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New and improved: grey multi-granulation rough sets

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  • Yun Kang
  • Shunxiang Wu
  • Yuwen Li
  • Wei Weng

Abstract

Rough set has drawn great attention in recent decades, among which multi-granulation rough set (MGRS) is an arresting direction. It constructs a formal theoretical framework to solve complex problems under the circumstance of multiple binary relations. However, the fusion of multi-granulation rough set and grey system for acquiring knowledge is still a gap. Toward this end, we devise a grey multi-granulation rough set (GMGRS) by taking multiple grey relational relations into consideration under the framework of MGRS. In grey information system, the constructed grey relational relation that measures the relationship among objects can be used to further establish multiple binary relations. Based on two different approximate strategies (seeking common reserving difference and seeking common eliminating difference), two types of GMGRS are presented, respectively. After discussing several important properties of GMGRS, we discover that the properties of the proposed GMGRS are synchronous with the classical MGRS. Meanwhile, to obtain the attribute reduction under GMGRS, we reconstruct significance measure and termination criterion based on the θ-precision pessimistic GMGRS. Last but not least, theoretical studies and practical examples demonstrate that our proposed GMGRS largely enrich the MGRS theory and provide a new technique for knowledge discovery, which is practical in real-world scenarios.

Suggested Citation

  • Yun Kang & Shunxiang Wu & Yuwen Li & Wei Weng, 2017. "New and improved: grey multi-granulation rough sets," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(12), pages 2575-2589, September.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:12:p:2575-2589
    DOI: 10.1080/00207721.2017.1324922
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    References listed on IDEAS

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    1. Kadier, Abudukeremu & Abdeshahian, Peyman & Simayi, Yibadatihan & Ismail, Manal & Hamid, Aidil Abdul & Kalil, Mohd Sahaid, 2015. "Grey relational analysis for comparative assessment of different cathode materials in microbial electrolysis cells," Energy, Elsevier, vol. 90(P2), pages 1556-1562.
    2. Bai, Chunguang & Sarkis, Joseph, 2010. "Integrating sustainability into supplier selection with grey system and rough set methodologies," International Journal of Production Economics, Elsevier, vol. 124(1), pages 252-264, March.
    3. Dimitras, A. I. & Slowinski, R. & Susmaga, R. & Zopounidis, C., 1999. "Business failure prediction using rough sets," European Journal of Operational Research, Elsevier, vol. 114(2), pages 263-280, April.
    4. Pawlak, Zdzislaw, 2005. "Some remarks on conflict analysis," European Journal of Operational Research, Elsevier, vol. 166(3), pages 649-654, November.
    5. Pawlak, Zdzisaw & Sowinski, Roman, 1994. "Rough set approach to multi-attribute decision analysis," European Journal of Operational Research, Elsevier, vol. 72(3), pages 443-459, February.
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