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Advanced Methods and Applications in Computational Intelligence pp 25–41Cite as

Fast Algorithm of Attribute Reduction Based on the Complementation of Boolean Function

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Part of the book series: Topics in Intelligent Engineering and Informatics ((TIEI,volume 6))

Abstract

In this chapter we propose a new method of solving the attribute reduction problem. Our method is different to the classical approach using the so-called discernibility function and its CNF into DNF transformation. We have proved that the problem is equivalent to very efficient unate complementation algorithm. That is why we propose new algorithm based on recursive execution of the procedure, which at every step of recursion selects the splitting variable and then calculates the cofactors with respect to the selected variables (Shannon expansion procedure). The recursion continues until at each leaf of the recursion tree the easily computable rules for complement process can be applied. The recursion process creates a binary tree so that the final result is obtained merging the results in the subtrees. The final matrix represents all the minimal reducts of a decision table or all the minimal dependence sets of input variables, respectively. According to the results of computer tests, better results can be achieved by application of our method in combination with the classical method.

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Author information

Authors and Affiliations

  1. Institute of Telecommunications, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Grzegorz Borowik & Tadeusz Łuba

Authors
  1. Grzegorz Borowik
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  2. Tadeusz Łuba
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Corresponding author

Correspondence to Grzegorz Borowik .

Editor information

Editors and Affiliations

  1. Wroclaw University of Technology, Wybrzeze Wyspianskiego Street 27, Wroclaw, 50-370, Poland

    Ryszard Klempous

  2. Wroclaw University of Technology, Wybrzeze Wyspianskiego Street 27, Wroclaw, 50-370, Poland

    Jan Nikodem

  3. of Applied Sciences, Upper Austria University, Softwarepark 11, Hagenberg, 4232, Austria

    Witold Jacak

  4. , Bld 1 Level 22, University of Technology, Broadway, Ultimo/Syd, Sydney, 2007, New South Wales, Australia

    Zenon Chaczko

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Borowik, G., Łuba, T. (2014). Fast Algorithm of Attribute Reduction Based on the Complementation of Boolean Function. In: Klempous, R., Nikodem, J., Jacak, W., Chaczko, Z. (eds) Advanced Methods and Applications in Computational Intelligence. Topics in Intelligent Engineering and Informatics, vol 6. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-01436-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-01436-4_2

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-01435-7

  • Online ISBN: 978-3-319-01436-4

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