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Generalization of Rough Topology

Affiliations

  • Department of Mathematics, Jaypee Institute of Information Technology, Noida – 201307, Uttar Pradesh, India

Abstract


Background/Objectives: The essential part of rough set theory is an approximation space. This theory can be defined as lower and upper approximations and these approximations are defined using the equivalence classes. We need to generalize this theory in uncertain environment. Our objective is to propose a generalized rough topology. Methods/ Statistical Analysis: Interior and closure of rough topology are same as lower, upper approximations of a rough set. We will find interior and closure of rough topology and obtain extended rough topology. Findings: In this paper, we have studied rough set topologically and proposed a definition of rough fuzzy topology by considering approximations and boundary. Theorems and propositions related to rough fuzzy topology are proposed in this paper. Application/Improvements: Our rough fuzzy topology can be applied to solve real life issues where decision values are in fuzzy form. An algorithm is proposed for the same.

Keywords

Lower Approximations, Rough Fuzzy Topology, Rough Set, Rough Topology, Upper Approximations.

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