New Approaches of Rough Sets via Ideals

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Author(s): Ali Kandil (Helwan University, Egypt), M. M. Yakout (Ain Shams University, Egypt)and A. Zakaria (Ain Shams University, Egypt)
Copyright: 2016
Pages: 18
Source title: Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing
Source Author(s)/Editor(s): Sunil Jacob John (National Institute of Technology Calicut, India)
DOI: 10.4018/978-1-4666-9798-0.ch012

Keywords: Artificial Intelligence / Information Science Reference / Library & Information Science / Theoretical Studies

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Abstract

An ideal I on a nonempty set X is a subfamily of P(X) which is closed under finite unions and subsets. In this chapter, a new definition of approximation operators and rough membership functions via ideal has been introduced. The concepts of lower and upper approximations via ideals have been mentioned. These new definitions are comparing with Pawlak's, Yao's and Allam's definitions. It's therefore shown that the current definitions are more generally. Also, it's shown that the present method decreases the boundary region. In addition to these points, the topology generated via present method finer than Allam's one which is a generalization of that obtained by Yao's method. Finally, T1 topological spaces are obtained by relations and ideals which are not discrete.

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