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Analysis of alternative objective functions for attribute reduction in complete decision tables

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Abstract

Attribute reduction and reducts are important notions in rough set theory that can preserve discriminatory properties to the highest possible extent similar to the entire set of attributes. In this paper, the relationships among 13 types of alternative objective functions for attribute reduction are systematically analyzed in complete decision tables. For inconsistent and consistent decision tables, it is demonstrated that there are only six and two intrinsically different objective functions for attribute reduction, respectively. Some algorithms have been put forward for minimal attribute reduction according to different objective functions. Through a counterexample, it is shown that heuristic methods cannot always guarantee to produce a minimal reduct. Based on the general definition of discernibility function, a complete algorithm for finding a minimal reduct is proposed. Since it only depends on reasoning mechanisms, it can be applied under any objective function for attribute reduction as long as the corresponding discernibility matrix has been well established.

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Acknowledgments

The authors are grateful to the anonymous referees for their valuable comments and suggestions. This work is supported by National Natural Science Foundation of China (Serial Nos. 60475019, 61075056, 60970061) and the research fund for the Doctoral Program of Higher Education in China (Serial No. 20060247039).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, People’s Republic of China

    Jie Zhou, Duoqian Miao & Hongyun Zhang

  2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 2G7, Canada

    Jie Zhou & Witold Pedrycz

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  1. Jie Zhou
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  2. Duoqian Miao
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  3. Witold Pedrycz
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  4. Hongyun Zhang
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Correspondence to Jie Zhou.

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Zhou, J., Miao, D., Pedrycz, W. et al. Analysis of alternative objective functions for attribute reduction in complete decision tables. Soft Comput 15, 1601–1616 (2011). https://doi.org/10.1007/s00500-011-0690-7

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