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Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations

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  • Tlili, Ali
  • Belahcène, Khaled
  • Khaled, Oumaima
  • Mousseau, Vincent
  • Ouerdane, Wassila

Abstract

The Non-Compensatory Sorting model aims at assigning alternatives evaluated on multiple criteria to one of the predefined ordered categories. Computing parameters of the Non-Compensatory Sorting model compatible to a set of reference assignments is computationally demanding. To overcome this problem, two formulations based on Boolean satisfiability have recently been proposed to learn the parameters of the Non-Compensatory Sorting model from perfect preference information, i.e. when the set of reference assignments can be completely represented in the model. In this paper, two popular variants of the Non-Compensatory Sorting model are considered, the Non-Compensatory Sorting model with a unique profile and the Non-Compensatory Sorting model with a unique set of sufficient coalitions. For each variant, we start by extending the formulation based on a separation principle to the multiple category case. Moreover, we extend the two formulations to handle inconsistency in the preference information using the Maximum satisfiability problem language. A computational study is proposed to compare the efficiency of both formulations to learn the two Non-Compensatory Sorting models (with a unique profile and with a unique set of sufficient coalitions) from noiseless and noisy preference information.

Suggested Citation

  • Tlili, Ali & Belahcène, Khaled & Khaled, Oumaima & Mousseau, Vincent & Ouerdane, Wassila, 2022. "Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations," European Journal of Operational Research, Elsevier, vol. 298(3), pages 979-1006.
    • Handle: RePEc:eee:ejores:v:298:y:2022:i:3:p:979-1006
    DOI: 10.1016/j.ejor.2021.08.017
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    1. 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.
    2. Ali Tlili & Oumaima Khaled & Vincent Mousseau & Wassila Ouerdane, 2023. "Interactive portfolio selection involving multicriteria sorting models," Annals of Operations Research, Springer, vol. 325(2), pages 1169-1195, June.
    3. Wenfeng Zhu & Hengjie Zhang & Jing Xiao, 2023. "Coming to Consensus on Classification in Flexible Linguistic Preference Relations: The Role of Personalized Individual Semantics," Group Decision and Negotiation, Springer, vol. 32(5), pages 1237-1271, October.

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