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The logic transformations for reducing the complexity of the discernibility function-based attribute reduction problem

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Abstract

The basic solution for locating an optimal reduct is to generate all possible reducts and select the one that best meets the given criterion. Since this problem is NP-hard, most attribute reduction algorithms use heuristics to find a single reduct with the risk to overlook for the best ones. There is a discernibility function (DF)-based approach that generates all reducts but may fail due to memory overflows even for datasets with dimensionality much below the medium. In this study, we show that the main shortcoming of this approach is its excessively high space complexity. To overcome this, we first represent a DF of \(n\) attributes by a bit-matrix (BM). Second, we partition the BM into no more than \(n-1\) sub-BMs (SBMs). Third, we convert each SBM into a subset of reducts by preventing the generation of redundant products, and finally, we unite the subsets into a complete set of reducts. Among the SBMs of a BM, the most complex one is the first SBM with a space complexity not greater than the square root of that of the original BM. The proposed algorithm converts such a SBM with \(n\) attributes into the subset of reducts with the worst case space complexity of \(\left( _{n/2}^n \right) /2\).

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Authors and Affiliations

  1. Department of Computer Engineering, Necmettin Erbakan University, Konya, Turkey

    Mehmet Hacibeyoglu

  2. Department of Electrical and Electronic Engineering, Mevlana University, Konya, Turkey

    Mohammad Shukri Salman

  3. Technical Vocation School of Higher Education, Selcuk University, Konya, Turkey

    Murat Selek

  4. Department of Computer Education and Instructional Technologies Teaching, Mevlana University, Konya, Turkey

    Sirzat Kahramanli

Authors
  1. Mehmet Hacibeyoglu
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  2. Mohammad Shukri Salman
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  3. Murat Selek
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  4. Sirzat Kahramanli
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Correspondence to Mehmet Hacibeyoglu.

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Hacibeyoglu, M., Salman, M.S., Selek, M. et al. The logic transformations for reducing the complexity of the discernibility function-based attribute reduction problem. Knowl Inf Syst 46, 599–628 (2016). https://doi.org/10.1007/s10115-015-0824-9

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  • DOI: https://doi.org/10.1007/s10115-015-0824-9

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