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Published in:
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2017 | OriginalPaper | Chapter

An Algorithm for Computing Goldman Fuzzy Reducts

Authors : J. Ariel Carrasco-Ochoa, Manuel S. Lazo-Cortés, José Fco. Martínez-Trinidad

Published in: Pattern Recognition

Publisher: Springer International Publishing

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Abstract

Feature selection and attribute reduction have been tackled in the Rough Set Theory through fuzzy reducts. Recently, Goldman fuzzy reducts which are fuzzy subsets of attributes were introduced. In this paper, we introduce an algorithm for computing all Goldman fuzzy reducts of a decision system, this algorithm is the first one reported for this purpose. The experiments over standard and synthetic data sets show that the proposed algorithm is useful for datasets with up to twenty attributes.

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next chapter A Parallel Genetic Algorithm for Pattern Recognition in Mixed Databases
Footnotes
1
Since \(supp(t_1)\) and \(supp(t_2)\) are not fuzzy, \(\setminus \) denotes the classic set difference operation in Set Theory; on the other hand, \(\cup \) and \(\cap \) are, respectively, the union and intersection operations as classically defined in Fuzzy Set Theory.
 
Literature
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2.
Goldman, R.S.: Problems of fuzzy test theory. Avtomat. Telemech. 10, 146–153 (1980). (in Russian)
3.
Lazo-Cortés, M.S., Martínez-Trinidad, J.F., Carrasco-Ochoa, J.A.: A glance to the goldman’s testors from the point of view of rough set theory. In: Martínez-Trinidad, J.F., Carrasco-Ochoa, J.A., Ayala-Ramírez, V., Olvera-López, J.A., Jiang, X. (eds.) MCPR 2016. LNCS, vol. 9703, pp. 189–197. Springer, Cham (2016). doi:10.​1007/​978-3-319-39393-3_​19
4.
Lazo-Cortés, M.S., Martínez-Trinidad, J.F., Carrasco-Ochoa, J.A., Sanchez-Diaz, G.: A new algorithm for computing reducts based on the binary discernibility matrix. Intell. Data Anal. 20(2), 317–337 (2016)CrossRef
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6.
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefMATH
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Yao, Y.Y.: The two sides of the theory of rough sets. Knowl. Based Syst. 80, 67–77 (2015)CrossRef
Metadata
Title
An Algorithm for Computing Goldman Fuzzy Reducts
Authors
J. Ariel Carrasco-Ochoa
Manuel S. Lazo-Cortés
José Fco. Martínez-Trinidad
Copyright Year
2017
Book
Pattern Recognition

Print ISBN: 978-3-319-59225-1

Electronic ISBN: 978-3-319-59226-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-59226-8_1

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