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Rough Sets Based on Possibly Indiscernible Classes in Incomplete Information Tables with Continuous Values

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Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2019 (AISI 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1058))

Abstract

Rough sets under incomplete information with continuous domains are examined based on possible world semantics. We focus on possible indiscernibility relations, although the traditional approaches are done under possible tables. This is because we only obtain a finite number of possible indiscernibility relations even if infinite number of possible tables are derived from an incomplete information table. A possibly indiscernible class for an object is derived from a possible indiscernibility relation. The family of possibly indiscernible classes for the object is a lattice for inclusion. Lower and upper approximations are derived from using the minimal and the maximal elements in the lattice. Therefore, there is no computational complexity for the number of objects with incomplete information. Furthermore, the approach based on possible world semantics gives the same approximations as ones obtained from our extended approach, which is proposed in the previous work using indiscernible classes. Therefore, the approach developed in this paper justifies our extended approach.

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Notes

  1. 1.

    When threshold \(\delta \) requires to denote, \(R_{a_{i}}^{\delta }\) is used.

  2. 2.

    \(\delta _{a_{i}}\) is expressed by \(\delta \) omitting \(a_{i}\) for simplicity if no confusion.

  3. 3.

    When threshold \(\delta \) requires to denote, \([o]_{a_{i}}^{\delta }\) is used.

  4. 4.

    For the sake of simplicity and space limitation, We describe the case of an attribute, although our approach can be easily extended to the case of more than one attribute.

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Author information

Authors and Affiliations

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

    Michinori Nakata

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

    Hiroshi Sakai

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

    Keitarou Hara

Authors
  1. Michinori Nakata
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  2. Hiroshi Sakai
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  3. Keitarou Hara
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Correspondence to Michinori Nakata .

Editor information

Editors and Affiliations

  1. Cairo University, Giza, Egypt

    Aboul Ella Hassanien

  2. The British University in Dubai, Dubai, United Arab Emirates

    Khaled Shaalan

  3. Ain Shams University, Cairo, Egypt

    Mohamed Fahmy Tolba

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Nakata, M., Sakai, H., Hara, K. (2020). Rough Sets Based on Possibly Indiscernible Classes in Incomplete Information Tables with Continuous Values. In: Hassanien, A., Shaalan, K., Tolba, M. (eds) Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2019. AISI 2019. Advances in Intelligent Systems and Computing, vol 1058. Springer, Cham. https://doi.org/10.1007/978-3-030-31129-2_2

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