2016
DOI: 10.4018/978-1-4666-9798-0.ch012
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New Approaches of Rough Sets via Ideals

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 bou… Show more

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Cited by 6 publications
(11 citation statements)
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“…Set theoretic generalizations of the approach in [4,5,6] are proposed in this section by the present author.…”
Section: Set-theoretic Generalization Of Ideal-based Frameworkmentioning
confidence: 99%
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“…Set theoretic generalizations of the approach in [4,5,6] are proposed in this section by the present author.…”
Section: Set-theoretic Generalization Of Ideal-based Frameworkmentioning
confidence: 99%
“…All this is behind the motivation for the definition of GOSIH. In the relational approximation contexts of [4,5,6], subsets of generalized zeros are generalized zeros. Apart from wide differences in properties, major differences exist on the nature of ideals.…”
Section: Meanings Of Generalization and Parallel Rough Universesmentioning
confidence: 99%
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“…More recent approaches of rough set with its applications can be found in [30][31][32]. Other rough set theory applications in computer science (field of information retrievals) using topological generalizations can be found in [33][34][35][36][37][38][39][40].…”
Section: Introductionmentioning
confidence: 99%
“…A binary relation forming classes of objects, which are identical or at least not noticeably different in terms of the available description, can represent the similarities between objects [25,26,27,28,29]. More recent approaches of rough set with its applications can found in [31,32,33]. Other applications of rough set theory in computer science (field of information retrievals) using topological generalizations can be found in [34.35.36.37].…”
Section: Introductionmentioning
confidence: 99%