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Rough set approach to multiple criteria classification with imprecise evaluations and assignments

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  • Dembczynski, Krzysztof
  • Greco, Salvatore
  • Slowinski, Roman

Abstract

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.

Suggested Citation

  • Dembczynski, Krzysztof & Greco, Salvatore & Slowinski, Roman, 2009. "Rough set approach to multiple criteria classification with imprecise evaluations and assignments," European Journal of Operational Research, Elsevier, vol. 198(2), pages 626-636, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:626-636
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    References listed on IDEAS

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    1. 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.
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    5. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2004. "Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules," European Journal of Operational Research, Elsevier, vol. 158(2), pages 271-292, October.
    6. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2002. "Rough sets methodology for sorting problems in presence of multiple attributes and criteria," European Journal of Operational Research, Elsevier, vol. 138(2), pages 247-259, April.
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    3. Bernard Roy & Roman Slowinski, 2013. "Questions guiding the choice of a multicriteria decision aiding method," Post-Print hal-00874292, HAL.
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    15. Eduardo Fernandez & Jorge Navarro & Rafael Olmedo, 2018. "Characterization of the Effectiveness of Several Outranking-Based Multi-Criteria Sorting Methods," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1047-1084, July.
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    18. Mi, Yunlong & Quan, Pei & Shi, Yong & Wang, Zongrun, 2022. "Concept-cognitive computing system for dynamic classification," European Journal of Operational Research, Elsevier, vol. 301(1), pages 287-299.
    19. Liu, Jiapeng & Liao, Xiuwu & Yang, Jian-bo, 2015. "A group decision-making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty," European Journal of Operational Research, Elsevier, vol. 246(3), pages 858-873.
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