Results 261 to 270 of about 1,458,480 (298)
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Fuzzy Sets and Systems, 2000
In the paper the authors define a measure of fuzziness in a rough set and investigate its properties. Every approximation space \((U, R)\), where \(R\) is an equivalence relation on \(U\), and a subset \(X\) of \(U\) determine a rough set \(R(X)\). Let \(\operatorname {card}(Y)\) denote the cardinality of \(Y\). With \((U, R)\) and \(X\) we associate a
Kankana Chakrabarty +2 more
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In the paper the authors define a measure of fuzziness in a rough set and investigate its properties. Every approximation space \((U, R)\), where \(R\) is an equivalence relation on \(U\), and a subset \(X\) of \(U\) determine a rough set \(R(X)\). Let \(\operatorname {card}(Y)\) denote the cardinality of \(Y\). With \((U, R)\) and \(X\) we associate a
Kankana Chakrabarty +2 more
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2004
We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a ...
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We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a ...
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2014
We prove the recent result of Liu and Zhu [1] and discuss some consequences of that and related facts for the development of rough set theory.
Victor W. Marek, Andrzej Skowron
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We prove the recent result of Liu and Zhu [1] and discuss some consequences of that and related facts for the development of rough set theory.
Victor W. Marek, Andrzej Skowron
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International Journal of Machine Learning and Cybernetics, 2014
We introduce linguistic rough set (LRS) by integrating linguistic quantifiers in the rough set framework. The proposed LRS is inspired by the ways in which humans process imprecise information. It operates directly with the linguistic summaries and caters to imprecision implicit in the real world with partial knowledge.
Manish Agarwal, Themis Palpanas
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We introduce linguistic rough set (LRS) by integrating linguistic quantifiers in the rough set framework. The proposed LRS is inspired by the ways in which humans process imprecise information. It operates directly with the linguistic summaries and caters to imprecision implicit in the real world with partial knowledge.
Manish Agarwal, Themis Palpanas
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1994
It is shown that the modal system S5 captures the basic propositional aspects of rough set theory. The system S5 is enhanced to define a consequence relation called ‘rough consequence’ to ensure derivability of ‘roughly equal’ formulae. A predicate logic that includes in its ambit all the existing notions of rough set theory, is presented.
Mohua Banerjee, Mihir K. Chakraborty
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It is shown that the modal system S5 captures the basic propositional aspects of rough set theory. The system S5 is enhanced to define a consequence relation called ‘rough consequence’ to ensure derivability of ‘roughly equal’ formulae. A predicate logic that includes in its ambit all the existing notions of rough set theory, is presented.
Mohua Banerjee, Mihir K. Chakraborty
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Information Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingzhao Kong, Conghao Yan, Weihua Xu
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingzhao Kong, Conghao Yan, Weihua Xu
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On Rough Equalities and Rough Equivalences of Sets
2008The different types of rough equalities [4,5,6] of sets deal with approximate equalities of sets which may not be equal in the usual sense of classical set theory. In this article, we make further study of the properties of rough equalities. A more general kind of equality of sets (we call it rough equivalence) shall be introduced, which captures ...
Bala Krushna Tripathy +2 more
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2005
This article presents some general remarks on rough sets and their place in general picture of research on vagueness and uncertainty – concepts of utmost interest, for many years, for philosophers, mathematicians, logicians and recently also for computer scientists and engineers particularly those working in such areas as AI, computational intelligence,
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This article presents some general remarks on rough sets and their place in general picture of research on vagueness and uncertainty – concepts of utmost interest, for many years, for philosophers, mathematicians, logicians and recently also for computer scientists and engineers particularly those working in such areas as AI, computational intelligence,
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2007
This paper is devoted to the discussion of extended covering rough set models. Based on the notion of neighborhood, five pairs of dual covering approximation operators were defined with their properties being discussed. The relationships among these operators were investigated.
Keyun Qin, Yan Gao, Zheng Pei 0001
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This paper is devoted to the discussion of extended covering rough set models. Based on the notion of neighborhood, five pairs of dual covering approximation operators were defined with their properties being discussed. The relationships among these operators were investigated.
Keyun Qin, Yan Gao, Zheng Pei 0001
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The connections of vague set and rough set
Kybernetes, 2012PurposeThe purpose of this paper is to present research methods in processing uncertain information.Design/methodology/approachVague set and rough set are both‐wings‐mode for expressing uncertainty systems, and based on the both‐wings‐mode of expressing uncertainty systems, the connections of vague set and rough set are discussed.FindingsThis paper ...
Ruixia Yan +2 more
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