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Kryszkiewicz’s Relation for Indiscernibility of Objects in Data Tables Containing Missing Values

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Rough Sets (IJCRS 2023)

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Abstract

We check Kryszkiewicz’s approach for rough sets in data tables containing missing values in terms of Lipski’s approach based on possible world semantics. The relation for indiscernibility of objects used by Kryszkiewicz, which most authors use, derives a pair of lower and upper approximations as the actual approximations to a target set. This means that Kryszkiewicz’s approach is accompanied by information loss because what Lipski’s approach derives is the lower and upper bounds of the actual approximations. It is clarified that Kryszkiewicz’s relation for indiscernibility is equal to the union of possible indiscernibility relations in Lipski’s approach. As a result, the lower and the upper approximation derived from Kryszkiewicz’s relation are equal to the lower bound of the actual lower approximation and the upper bound of the actual upper approximation, respectively. Bridging the gap between the two approaches, we propose another relation for indiscernibility that is equal to the intersection of possible indiscernibility relations. By using Kryszkiewicz’s relation and the proposed relation, Kryszkiewicz’s approach can derive the same approximations as Lipski’s one. Therefore, we can keep using Kryszkiewicz’s approach without information loss.

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Acknowledgment

Part of this work is supported by JSPS KAKENHI Grant Number JP20K11954.

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Authors and Affiliations

  1. Faculty of Management and Information Science, Josai International University, 1 Gumyo, Togane, Chiba, 283-8555, Japan

    Michinori Nakata & Norio Saito

  2. Department of Mathematics and Computer Aided Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550, Japan

    Hiroshi Sakai

  3. Faculty of Informatics, Tokyo University of Information Sciences, 4-1 Onaridai, Wakaba-ku, Chiba, 265-8501, Japan

    Takeshi Fujiwara

Authors
  1. Michinori Nakata
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  2. Norio Saito
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  3. Hiroshi Sakai
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  4. Takeshi Fujiwara
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Corresponding author

Correspondence to Michinori Nakata .

Editor information

Editors and Affiliations

  1. IRCCS Istituto Ortopedico Galeazzi, Milano, Italy

    Andrea Campagner

  2. Ghent University, Ghent, Belgium

    Oliver Urs Lenz

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Shuyin Xia

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. AGH University of Science and Technology, Kraków, Poland

    Jarosław Wąs

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Nakata, M., Saito, N., Sakai, H., Fujiwara, T. (2023). Kryszkiewicz’s Relation for Indiscernibility of Objects in Data Tables Containing Missing Values. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_12

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  • DOI: https://doi.org/10.1007/978-3-031-50959-9_12

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