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Modeling assignment-based pairwise comparisons within integrated framework for value-driven multiple criteria sorting

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  • Kadziński, Miłosz
  • Ciomek, Krzysztof
  • Słowiński, Roman

Abstract

We introduce a new preference disaggregation modeling formulations for multiple criteria sorting with a set of additive value functions. The preference information supplied by the Decision Maker (DM) is composed of: (1) possibly imprecise assignment examples, (2) desired class cardinalities, and (3) assignment-based pairwise comparisons. The latter have the form of imprecise statements referring to the desired assignments for pairs of alternatives, but without specifying any concrete class. Additionally, we account for preferences concerning the shape of the marginal value functions and desired comprehensive values of alternatives assigned to a given class or class range. The exploitation of all value functions compatible with these preferences results in three types of results: (1) necessary and possible assignments, (2) extreme class cardinalities, and (3) necessary and possible assignment-based preference relations. These outputs correspond to different types of admitted preference information. By exhibiting different outcomes, we encourage the DM in various ways to enrich her/his preference information interactively. The applicability of the framework is demonstrated on data involving the classification of cities into liveability classes.

Suggested Citation

  • Kadziński, Miłosz & Ciomek, Krzysztof & Słowiński, Roman, 2015. "Modeling assignment-based pairwise comparisons within integrated framework for value-driven multiple criteria sorting," European Journal of Operational Research, Elsevier, vol. 241(3), pages 830-841.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:830-841
    DOI: 10.1016/j.ejor.2014.09.050
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    Cited by:

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    2. Kadziński, Miłosz & Cinelli, Marco & Ciomek, Krzysztof & Coles, Stuart R. & Nadagouda, Mallikarjuna N. & Varma, Rajender S. & Kirwan, Kerry, 2018. "Co-constructive development of a green chemistry-based model for the assessment of nanoparticles synthesis," European Journal of Operational Research, Elsevier, vol. 264(2), pages 472-490.
    3. Liu, Jiapeng & Liao, Xiuwu & Kadziński, Miłosz & Słowiński, Roman, 2019. "Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1071-1089.
    4. Miłosz Kadziński & Magdalena Martyn, 2021. "Enriched preference modeling and robustness analysis for the ELECTRE Tri-B method," Annals of Operations Research, Springer, vol. 306(1), pages 173-207, November.
    5. 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.
    6. Adiel Teixeira Almeida & Eduarda Asfora Frej & Lucia Reis Peixoto Roselli, 2021. "Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff," 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. 29(1), pages 7-47, March.
    7. Francineide Morais Bezerra & Paulo Melo & João Paulo Costa, 2017. "Reaching Consensus with VICA-ELECTRE TRI: A Case Study," Group Decision and Negotiation, Springer, vol. 26(6), pages 1145-1171, November.
    8. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods—Part I: survey of the literature," 4OR, Springer, vol. 21(1), pages 1-46, March.
    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.
    10. Anna Kędzior & Konrad Kułakowski, 2023. "Multiple-Criteria Heuristic Rating Estimation," Mathematics, MDPI, vol. 11(13), pages 1-19, June.
    11. Selin Özpeynirci & Özgür Özpeynirci & Vincent Mousseau, 2018. "An interactive algorithm for multiple criteria constrained sorting problem," Annals of Operations Research, Springer, vol. 267(1), pages 447-466, August.
    12. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    13. Wu, Xingli & Liao, Huchang, 2023. "Value-driven preference disaggregation analysis for uncertain preference information," Omega, Elsevier, vol. 115(C).
    14. Chao, Xiangrui & Kou, Gang & Li, Tie & Peng, Yi, 2018. "Jie Ke versus AlphaGo: A ranking approach using decision making method for large-scale data with incomplete information," European Journal of Operational Research, Elsevier, vol. 265(1), pages 239-247.
    15. Vincent Mousseau & Özgür Özpeynirci & Selin Özpeynirci, 2018. "Inverse multiple criteria sorting problem," Annals of Operations Research, Springer, vol. 267(1), pages 379-412, August.
    16. Marcin Anholcer & János Fülöp, 2019. "Deriving priorities from inconsistent PCM using network algorithms," Annals of Operations Research, Springer, vol. 274(1), pages 57-74, March.
    17. Ru, Zice & Liu, Jiapeng & Kadziński, Miłosz & Liao, Xiuwu, 2023. "Probabilistic ordinal regression methods for multiple criteria sorting admitting certain and uncertain preferences," European Journal of Operational Research, Elsevier, vol. 311(2), pages 596-616.
    18. Costa, Ana Sara & Corrente, Salvatore & Greco, Salvatore & Figueira, José Rui & Borbinha, José, 2020. "A robust hierarchical nominal multicriteria classification method based on similarity and dissimilarity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 986-1001.
    19. Cinelli, Marco & Kadziński, Miłosz & Miebs, Grzegorz & Gonzalez, Michael & Słowiński, Roman, 2022. "Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 633-651.

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