Results 251 to 260 of about 5,204,108 (294)
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2007
The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzislaw Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets ...
Zbigniew Bonikowski +1 more
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The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzislaw Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets ...
Zbigniew Bonikowski +1 more
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2015
This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based ...
Yao, J, CIUCCI, DAVIDE ELIO, Zhang, Y.
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This chapter reviews three formulations of rough set theory, i. e., element-based definition, granule-based definition, and subsystem-based definition. These formulations are adopted to generalize rough sets from three directions. The first direction is to use an arbitrary binary relation to generalize the equivalence relation in the element-based ...
Yao, J, CIUCCI, DAVIDE ELIO, Zhang, Y.
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Using rough sets for rough classification
Proceedings of 7th International Conference and Workshop on Database and Expert Systems Applications: DEXA 96, 2002Rough sets theory is emerging as a powerful tool for knowledge discovery in databases. The author introduce a rough sets based method for learning classification rules. The author's method will not necessarily derive all the consistent classification rules from a database, nor will the rules derived be totally consistent with the database.
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Information Sciences, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohua Banerjee, Sankar K. Pal
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohua Banerjee, Sankar K. Pal
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2015
As quantitative generalizations of Pawlak rough sets, probabilistic rough sets consider degrees of overlap between equivalence classes and the set. An equivalence class is put into the lower approximation if the conditional probability of the set, given the equivalence class, is equal to or above one threshold; an equivalence class is put into the ...
Yao, Yiyu +2 more
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As quantitative generalizations of Pawlak rough sets, probabilistic rough sets consider degrees of overlap between equivalence classes and the set. An equivalence class is put into the lower approximation if the conditional probability of the set, given the equivalence class, is equal to or above one threshold; an equivalence class is put into the ...
Yao, Yiyu +2 more
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2012
There are multiple kinds of data in information systems, e.g., categorical data, numerical data, set-valued data, interval-valued data and missing data. Such information systems are called as composite information systems in this paper. To process such data, composite rough sets are introduced, composite relation is defined and composite classes are ...
Junbo Zhang 0004 +2 more
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There are multiple kinds of data in information systems, e.g., categorical data, numerical data, set-valued data, interval-valued data and missing data. Such information systems are called as composite information systems in this paper. To process such data, composite rough sets are introduced, composite relation is defined and composite classes are ...
Junbo Zhang 0004 +2 more
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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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