Fuzziness in rough sets
type: Item
instance of: scholarly article
title: Fuzziness in rough sets
zbMATH Open document ID: 0943.03040
DOI: 10.1016/S0165-0114(97)00414-4
author: Kankana Chakrabarty
author: Ranjit Biswas
author: Sudarsan Nanda
published in: Fuzzy Sets and Systems
publication date: 2000-08-27T00:00:00Z
review text: 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 fuzzy set \(F^{R}_{X}\) of \(U\): \[ F^{R}_{X}=\{(u, \mu_{F^{R}_{X}}(u)) |u\in U\wedge \mu_{F^{R}_{X}}(u)= \operatorname {card}(\{[u]_{R}\cap X\})/\operatorname {card}([u]_{R})\} \] The fuzziness in \(R(X)\) is defined by the amount of fuzziness in \(F^{R}_{X}\) and measured by a suitable (linear or quadratic) index of fuzziness.
reviewed by: Anna Gomolińska
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1423470
zbMATH Keywords: rough sets
zbMATH Keywords: fuzzy sets
zbMATH Keywords: index of fuzziness
zbMATH Keywords: measure of fuzziness
zbMATH Keywords: approximation space
MaRDI profile type: Publication
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full work available at URL: s0165-0114(97)00414-4
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description: scientific article; zbMATH DE number 1423470