A comparative study of fuzzy rough sets

Radzikowska, Anna Maria; Kerre, Etienne

doi:10.1016/s0165-0114(01)00032-x

Cited by 893 publications

(399 citation statements)

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“…The pair ( , ) X R (where R is a fuzzy relation on X ) constructs the central notion of fuzzy rough sets and is called fuzzy approximation space [16]. For x X  , the fuzzy equivalence…”

Section: Linguistic Fuzzy Rough Setsmentioning

confidence: 99%

Linguistic Fuzzy Rough Sets for Multi Criteria Group Decision Making

Wang¹,

Xu²

2015

Proceedings of the 2015 International Conference on Sustainable Energy and Environmental Engineering

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Abstract-Linguistic variables usually take the form of a base term modified by a hedge in qualitative evaluations of multi criteria decision making problems. In this paper, the linguistic fuzzy rough set is presented to objectively model non-inclusive hedges, such as more or less and roughly, with semantics. Based on the predefined resemblance relation, hedges can be represented by some compact formulae whenever the linguistic term set is uniformed distributed or non-uniformed distributed. Then a corresponding multi criteria group decision making approach is supplied for potential application and illustrated by a problem of evaluating new energy technologies.

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“…The pair ( , ) X R (where R is a fuzzy relation on X ) constructs the central notion of fuzzy rough sets and is called fuzzy approximation space [16]. For x X  , the fuzzy equivalence…”

Section: Linguistic Fuzzy Rough Setsmentioning

confidence: 99%

Linguistic Fuzzy Rough Sets for Multi Criteria Group Decision Making

Wang¹,

Xu²

2015

Proceedings of the 2015 International Conference on Sustainable Energy and Environmental Engineering

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“…Definitions for the fuzzy lower and upper approximations can be found in [13], where a T -transitive fuzzy similarity relation is used to approximate a fuzzy concept X:…”

Section: Fuzzy-rough Feature Selectionmentioning

confidence: 99%

Measures for unsupervised fuzzy-rough feature selection

Parthaláin

Jensen

2010

HIS

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For supervised learning, feature selection algorithms attempt to maximise a given function of predictive accuracy. This function usually considers the ability of feature vectors to reflect decision class labels. It is therefore intuitive to retain only those features that are related to or lead to these decision classes. However, in unsupervised learning, decision class labels are not provided, which poses questions such as; which features should be retained? and, why not use all of the information? The problem is that not all features are important. Some of the features may be redundant, and others may be irrelevant and noisy. In this paper, some new fuzzy-rough set-based approaches to unsupervised feature selection are proposed. These approaches require no thresholding or domain information, and result in a significant reduction in dimensionality whilst retaining the semantics of the data.

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“…Each object x i 2 U is classified by a set of classes A(Q) = Each Fl 2 A(Q) may be a crisp or fuzzy set and Q is decision attribute. can be regarded as fuzzy partitions of U by a set of attributes P using fuzzy similarity relations R on U (Radzikowska and Kerre, 2002). The set U/P builds basic partitions about the domain of interest.…”

Section: Theoretical Foundationsmentioning

confidence: 99%

“…[0,1]; "x 2 U and F ik 2 U/P. According to (Radzikowska and Kerre, 2002) the fuzzyrough set is a tuple O^,/^), where lower and upper approximation membership functions are defined by…”

Section: Theoretical Foundationsmentioning

confidence: 99%