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Probabilistic Rough Sets

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Springer Handbook of Computational Intelligence

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Abstract

As quantitative generalizations of Pawlak rough sets, probabilistic rough sets consider degrees of overlap between equivalence classes and the set. An equivalence class is put into the lower approximation if the conditional probability of the set, given the equivalence class, is equal to or above one threshold; an equivalence class is put into the upper approximation if the conditional probability is above another threshold hold. We review a basic model of probabilistic rough sets (i. e., decision-theoretic rough set model) and variations. We present the main results of probabilistic rough sets by focusing on three issues: (a) interpretation and calculation of the required thresholds, (b) estimation of the required conditional probabilities, and (c) interpretation and applications of probabilistic rough set approximations.

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Abbreviations

DRSA:

dominance-based rough set approach

DTRS:

decision-theoretic rough set

MCDA:

multiple criteria decision aiding

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Authors and Affiliations

  1. Inst. Computing Science, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  2. Dep. Computer Science, University of Regina, 3737 Wascana Parkway, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  3. Dep. Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

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  1. Yiyu Yao
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  2. Salvatore Greco
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  3. Roman Słowiński
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Correspondence to Yiyu Yao .

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Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Yao, Y., Greco, S., Słowiński, R. (2015). Probabilistic Rough Sets. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_24

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