Results 241 to 250 of about 1,235,954 (283)
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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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International Journal of Computer & Information Sciences, 1982
Summary: We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy set theory and tolerance theory. Some applications are outlined.
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Summary: We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy set theory and tolerance theory. Some applications are outlined.
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Information Sciences, 1996
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Mohua Banerjee, Sankar K. Pal
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Mohua Banerjee, Sankar K. Pal
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Kybernetes, 2004
The differences and relations between grey sets and rough sets are discussed. Based on the concept of a rough grey set, its entropy is studied. Moreover, the grey inference resulting from a rough grey set is pointed out. The relative propositions and theorems are obtained.
Zhang Qi-shan, Chen Guo-hong
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The differences and relations between grey sets and rough sets are discussed. Based on the concept of a rough grey set, its entropy is studied. Moreover, the grey inference resulting from a rough grey set is pointed out. The relative propositions and theorems are obtained.
Zhang Qi-shan, Chen Guo-hong
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Chaos, Solitons & Fractals, 2004
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A. M. Kozae +2 more
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A. M. Kozae +2 more
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Fuzzy Sets and Systems, 1985
In this note we compare notions of rough set and fuzzy set, and we show that these two notions are different.
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In this note we compare notions of rough set and fuzzy set, and we show that these two notions are different.
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Roughness Bounds in Set-oriented Rough Set Operations
2006 IEEE International Conference on Fuzzy Systems, 2006Roughness is an important indicator for the uncertainty of a rough set. This paper analyses the roughness bounds for set-oriented rough set operations. A bound of the roughness of the union between two set-oriented rough sets could be determined by the roughness of the two operand set-oriented sets.
Robert John, Yingjie Yang
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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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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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, 2017 This chapter discusses the basic preliminaries of rough set theory (RST). Since its inception, RST has been a prominent tool for data analysis due to its analysis friendly nature. RST provides a range of data structures, e.g. information systems, decision systems and approximations, to represent the real-world data.
Usman Qamar, Muhammad Summair Raza
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