Algebras of Definable and Rough Sets in Quasi Order-based Approximation Spaces

• Autorzy: Kumar A. , Banerjee M.

Identyfikatory

DOI

10.3233/FI-2015-1262

• Języki publikacji: EN

Abstrakty

EN

A pair of approximation operators, based on the notion of granules in generalized approximation spaces, was studied in an earlier work by the authors. In this article, we investigate algebraic structures formed by the definable sets and also by the rough sets determined by this pair of approximation operators. The definable sets are open sets of an Alexandrov topological space, and form a completely distributive lattice in which the set of completely join irreducible elements is join dense. The collection of rough sets also forms a similar structure. Representation results for such classes of completely distributive lattices as well as Heyting algebras in terms of definable and rough sets are obtained. Further, two unary operators on rough sets are considered, making the latter constitute a structure that is named a ‘rough lattice’. Representation results for rough lattices are proved.

Słowa kluczowe

EN

granules; approximation operators; definable sets; rough sets; completely distributive lattices; Heyting algebra

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2015
• Tom: Vol. 141, nr 1
• Strony: 37--55
• Opis fizyczny: Bibliogr. 21 poz., tab.

Twórcy

autor

Kumar A.

• Department of Mathematics and Statistics Indian Institute of Technology Kanpur, Kanpur, India

autor

Banerjee M.

• Department of Mathematics and Statistics Indian Institute of Technology Kanpur, Kanpur, India

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