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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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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    2. 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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    Cited by:

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    2. Bernard Roy & Roman Slowinski, 2013. "Questions guiding the choice of a multicriteria decision aiding method," Post-Print hal-00874292, HAL.
    3. Du, Wen Sheng & Hu, Bao Qing, 2017. "Dominance-based rough fuzzy set approach and its application to rule induction," European Journal of Operational Research, Elsevier, vol. 261(2), pages 690-703.
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    7. Liu, Jiapeng & Liao, Xiuwu & Huang, Wei & Yang, Jian-bo, 2018. "A new decision-making approach for multiple criteria sorting with an imbalanced set of assignment examples," European Journal of Operational Research, Elsevier, vol. 265(2), pages 598-620.
    8. 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.
    9. 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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    15. Zhen Zhang & Zhuolin Li, 2023. "Consensus-based TOPSIS-Sort-B for multi-criteria sorting in the context of group decision-making," Annals of Operations Research, Springer, vol. 325(2), pages 911-938, June.
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    18. Nejc Trdin & Marko Bohanec, 2018. "Extending the multi-criteria decision making method DEX with numeric attributes, value distributions and relational models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 1-41, March.
    19. Wang, Hailiang & Zhou, Mingtian & She, Kun, 2015. "Induction of ordinal classification rules from decision tables with unknown monotonicity," European Journal of Operational Research, Elsevier, vol. 242(1), pages 172-181.
    20. Salvatore Corrente & Salvatore Greco & Roman Słowiński, 2017. "Handling imprecise evaluations in multiple criteria decision aiding and robust ordinal regression by n-point intervals," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 127-157, June.
    21. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2012. "A multiple criteria sorting method where each category is characterized by several reference actions: The Electre Tri-nC method," European Journal of Operational Research, Elsevier, vol. 217(3), pages 567-579.
    22. Yi-Shian Lee & Lee-Ing Tong, 2012. "Predicting High or Low Transfer Efficiency of Photovoltaic Systems Using a Novel Hybrid Methodology Combining Rough Set Theory, Data Envelopment Analysis and Genetic Programming," Energies, MDPI, vol. 5(3), pages 1-16, February.
    23. Copiello, Sergio, 2016. "Leveraging energy efficiency to finance public-private social housing projects," Energy Policy, Elsevier, vol. 96(C), pages 217-230.
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