Rough Sets

Pawlak, Zdzisław

doi:10.1007/978-94-011-3534-4

Cited by 3,447 publications

(1,087 citation statements)

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“…Rough set theory introduced by Pawlak in 1982 is a mathematical tool to deal with vagueness and uncertainty of information. This approach seems to be of fundamental importance to artificial intelligence, especially in the areas of machine learning and decision support systems [22]. Rough sets theory makes use of lower and upper approximations to set boundaries, and one of its main advantages is that it does not need any preliminary or additional information about data, such as grade of membership or the value of possibility in fuzzy set theory [23].…”

Section: Introductionmentioning

confidence: 99%

A quantifier-based fuzzy classification system for breast cancer patients

Soria

Garibaldi

Green

et al. 2013

Artificial Intelligence in Medicine

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Consensus between unsupervised classification algorithms has been successfully used to categorise patients into these specific groups, but often at the expenses of not classifying the whole set. It is known that fuzzy methodologies can provide linguistic based classification rules. The objective of this study was to investigate the use of fuzzy methodologies to create an easy to interpret set of classification rules, capable of placing the large majority of patients into one of the specified groups. Methods and materials:In this paper, we extend a data-driven fuzzy rule-based system for classification purposes (called 'fuzzy quantification subsethood-based algorithm') and combine it with a novel class assignment procedure. The whole approach is then applied to a well characterised breast cancer dataset consisting of ten protein markers for over 1,000 patients to refine previously identified groups and to present clinicians with a linguistic ruleset. A range of statistical approaches were used to compare the obtained classes to previously obtained groupings and to assess the proportion of unclassified patients.Results: A rule set was obtained from the algorithm which features one classification rule per class, using labels of High, Low or Omit for each biomarker, to determine the most appropriate class for each patient. When applied to the whole set of patients, the distribution of the obtained classes had an agreement of 0.9 when assessed using Kendall's Tau with the original reference class distribution. In doing so, only 38 patients out of 1,073 remain unclassified, representing a more clinically usable class assignment algorithm. Conclusion:The fuzzy algorithm provides a simple to interpret, linguistic rule set which classifies over 95% of breast cancer patients into one of seven clinical groups.

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Section: Introductionmentioning

confidence: 99%

A quantifier-based fuzzy classification system for breast cancer patients

Soria

Garibaldi

Green

et al. 2013

Artificial Intelligence in Medicine

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“…Rough set theory was developed by Zdzis law Pawlak [9], [10], [11] in the early 1980's. It deals with the classificatory analysis of data tables.…”

Section: Rough Set Theory -Fundamentalsmentioning

confidence: 99%

A Note on the Rough P Systems

Fathey¹,

Badr²,

Farag³

2012

IJCTE

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Abstract-A new variant of P Systems is considered, a rough p system which discussed before as an open problem. The proposed rough p system definition is based on boundary rules and on conditional communication, where communication is controlled by the contents of the strings not by the evolution rules for obtaining these strings.Index Terms-P systems, membrane computing, rough set, rough P systems.

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“…Presently, the soft set theory is making progress rapidly [1,4]. Pawlak's rough set [12,13] can be viewed as a special case of soft rough sets [4]. The topological structures of soft sets have been developed by many researchers [2,[7][8][9][15][16][17].…”

Section: Introductionmentioning

confidence: 99%