[en] Multiple criteria sorting methods assign objects into ordered categories while objects are characterized by a vector of n attributes values. Categories are ordered, and the assignment of the object is monotonic w.r.t. to some underlying order on the attributes scales (criteria). Our goal is to offer a survey of the literature on multiple criteria sorting methods, since the origins, in the 1980’s, focusing on the underlying models. In the first part of the paper, we start by recalling two main models, one based on additive value functions (UTADIS) and the other one an outranking relation (Electre Tri). Then we draw a (structured) picture of multiple criteria sorting models and the methods designed for eliciting their parameters or learning them based on assignment examples. In a second part of the paper, we attempt to provide a theoretical view of the field and position some existing models within it. We then discuss issues related to imperfect or insufficient information.
Disciplines :
Computer science
Author, co-author :
Belahcène, Khaled; MICS, CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France
Mousseau, Vincent; MICS, CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France
Ouerdane, Wassila; MICS, CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France
Pirlot, Marc ; Université de Mons - UMONS > Faculté Polytechnique > Service de Mathématique et Recherche opérationnelle
Sobrie, Olivier ; Université de Mons - UMONS > Faculté Polytechnique > Service de Mathématique et Recherche opérationnelle
Language :
English
Title :
A guided tour of multiple criteria sorting models and methods
We are grateful to Denis Bouyssou for reading a previous version of the manuscript and making a number of relevant comments. We also thank the Editors for inviting us to write this survey and for their observations on the final draft. Of course, the responsibility for errors and omissions in this paper as well as the opinions that are expressed remains entirely with the authors.
C.C. Aggarwal C. Chen J. Han The inverse classification problem Journal of Computer Science and Technology 25 3 458 468 10.1007/s11390-010-9337-x
M. Alaya S. Bussy S. Gaïffas A. Guilloux Binarsity: A penalization for one-hot encoded features in linear supervised learning Journal of Machine Learning Research 20 118:1 118:34
J. Almeida-Dias J.R. Figueira B. Roy ELECTRE TRI-C: A multiple criteria sorting method based on characteristic reference actions European Journal of Operational Research 204 3 565 580 10.1016/j.ejor.2009.10.018
J. Almeida-Dias J.R. Figueira B. Roy A multiple criteria sorting method where each category is characterized by several reference actions: The ELECTRE TRI-nC method European Journal of Operational Research 217 3 567 579 10.1016/j.ejor.2011.09.047
P.A. Alvarez A. Ishizaka L. Martínez Multiple-criteria decision-making sorting methods: A survey Expert Systems with Applications 183 10.1016/j.eswa.2021.115368 115368
M. Amoussou K. Belahcène C. Labreuche Ch N. Maudet V. Mousseau W. Ouerdane Questionable stepwise explanations for a robust additive preference model International Journal of Approximate Reasoning 171 10.1016/j.ijar.2023.108982 108982
S. Angilella S. Greco B. Matarazzo Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral European Journal of Operational Research 201 1 277 288 10.1016/j.ejor.2009.02.023
C. Araz I. Ozkarahan Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure International Journal of Production Economics 106 2 585 606 10.1016/j.ijpe.2006.08.008
S.G. Arcidiacono S. Corrente S. Greco Robust stochastic sorting with interacting criteria hierarchically structured European Journal of Operational Research 292 2 735 754 10.1016/j.ejor.2020.11.024
C.A. Bana e Costa J.-C. Vansnick MACBETH, an interactive path towards the construction of cardinal value functions International Transactions in Operational Research 1 4 489 500 10.1016/0969-6016(94)90010-8
C.A. Bana e Costa J.-M. De Corte J.-C. Vansnick S. Greco M. Ehrgott J.R. Figueira On the mathematical foundations of MACBETH Multiple criteria decision analysis: State of the art surveys, international series in operations research and management science Cham Springer 409 437
Bazin, A., Couceiro, M., Devignes, M.-D., & Napoli, A. (2020). Explaining multicriteria decision making with formal concept analysis. In Concept lattices and applications 2020, volume 2668 of CEUR workshop proceedings (pp. 119–130).
N. Belacel Multicriteria assignment method PROAFTN: Methodology and medical application European Journal of Operational Research 125 1 175 183 10.1016/S0377-2217(99)00192-7
N. Belacel H.B. Raval A.P. Punnen Learning multicriteria fuzzy classification method PROAFTN from data Computers & Operations Research 34 7 1885 1898 10.1016/j.cor.2005.07.019
Belahcène, K., Labreuche, C., Maudet, N., Mousseau, V., & Ouerdane, W. (2017a). Explaining robust additive utility models by sequences of preference swaps. Theory and Decision,82(2), 151–183.
Belahcène, K., Labreuche, C., Maudet, N., Mousseau, V., & Ouerdane, W. (2017b). A model for accountable ordinal sorting. In Sierra, C. (Ed.), Proceedings of the twenty-sixth international joint conference on artificial intelligence, IJCAI 2017, Melbourne, Australia, August 19–25, 2017 (pp. 814–820).
Belahcène, K., Labreuche, C., Maudet, N., Mousseau, V., & Ouerdane, W. (2018a). An efficient SAT formulation for learning multiple criteria non-compensatory sorting rules from examples. Computers & Operations Research,97, 58–71.
Belahcène, K., Labreuche, C., Maudet, N., Mousseau, V., & Ouerdane, W. (2018b). Accountable approval sorting. In Proceedings of the 27th international joint conference on artificial intelligence (IJCAI 2018).
Belahcène, K., Mousseau, V., Ouerdane, W., Pirlot, M., & Sobrie, O. (2023a). Multiple criteria sorting models and methods. Part I: Survey of the literature. 4OR,21(1), 1–46.
Belahcène, K., Mousseau, V., Ouerdane, W., Pirlot, M., & Sobrie, O. (2023b). Multiple criteria sorting models and methods. Part II: Theoretical results and general issues. 4OR,21(2), 181–204.
N. Benabbou P. Perny P. Viappiani Incremental elicitation of Choquet capacities for multicriteria choice, ranking and sorting problems Artificial Intelligence 246 152 180 10.1016/j.artint.2017.02.001
G. Bous P. Fortemps F. Glineur M. Pirlot ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements European Journal of Operational Research 206 2 435 444 10.1016/j.ejor.2010.03.009
Bouyssou, D., & Marchant, T. (2007a). An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories. European Journal of Operational Research,178(1), 217–245.
Bouyssou, D., & Marchant, T. (2007b). An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories. European Journal of Operational Research,178(1), 246–276.
D. Bouyssou T. Marchant Ordered categories and additive conjoint measurement on connected sets Journal of Mathematical Psychology 53 2 92 105 10.1016/j.jmp.2008.12.004
D. Bouyssou T. Marchant Additive conjoint measurement with ordered categories European Journal of Operational Research 203 1 195 204 10.1016/j.ejor.2009.07.032
D. Bouyssou T. Marchant On the relations between ELECTRE TRI-B and ELECTRE TRI-C and on a new variant of ELECTRE TRI-B European Journal of Operational Research 242 1 201 211 10.1016/j.ejor.2014.09.057
D. Bouyssou T. Marchant M. Pirlot A. Tsoukiàs P. Vincke Evaluation and decision models with multiple criteria: Stepping stones for the analyst New York Springer
D. Bouyssou T. Marchant M. Pirlot S. Brams W.V. Gehrlein F.S. Roberts A conjoint measurement approach to the discrete Sugeno integral The mathematics of preference, choice and order. Essays in honor of Peter C. Fishburn Cham Springer 85 109 10.1007/978-3-540-79128-7_6
D. Bouyssou T. Marchant M. Pirlot A note on ELECTRE TRI-nB with few limiting profiles 4OR 20 443 463 10.1007/s10288-021-00485-y
D. Bouyssou T. Marchant M. Pirlot A theoretical look at Electre Tri-nB and related sorting models 4OR 21 1 31 10.1007/s10288-022-00501-9
J.P. Brans P. Vincke A preference ranking organization method Management Science 31 6 647 656 10.1287/mnsc.31.6.647
J.-R. Cano P.A. Gutiérrez B. Krawczyk M. Woźniak S. García Monotonic classification an overview on algorithms, performance measures and data sets Neurocomputing 341 168 182 10.1016/j.neucom.2019.02.024
Y. Chen K.W. Hipel D.M. Kilgour Multiple-criteria sorting using case-based distance models with an application in water resources management IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 37 5 680 691 10.1109/TSMCA.2007.902629
Y. Chen K.W. Li D.M. Kilgour K.W. Hipel A case-based distance model for multiple criteria ABC analysis Computers & Operations Research 35 3 776 796 10.1016/j.cor.2006.03.024
Y. Chen D.M. Kilgour K.W. Hipel A decision rule aggregation approach to multiple criteria-multiple participant sorting Group Decision and Negotiation 21 5 727 745 10.1007/s10726-011-9246-6
M. Cinelli M. Kadziński G. Miebs M. Gonzalez R. Słowiński Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system European Journal of Operational Research 302 633 651 10.1016/j.ejor.2022.01.011
A. Colorni A. Tsoukiàs Rating or sorting: Terminology matters Journal of Multi-Criteria Decision Analysis 28 3–4 131 133 10.1002/mcda.1733
S. Corrente M. Doumpos S. Greco R. Słowiński C. Zopounidis Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions Annals of Operations Research 251 1–2 117 139
S. Corrente S. Greco R. Słowiński Multiple criteria hierarchy process for ELECTRE Tri methods European Journal of Operational Research 252 1 191 203 10.1016/j.ejor.2015.12.053
A.S. Costa J.R. Figueira J. Borbinha A multiple criteria nominal classification method based on the concepts of similarity and dissimilarity European Journal of Operational Research 271 1 193 209 10.1016/j.ejor.2018.05.029
A.S. Costa S. Corrente S. Greco J.R. Figueira J. Borbinha A robust hierarchical nominal multicriteria classification method based on similarity and dissimilarity European Journal of Operational Research 286 3 986 1001 10.1016/j.ejor.2020.04.021
S. Damart L.C. Dias V. Mousseau Supporting groups in sorting decisions: Methodology and use of a multi-criteria aggregation/disaggregation DSS Decision Support Systems 43 4 1464 1475 10.1016/j.dss.2006.06.002
F. de Morais Bezerra P. Melo J.P. Costa Reaching consensus with VICA-ELECTRE TRI: A case study Group Decision and Negotiation 26 6 1145 1171 10.1007/s10726-017-9539-5
De Smet, Y. (2019). Beyond multicriteria ranking problems: The case of PROMETHEE. In Multiple criteria decision making (pp. 95–114). Springer.
Y. De Smet L. Montano Guzmán Towards multicriteria clustering: An extension of the k-means algorithm European Journal of Operational Research 158 2 390 398 10.1016/j.ejor.2003.06.012
Y. De Smet P. Nemery R. Selvaraj An exact algorithm for the multicriteria ordered clustering problem Omega 40 6 861 869 10.1016/j.omega.2012.01.007
K. Dembczyński W. Kotlowski R. Słowiński L. Rutkowski R. Tadeusiewicz L.A. Zadeh J.M. Zurada Additive preference model with piecewise linear components resulting from dominance-based rough set approximations ICAISC, volume 4029 of lecture notes in computer science Cham Springer 499 508 ISBN 3-540-35748-3
L. Demir M.E. Akpınar C. Araz M.A. Ilgın A green supplier evaluation system based on a new multi-criteria sorting method: VIKORSORT Expert Systems with Applications 114 479 487 10.1016/j.eswa.2018.07.071
L. Dias V. Mousseau J.R. Figueira J. Clímaco An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI European Journal of Operational Research 138 1 332 348 10.1016/S0377-2217(01)00250-8
R. Diaz E. Fernández J.R. Figueira J. Navarro E. Solares Revisiting relational-based ordinal classification methods from a more flexible conception of characteristic profiles Omega 127 10.1016/j.omega.2024.103080 103080
Doshi-Velez, F., Kortz, M., Budish, R., Bavitz, Ch., Gershman, S., O’Brien, D., Schieber, S., Waldo, J., Weinberger, D., & Wood, A. (2017). Accountability of AI under the law: The role of explanation. CoRR, arXiv:1711.01134.
M. Doumpos C. Zopounidis Multicriteria decision aid classification methods Dordrecht Kluwer Academic Publishers
M. Doumpos C. Zopounidis Regularized estimation for preference disaggregation in multiple criteria decision making Computational Optimization and Applications 38 1 61 80 10.1007/s10589-007-9037-9
M. Doumpos C. Zopounidis Preference disaggregation and statistical learning for multicriteria decision support: A review European Journal of Operational Research 209 3 203 214 10.1016/j.ejor.2010.05.029
M. Doumpos Y. Marinakis M. Marinaki C. Zopounidis An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method European Journal of Operational Research 199 2 496 505 10.1016/j.ejor.2008.11.035
M. Doumpos C. Zopounidis E. Galariotis Inferring robust decision models in multicriteria classification problems: An experimental analysis European Journal of Operational Research 236 2 601 611 10.1016/j.ejor.2013.12.034
D. Dubois J.-L. Marichal H. Prade M. Roubens R. Sabbadin The use of the discrete Sugeno integral in decision making: A survey International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9 539 561 10.1142/S0218488501001058
L. Duckstein S. Opricovic Multiobjective optimization in river basin development Water Resources Research 16 1 14 20 10.1029/WR016i001p00014
J.S. Dyer Remarks on the analytic hierarchy process Management Science 36 3 249 258 10.1287/mnsc.36.3.249
S. Eppe J. Roland Y. De Smet On the use of valued action profiles for relational multi-criteria clustering International Journal of Multicriteria Decision Making 4 201 233 10.1504/IJMCDM.2014.064796
E. Ersek Uyanık O. Sobrie V. Mousseau M. Pirlot Enumerating and categorizing positive Boolean functions separable by a k-additive capacity Discrete Applied Mathematics 229 17 30 10.1016/j.dam.2017.04.010
E. Fernández J. Navarro A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method European Journal of Operational Research 213 2 405 413 10.1016/j.ejor.2011.03.036
E. Fernández J.R. Figueira J. Navarro B. Roy ELECTRE TRI-nB: A new multiple criteria ordinal classification method European Journal of Operational Research 263 1 214 224 10.1016/j.ejor.2017.04.048
Fernández, E., Figueira, J. R., & Navarro, J. (2019a). An interval extension of the outranking approach and its application to multiple-criteria ordinal classification. Omega,84, 189–198.
Fernández, E., Figueira, J. R., & Navarro, J. (2019b). An indirect elicitation method for the parameters of the ELECTRE TRI-nB model using genetic algorithms. Applied Soft Computing,77, 723–733.
E. Fernández J.R. Figueira J. Navarro Interval-based extensions of two outranking methods for multi-criteria ordinal classification Omega 95 10.1016/j.omega.2019.05.001 102065
E. Fernández J. Navarro E. Solares A hierarchical interval outranking approach with interacting criteria European Journal of Operational Research 298 1 293 307 10.1016/j.ejor.2021.06.065
E. Fernández J.R. Figueira J. Navarro A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes Annals of Operations Research 325 2 819 843 10.1007/s10479-022-04554-1
Figueira, J.R., De Smet, Y., & Brans, J.-P. (2004). MCDA methods for sorting and clustering problems: PROMETHEE TRI and PROMETHEE CLUSTER. Research report, SMG - ULB.
J.R. Figueira S. Greco B. Roy ELECTRE methods with interaction between criteria: An extension of the concordance index European Journal of Operational Research 199 2 478 495 10.1016/j.ejor.2008.11.025
B.E. Flores D.C. Whybark Multiple criteria ABC analysis International Journal of Operations & Production Management 6 38 46 10.1108/eb054765
J. Fürnkranz E. Hüllermeier J. Fürnkranz E. Hüllermeier Preference learning: An introduction Preference learning Cham Springer 1 17
A. Ghahraman D. Prior A learning ladder toward efficiency: Proposing network-based stepwise benchmark selection Omega 63 83 93 10.1016/j.omega.2015.10.004
M. Grabisch Remarkable polyhedra related to set functions, games and capacities TOP 24 301 326 10.1007/s11750-016-0421-4
M. Grabisch Set functions, games and capacities in decision making. Theory and decision library C Basel Springer 10.1007/978-3-319-30690-2
S. Greco B. Matarazzo R. Słowiński A. Colorni M. Paruccini B. Roy Conjoint measurement and rough set approach for multicriteria sorting problems in presence of ordinal criteria A-MCD-A. Aide Multicritère à la Décision/Multiple criteria decision aid Luxembourg European Commission, Joint Research Centre 117 144
S. Greco B. Matarazzo R. Słowiński Rough sets methodology for sorting problems in presence of multiple attributes and criteria European Journal of Operational Research 138 2 247 259 10.1016/S0377-2217(01)00244-2
S. Greco V. Mousseau R. Słowiński Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions European Journal of Operational Research 191 2 416 436 10.1016/j.ejor.2007.08.013
S. Greco V. Mousseau R. Słowiński Multiple criteria sorting with a set of additive value functions European Journal of Operational Research 207 3 1455 1470 10.1016/j.ejor.2010.05.021
S. Greco M. Kadziński R. Słowiński Selection of a representative value function in robust multiple criteria sorting Computers & Operations Research 38 11 1620 1637 10.1016/j.cor.2011.02.003
S. Greco M. Kadziński V. Mousseau R. Słowiński Robust ordinal regression for multiple criteria group decision: UTAGMS-GROUP and UTADISGMS-GROUP Decision Support Systems 52 3 549 561 10.1016/j.dss.2011.10.005
S. Greco V. Mousseau R. Słowiński Robust ordinal regression for value functions handling interacting criteria European Journal of Operational Research 239 3 711 730 10.1016/j.ejor.2014.05.022
S. Greco B. Matarazzo R. Słowiński J. Figueira S. Greco M. Ehrgott Decision rule approach Multiple criteria decision analysis: State of the art surveys, number 233 in international series in operations research & management science New York Springer 497 552 10.1007/978-1-4939-3094-4_13 First Edition: 2005
D. Gunning E. Vorm J.Y. Wang M. Turek Darpa’s explainable AI (XAI) program: A retrospective Applied AI Letters 2 4 10.1002/ail2.61 e61
M. Guo X. Liao J. Liu A progressive sorting approach for multiple criteria decision aiding in the presence of non-monotonic preferences Expert Systems and Applications 123 1 17 10.1016/j.eswa.2019.01.033
P.T. Harker L.G. Vargas Reply to ‘Remarks on the Analytic Hierarchy Process’ by J. S. Dyer Management Science 36 3 269 273 10.1287/mnsc.36.3.269
C.-L. Hwang K. Yoon Multiple attribute decision making Berlin Springer 10.1007/978-3-642-48318-9
A. Ishizaka M. Gordon MACBETHSort: A multiple criteria decision aid procedure for sorting strategic products Journal of the Operational Research Society 68 1 53 61 10.1057/s41274-016-0002-9
A. Ishizaka C. Pearman P. Nemery AHPSort: An AHP-based method for sorting problems International Journal of Production Research 50 17 4767 4784 10.1080/00207543.2012.657966
A. Ishizaka F. Lolli E. Balugani R. Cavallieri R. Gamberini DEASort: Assigning items with data envelopment analysis in ABC classes International Journal of Production Economics 199 7 15 10.1016/j.ijpe.2018.02.007
E. Jacquet-Lagrèze Binary preference indices: A new look on multicriteria aggregation procedures European Journal of Operational Research 10 1 25 32 10.1016/0377-2217(82)90128-X
E. Jacquet-Lagrèze Y. Siskos Assessing a set of additive utility functions for multicriteria decision making: The UTA method European Journal of Operational Research 10 151 164 10.1016/0377-2217(82)90155-2
E. Jacquet-Lagrèze Y. Siskos Preference disaggregation: 20 years of MCDA experience European Journal of Operational Research 130 2 233 245 10.1016/S0377-2217(00)00035-7
P. Janssen P. Nemery An extension of the FlowSort sorting method to deal with imprecision 4OR 11 2 171 193 10.1007/s10288-012-0219-7
M. Kadziński K. Ciomek Integrated framework for preference modeling and robustness analysis for outranking-based multiple criteria sorting with ELECTRE and PROMETHEE Information Sciences 352–353 167 187 10.1016/j.ins.2016.02.059
M. Kadziński K. Ciomek Active learning strategies for interactive elicitation of assignment examples for threshold-based multiple criteria sorting European Journal of Operational Research 293 2 658 680 10.1016/j.ejor.2020.12.055
M. Kadziński M. Martyn Enriched preference modeling and robustness analysis for the ELECTRE Tri-B method Annals of Operations Research 306 1 173 207 10.1007/s10479-020-03833-z
M. Kadziński R. Słowiński DIS-CARD: A new method of multiple criteria sorting to classes with desired cardinality Journal of Global Optimization 56 3 1143 1166 10.1007/s10898-012-9945-9
M. Kadziński T. Tervonen Stochastic ordinal regression for multiple criteria sorting problems Decision Support Systems 55 1 55 66 10.1016/j.dss.2012.12.030
M. Kadziński S. Greco R. Słowiński Robust ordinal regression for dominance-based rough set approach to multiple criteria sorting Information Sciences 283 211 228 10.1016/j.ins.2014.06.038
M. Kadziński K. Ciomek R. Słowiński Modeling assignment-based pairwise comparisons within integrated framework for value-driven multiple criteria sorting European Journal of Operational Research 241 3 830 841 10.1016/j.ejor.2014.09.050
M. Kadziński T. Tervonen J.R. Figueira Robust multi-criteria sorting with the outranking preference model and characteristic profiles Omega 55 126 140 10.1016/j.omega.2014.06.004
M. Kadziński K. Ciomek P. Rychly R. Słowiński Post factum analysis for robust multiple criteria ranking and sorting Journal of Global Optimization 65 3 531 562 10.1007/s10898-015-0359-3
M. Kadziński M. Ghaderi M. Dąbrowski Contingent preference disaggregation model for multiple criteria sorting problem European Journal of Operational Research 281 2 369 387 10.1016/j.ejor.2019.08.043
M. Kadziński M. Stamenković M. Uniejewski Stepwise benchmarking for multiple criteria sorting Omega 108 10.1016/j.omega.2021.102579 102579
E. Karasakal P. Aker A multicriteria sorting approach based on data envelopment analysis for R &D project selection problem Omega 73 79 92 10.1016/j.omega.2016.12.006
R.L. Keeney H. Raiffa Decisions with multiple objectives: Preferences and value tradeoffs New York Wiley
S. Kheybari S. Ali Naji F.M. Rezaie R. Salehpour ABC classification according to Pareto’s principle: A hybrid methodology Opsearch 56 2 539 562 10.1007/s12597-019-00365-4
M. Köksalan V. Mousseau Ö. Özpeynirci S.B. Özpeynirci A new outranking-based approach for assigning alternatives to ordered classes Naval Research Logistics 56 74 85 10.1002/nav.20315
M. Köksalan V. Mousseau S. Özpeynirci Multi-criteria sorting with category size restrictions International Journal of Information Technology & Decision Making 16 01 5 23 10.1142/S0219622016500061
D.H. Krantz R.D. Luce P. Suppes A. Tversky Foundations of measurement, volume 1: Additive and polynomial representations New York Academic Press
C. Labreuche A general framework for explaining the results of a multi-attribute preference model Artificial Intelligence 175 7 1410 1448 10.1016/j.artint.2010.11.008
Labreuche, C., & Fossier, S. (2018). Explaining multi-criteria decision aiding models with an extended shapley value. In IJCAI international joint conference on artificial intelligence (pp. 331–339).
Labreuche, C., Maudet, N., & Ouerdane, W. (2011). Minimal and complete explanations for critical multi-attribute decisions. In Algorithmic decision theory (pp. 121–134).
Labreuche, C., Maudet, N., & Ouerdane, W. (2012). Justifying dominating options when preferential information is incomplete. In Proceedings of the 20th European conference on artificial intelligence, ECAI’12 (pp. 486–491). IOS Press.
Labreuche, C., Maudet, N., Ouerdane, W., & Parsons, S. (2015). A dialogue game for recommendation with adaptive preference models. In Proceedings of the 2015 international conference on autonomous agents and multiagent systems, AAMAS ’15 (pp. 959–967).
R. Lahdelma J. Hokkanen P. Salminen SMAA—Stochastic multiobjective acceptability analysis European Journal of Operational Research 106 1 137 143 10.1016/S0377-2217(97)00163-X
J. Léger J.-M. Martel A multicriteria assignment procedure for a nominal sorting problematic European Journal of Operational Research 138 2 349 364 10.1016/S0377-2217(01)00251-X
A. Leroy V. Mousseau M. Pirlot R.I. Brafman F.S. Roberts A. Tsoukiàs Learning the parameters of a multiple criteria sorting method Algorithmic decision theory, volume 6992 of lecture notes in artificial intelligence Cham Springer 219 233
J. Liu X. Liao W. Zhao N. Yang A classification approach based on the outranking model for multiple criteria ABC analysis Omega 61 19 34 10.1016/j.omega.2015.07.004
J. Liu X. Liao M. Kadziński R. Słowiński Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria European Journal of Operational Research 276 3 1071 1089 10.1016/j.ejor.2019.01.058
J. Liu M. Kadziński X. Liao X. Mao Y. Wang A preference learning framework for multiple criteria sorting with diverse additive value models and valued assignment examples European Journal of Operational Research 286 3 963 985 10.1016/j.ejor.2020.04.013
P. Madhooshiarzanagh I. Abi-Zeid A disaggregation approach for indirect preference elicitation in ELECTRE TRI-nC: Application and validation Journal of Multi-Criteria Decision Analysis 28 3–4 144 159 10.1002/mcda.1730
J.-L. Marichal P. Meyer M. Roubens Sorting multi-attribute alternatives: The TOMASO method Computers & Operations Research 32 4 861 877 10.1016/j.cor.2003.09.002
Massaglia, R., & Ostanello, A. (1991). N-tomic: A support system for multicriteria segmentation problems. In Korhonen, P., Lewandowski, A., Wallenius, J. (Eds.), Multiple criteria decision support, volume 356 of lecture notes in economics and mathematical systems. IIASA. Proceedings of the international workshop, Helsinki (pp. 167–174).
P. Meyer A.-L. Olteanu Handling imprecise and missing evaluations in multi-criteria majority-rule sorting Computers & Operations Research 110 135 147 10.1016/j.cor.2019.05.027
P. Minoungou V. Mousseau W. Ouerdane P. Scotton A MIP-based approach to learn MR-Sort models with single-peaked preferences Annals of Operations Research 325 795 817 10.1007/s10479-022-05007-5
J. Moscarola B. Roy Procédure automatique d’examen de dossiers fondée sur une segmentation trichotomique en présence de critères multiples RAIRO/Operations Resarch 11 2 145 173
V. Mousseau R. Słowiński Inferring an ELECTRE TRI model from assignment examples Journal of Global Optimization 12 1 157 174 10.1023/A:1008210427517
V. Mousseau J.R. Figueira J.-P. Naux Using assignment examples to infer weights for ELECTRE TRI method: Some experimental results European Journal of Operational Research 130 1 263 275 10.1016/S0377-2217(00)00041-2
V. Mousseau J.R. Figueira L.C. Dias C. Gomes da Silva J. Clímaco Resolving inconsistencies among constraints on the parameters of an MCDA model European Journal of Operational Research 147 1 72 93 10.1016/S0377-2217(02)00233-3
V. Mousseau L.C. Dias J. Figueira Dealing with inconsistent judgments in multiple criteria sorting models 4OR 4 3 145 158 10.1007/s10288-005-0076-8
V. Mousseau Ö. Özpeynirci S. Özpeynirci Inverse multiple criteria sorting problem Annals of Operations Research 267 1–2 379 412 10.1007/s10479-017-2420-8
P. Nemery C. Lamboray FlowSort: A flow-based sorting method with limiting or central profiles TOP 16 1 90 113 10.1007/s11750-007-0036-x
A. Ngo The V. Mousseau Using assignment examples to infer category limits for the ELECTRE tri method Journal of Multi-criteria Decision Analysis 11 1 29 43 10.1002/mcda.314
S. Opricovic G.-H. Tzeng Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS European Journal of Operational Research 156 2 445 455 10.1016/S0377-2217(03)00020-1
S. Özpeynirci Ö. Özpeynirci V. Mousseau An interactive algorithm for multiple criteria constrained sorting problem Annals of Operations Research 267 1 447 466 10.1007/s10479-017-2418-2
G.D. Pelegrina L.T. Duarte M. Grabisch J.M. Travassos Romano The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification European Journal of Operational Research 282 3 945 956 10.1016/j.ejor.2019.10.005
R. Pelissari M.C. Oliveira S. Ben Amor A. Kandakoglu A.L. Helleno SMAA methods and their applications: A literature review and future research directions Annals of Operations Research 293 2 433 493 10.1007/s10479-019-03151-z
R. Pelissari M.C. Oliveira A.J. Abackerli S. Ben Amor M.R. Pontes Assumpção Techniques to model uncertain input data of multi-criteria decision-making problems: A literature review International Transactions in Operational Research 28 2 523 559 10.1111/itor.12598
J. Pereira E.C.B. de Oliveira L.F.A.M. Gomes R.M. Araujo Sorting retail locations in a large urban city by using ELECTRE TRI-C and trapezoidal fuzzy numbers Soft Computing 23 12 4193 4206 10.1007/s00500-018-3068-2
J. Pereira E.C.B. de Oliveira D.C. Morais A.P.C.S. Costa P.A. López ELECTRE TRI-C with hesitant outranking functions: Application to supplier development Journal of Intelligent Fuzzy Systems 37 6 7923 7933 10.3233/JIFS-190166
P. Perny Multicriteria filtering methods based on concordance and non-discordance principles Annals of Operations Research 80 137 165 10.1023/A:1018907729570
M. Petrovic N. Bojkovic I. Anic M. Stamenkovic S. Pejcic-Tarle An ELECTRE-based decision aid tool for stepwise benchmarking: An application over EU Digital Agenda targets Decision Support Systems 59 230 241 10.1016/j.dss.2013.12.002
V.V. Podinovskii Criteria importance theory Mathematical Social Sciences 27 3 237 252 10.1016/0165-4896(93)00737-F
C. Rocha L.C. Dias An algorithm for ordinal sorting based on ELECTRE with categories defined by examples Journal of Global Optimization 42 2 255 277 10.1007/s10898-007-9240-3
C. Rocha L.C. Dias I. Dimas Multicriteria classification with unknown categories: A clustering-sorting approach and an application to conflict management Journal of Multi-criteria Decision Analysis 20 13 27 10.1002/mcda.1476
J. Rosenfeld Y. De Smet O. Debeir C. Decaestecker Assessing partially ordered clustering in a multicriteria comparative context Pattern Recognition 114 10.1016/j.patcog.2021.107850 107850
B. Roy P. Nijkamp J. Spronk A multicriteria analysis for trichotomic segmentation problems Multiple criteria analysis: Operational methods Aldershot, England Gower Publishing Company 245 257
Roy, B., & Bouyssou, D. (1993). Aide multicritère à la décision: méthodes et cas. Economica Paris.
B. Roy V. Mousseau A theoretical framework for analysing the notion of relative importance of criteria Journal of Multi-criteria Decision Analysis 5 145 159 10.1002/(SICI)1099-1360(199606)5:2<145::AID-MCDA99>3.0.CO;2-5
B. Roy R. Słowiński Handling effects of reinforced preference and counter-veto in credibility of outranking European Journal of Operational Research 188 1 185 190 10.1016/j.ejor.2007.04.005
T.L. Saaty A scaling method for priorities in hierarchical structures Journal of Mathematical Psychology 15 3 234 281 10.1016/0022-2496(77)90033-5
T.L. Saaty The analytic hierarchy process: Planning, priority setting, resource allocation New York McGraw-Hill International Book Company
H.F. Sabokbar A. Hosseini A. Banaitis N. Banaitiene A novel sorting method TOPSIS-sort: An application for Tehran environmental quality evaluation E+M Ekonomie a Management 19 2 87 104 10.15240/tul/001/2016-2-006
Y. Siskos D. Yannacopoulos Utastar: An ordinal regression method for building additive value functions Investigaçao Operacional 5 1 39 53
R. Słowiński S. Greco B. Matarazzo Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle Control and Cybernetics 31 4 1005 1035
O. Sobrie M.E.A. Lazouni S. Mahmoudi V. Mousseau M. Pirlot A new decision support model for preanesthetic evaluation Computer Methods and Programs in Biomedicine 133 183 193 10.1016/j.cmpb.2016.05.021
Sobrie, O., Mousseau, V., & Pirlot, M. (2017). A population-based algorithm for learning a majority rule sorting model with coalitional veto. In Trautmann, H., Rudolph, G., Klamroth, K., Schütze, O., Wiecek, M. M., Jin, Y., Grimme, C. (Eds.), Evolutionary multi-criterion optimization—9th international conference, EMO 2017, Münster, Germany, March 19–22, 2017, proceedings, volume 10173 of lecture notes in computer science (pp. 575–589). Springer.
O. Sobrie V. Mousseau M. Pirlot Learning monotone preferences using a majority rule sorting model International Transactions in Operational Research 26 5 1786 1809 10.1111/itor.12512
Sokolovska, N., Chevaleyre, Y., & Zucker, J.-D. (2018). A provable algorithm for learning interpretable scoring systems. In A. Storkey and F. Pérez-Cruz (Eds.), International conference on artificial intelligence and statistics, AISTATS 2018, volume 84 of proceedings of machine learning research (pp. 566–574). PMLR.
Tehrani, A. F., & Hüllermeier, E. (2013). Ordinal choquistic regression. In Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology. Atlantis Press.
A.F. Tehrani W. Cheng K. Dembczyński E. Hüllermeier Learning monotone nonlinear models using the Choquet integral Machine Learning 89 1–2 183 211
T. Tervonen J. Rui Figueira A survey on stochastic multicriteria acceptability analysis methods Journal of Multi-criteria Decision Analysis 15 1–2 1 14 10.1002/mcda.407
T. Tervonen J. Figueira R. Lahdelma J.A. Dias P. Salminen A stochastic method for robustness analysis in sorting problems European Journal of Operational Research 192 1 236 242 10.1016/j.ejor.2007.09.008
A. Tlili K. Belahcène O. Khaled V. Mousseau W. Ouerdane Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations European Journal of Operational Research 298 3 979 1006 10.1016/j.ejor.2021.08.017
B. Ustun C. Rudin Supersparse linear integer models for optimized medical scoring systems Machine Learning 102 3 349 391 10.1007/s10994-015-5528-6
B. Ustun C. Rudin Learning optimized risk scores Journal of Machine Learning Research 20 150:1 150:75
P. Vincke Ph Multicriteria decision-aid New York Wiley
D. von Winterfeldt W. Edwards Decision analysis and behavioral research Cambridge Cambridge University Press
S. Wachter B. Mittelstadt L. Floridi Why a right to explanation of automated decision-making does not exist in the general data protection regulation International Data Privacy Law 7 2 76 99 10.1093/idpl/ipx005
P.P. Wakker Additive representations of preferences: A new foundation of decision analysis Dordrecht Kluwer 10.1007/978-94-015-7815-8
D. Walton Argumentation schemes for presumptive reasoning Mahwah Erlbaum
Wei, Y. (1992). Aide multicritère à la décision dans le cadre de la problématique du tri: concepts, méthodes et applications. These de doctorat: Université Paris Dauphine, Paris, France (in French).
M. Wójcik M. Kadziński K. Ciomek Selection of a representative sorting model in a preference disaggregation setting: A review of existing procedures, new proposals, and experimental comparison Knowledge-Based Systems 278 10.1016/j.knosys.2023.110871 110871 ISSN 0950-7051
M. Zeleny J. Cochrane M. Zeleny Compromise programming Multiple criteria decision making Columbia University of South Carolina Press 262 301
Q. Zhong X. Fan X. Luo F. Toni An explainable multi-attribute decision model based on argumentation Expert Systems with Application 117 42 61 10.1016/j.eswa.2018.09.038
C. Zopounidis M. Doumpos Building additive utilities for multi-group hierarchical discrimination: The M.H.DIS method Optimization Methods & Software 14 3 219 240 10.1080/10556780008805801
Zopounidis, C., & Doumpos, M. (2002). Multicriteria classification and sorting methods: A literature review. European Journal of Operational Research,138(2), 229–246.
