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Evaluation functions and decision conditions of three-way decisions with game-theoretic rough sets

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  • Azam, Nouman
  • Zhang, Yan
  • Yao, JingTao

Abstract

Three-way decisions have been used over the years in many application areas. The rough sets and its extensions provide useful approaches for three-way decisions. Typically, these approaches employ a single evaluation function or criterion to induce three-way decisions. When extending the rough set based three-way decisions to multiple criteria decision making (MCDM), two issues are encountered. The first issue is related to the construction and definition of aggregation mechanisms for dealing with differences in results of evaluation functions. The second issue is related to the setting of choice structure for selecting the three types of decision choices. In this article, we consider the role and use of game-theoretic rough set (GTRS) model to resolve and address these two issues. The issue related to differences in evaluation functions is addressed with GTRS by implementing a game that considers multiple evaluation functions as game players. The game-theoretic analysis in the GTRS is employed to resolve the differences by determining a tradeoff between evaluation functions. The issue related to choice structure is addressed by considering the conditions under which different game outcomes could constitute a game solution. In particular, the equilibrium analysis within games is used to construct the rules for three-way decisions. A demonstrative example is used to explain the use of the proposed approach. The relationship between the proposed approach and the probabilistic rough sets is also discussed.

Suggested Citation

  • Azam, Nouman & Zhang, Yan & Yao, JingTao, 2017. "Evaluation functions and decision conditions of three-way decisions with game-theoretic rough sets," European Journal of Operational Research, Elsevier, vol. 261(2), pages 704-714.
    • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:704-714
    DOI: 10.1016/j.ejor.2016.12.048
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    1. Korhonen, Pekka & Soleimani-damaneh, Majid & Wallenius, Jyrki, 2016. "Dual cone approach to convex-cone dominance in multiple criteria decision making," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1139-1143.
    2. Li, Renpu & Wang, Zheng-ou, 2004. "Mining classification rules using rough sets and neural networks," European Journal of Operational Research, Elsevier, vol. 157(2), pages 439-448, September.
    3. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    4. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 1999. "Rough approximation of a preference relation by dominance relations," European Journal of Operational Research, Elsevier, vol. 117(1), pages 63-83, August.
    5. Chakhar, Salem & Ishizaka, Alessio & Labib, Ashraf & Saad, Inès, 2016. "Dominance-based rough set approach for group decisions," European Journal of Operational Research, Elsevier, vol. 251(1), pages 206-224.
    6. Pawlak, Zdzislaw, 2002. "Rough sets, decision algorithms and Bayes' theorem," European Journal of Operational Research, Elsevier, vol. 136(1), pages 181-189, January.
    7. Blaszczynski, Jerzy & Greco, Salvatore & Slowinski, Roman, 2007. "Multi-criteria classification - A new scheme for application of dominance-based decision rules," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1030-1044, September.
    8. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    9. 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.
    10. Tülin Erdem & Michael P. Keane, 1996. "Decision-Making Under Uncertainty: Capturing Dynamic Brand Choice Processes in Turbulent Consumer Goods Markets," Marketing Science, INFORMS, vol. 15(1), pages 1-20.
    11. Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
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    Cited by:

    1. Chao, Xiangrui & Kou, Gang & Peng, Yi & Viedma, Enrique Herrera, 2021. "Large-scale group decision-making with non-cooperative behaviors and heterogeneous preferences: An application in financial inclusion," European Journal of Operational Research, Elsevier, vol. 288(1), pages 271-293.
    2. Huang, Bing & Li, Huaxiong & Feng, Guofu & Zhou, Xianzhong, 2019. "Dominance-based rough sets in multi-scale intuitionistic fuzzy decision tables," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 487-512.
    3. Wang, Mingwei & Zhang, Junping & Liang, Decui, 2024. "Multi-period share pledging with sequential three-way proportion decision," Omega, Elsevier, vol. 127(C).

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