Sheaf Representation of an Information System

Sheaf Representation of an Information System

Pyla Vamsi Sagar (Rayalaseema University, Kurnool, India) and M. Phani Krishna Kishore (Gayatri Vidya Parishad College of Engineering, Visakhapatnam, India)
Copyright: © 2019 |Pages: 11
DOI: 10.4018/IJRSDA.2019040106

Abstract

Ever since Pawlak introduced the concepts of rough sets, it has attracted many researchers and scientists from various fields of science and technology. Particularly for algebraists as it presented a gold mine to explore the algebraic and topological connections with rough set theory. The present article deals with the connections between rough sets and sheaves. The authors studied sheaf representation of an information system in rough set framework and illustrated how it helps information retrieval.
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2.Preliminaries

We presented some fundamental concepts of sheaves and some of the definitions in this section.

  • Definition 2.1. A relation defined on a set is said to be an equivalence relation if it is reflexive, symmetric and transitive.

  • Definition 2.2. Consider a non-empty finite set IJRSDA.2019040106.m01 and equivalence IJRSDA.2019040106.m02 on IJRSDA.2019040106.m03. The set of all equivalences on IJRSDA.2019040106.m04 is represented byIJRSDA.2019040106.m05. For any IJRSDA.2019040106.m06 an equivalence class of an elementIJRSDA.2019040106.m07 is IJRSDA.2019040106.m08 we denote IJRSDA.2019040106.m09 by IJRSDA.2019040106.m10. Two equivalence classes IJRSDA.2019040106.m11 and IJRSDA.2019040106.m12 are either disjoint or equal.

  • Definition 2.3. Let IJRSDA.2019040106.m13 be an equivalence relation defined on the universe IJRSDA.2019040106.m14. For any subset IJRSDA.2019040106.m15, the approximation space is denoted by the pair IJRSDA.2019040106.m16.

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