulness and illustrate of the paper.
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