Results 271 to 280 of about 156,977 (313)
Some of the next articles are maybe not open access.
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
Information Sciences
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingzhao Kong, Conghao Yan, Weihua Xu
openaire +2 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingzhao Kong, Conghao Yan, Weihua Xu
openaire +2 more sources
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 ...
openaire +1 more source
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 ...
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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.
openaire +2 more sources
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.
openaire +2 more sources
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source