Monotone classification; Multiple criteria decision making; Multiple criteria sorting; Preference learning; Management Information Systems; Theoretical Computer Science; Management Science and Operations Research; Computational Theory and Mathematics
Abstract :
[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 1980s, focusing on the underlying models. Our proposal is organized into two parts. In Part I, we start by recalling two main models, one based on additive value functions (UTADIS) and the other on 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 Part II (to appear in a forthcoming issue of this journal), 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.
Research center :
CRTI - Centre de Recherche en Technologie de l'Information
Disciplines :
Computer science
Author, co-author :
Belahcène, Khaled; Heudiasyc, Université de Technologie de Compiègne, Compiègne, 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 Polytechniqu > Service de Mathématique et Recherche opérationnelle
Sobrie, Olivier ; Université de Mons - UMONS > Faculté Polytechniqu > Service de Mathématique et Recherche opérationnelle
Language :
English
Title :
Multiple criteria sorting models and methods—Part I: survey of the literature
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.
Alaya M, Bussy S, Gaïffas S, Guilloux A (2019) Binarsity: a penalization for one-hot encoded features in linear supervised learning. J Mach Learn Res 20:118:1–118:34
Almeida-Dias J, Figueira JR, Roy B (2010) ELECTRE TRI-C: A multiple criteria sorting method based on characteristic reference actions. Eur J Oper Res 204(3):565–580 DOI: 10.1016/j.ejor.2009.10.018
Almeida-Dias J, Figueira JR, Roy B (2012) A multiple criteria sorting method where each category is characterized by several reference actions: the ELECTRE TRI-nC method. Eur J Oper Res 217(3):567–579 DOI: 10.1016/j.ejor.2011.09.047
Alvarez PA, Ishizaka A, Martínez L (2021) Multiple-criteria decision-making sorting methods: a survey. Expert Syst Appl 183:115368 DOI: 10.1016/j.eswa.2021.115368
Angilella S, Greco S, Matarazzo B (2010) Non-additive robust ordinal regression: a multiple criteria decision model based on the Choquet integral. Eur J Oper Res 201(1):277–288 DOI: 10.1016/j.ejor.2009.02.023
Araz C, Ozkarahan I (2007) Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure. Int J Prod Econ 106(2):585–606 DOI: 10.1016/j.ijpe.2006.08.008
Arcidiacono SG, Corrente S, Greco S (2021) Robust stochastic sorting with interacting criteria hierarchically structured. Eur J Oper Res 292(2):735–754 DOI: 10.1016/j.ejor.2020.11.024
Bana e Costa CA, Vansnick J-C (1994) MACBETH, an interactive path towards the construction of cardinal value functions. Int Trans Oper Res 1(4):489–500 DOI: 10.1016/0969-6016(94)90010-8
Bana e Costa CA, De Corte J-M, Vansnick J-C (2005) On the mathematical foundations of MACBETH. In: Greco S, Ehrgott M, Figueira JR (eds) Multiple Criteria Decision Analysis: state of the art surveys, International Series in Operations Research and Management Science. Springer, New York, pp 409–437
Belacel N (2000) Multicriteria assignment method PROAFTN: methodology and medical application. Eur J Oper Res 125(1):175–183 DOI: 10.1016/S0377-2217(99)00192-7
Belacel N, Raval HB, Punnen AP (2007) Learning multicriteria fuzzy classification method proaftn from data. Comput Oper Res 34(7):1885–1898 DOI: 10.1016/j.cor.2005.07.019
Belahcène K, Labreuche C, Maudet N, Mousseau V, Ouerdane W (2018) An efficient SAT formulation for learning multiple criteria non-compensatory sorting rules from examples. Comput Oper Res 97:58–71 DOI: 10.1016/j.cor.2018.04.019
Belahcène K, Mousseau V, Ouerdane W, Pirlot M, Sobrie O (2022) Multiple criteria sorting models and methods. Part II: Theoretical results and general issues. 4OR, http://doi.org/10.1007/s10288-022-00531-3
Benabbou N, Perny P, Viappiani P (2017) Incremental elicitation of choquet capacities for multicriteria choice, ranking and sorting problems. Artif Intell 246:152–180 DOI: 10.1016/j.artint.2017.02.001
Bous G, Fortemps P, Glineur F, Pirlot M (2010) ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements. Eur J Oper Res 206(2):435–444 DOI: 10.1016/j.ejor.2010.03.009
Bouyssou D, Marchant T (2007) An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories. Eur J Oper Res 178(1):217–245 DOI: 10.1016/j.ejor.2006.01.027
Bouyssou D, Marchant T (2007) An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories. Eur J Oper Res 178(1):246–276 DOI: 10.1016/j.ejor.2006.01.033
Bouyssou D, Marchant T (2009) Ordered categories and additive conjoint measurement on connected sets. J Math Psychol 53(2):92–105 DOI: 10.1016/j.jmp.2008.12.004
Bouyssou D, Marchant T, Pirlot M, Tsoukiàs A, Vincke P (2006) Evaluation and decision models with multiple criteria: stepping stones for the analyst. Springer, New York
Cano J-R, Gutiérrez PA, Krawczyk B, Woźniak M, García S (2019) Monotonic classification: an overview on algorithms, performance measures and data sets. Neurocomputing 341:168–182 DOI: 10.1016/j.neucom.2019.02.024
Chen Y, Hipel KW, Kilgour DM (2007) Multiple-criteria sorting using case-based distance models with an application in water resources management. IEEE Trans Syst Man Cybern A: Syst Humans 37(5):680–691 DOI: 10.1109/TSMCA.2007.902629
Chen Y, Li KW, Kilgour DM, Hipel KW (2008) A case-based distance model for multiple criteria ABC analysis. Comput Oper Res 35(3):776–796 DOI: 10.1016/j.cor.2006.03.024
Chen Y, Kilgour DM, Hipel KW (2011) A decision rule aggregation approach to multiple criteria-multiple participant sorting. Group Decis Negot 21(5):727–745 DOI: 10.1007/s10726-011-9246-6
Cinelli M, Kadziński M, Miebs G, Gonzalez M, Słowiński R (2022) Recommending multiple criteria decision analysis methods with a new taxonomy-based decision support system. Eur J Oper Res
Colorni A, Tsoukiàs A (2021) Rating or sorting: terminology matters. J Multi-Criteria Decis Anal 28(3–4):131–133 DOI: 10.1002/mcda.1733
Corrente S, Doumpos M, Greco S, Słowiński R, Zopounidis C (2015) Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions. Ann Oper Res 251(1–2):117–139
Corrente S, Greco S, Słowiński R (2016) Multiple criteria hierarchy process for ELECTRE Tri methods. Eur J Oper Res 252(1):191–203 DOI: 10.1016/j.ejor.2015.12.053
Costa AS, Figueira JR, Borbinha J (2018) A multiple criteria nominal classification method based on the concepts of similarity and dissimilarity. Eur J Oper Res 271(1):193–209 DOI: 10.1016/j.ejor.2018.05.029
Costa AS, Corrente S, Greco S, Figueira JR, Borbinha J (2020) A robust hierarchical nominal multicriteria classification method based on similarity and dissimilarity. Eur J Oper Res 286(3):986–1001 DOI: 10.1016/j.ejor.2020.04.021
Damart S, Dias LC, Mousseau V (2007) Supporting groups in sorting decisions: methodology and use of a multi-criteria aggregation/disaggregation DSS. Decis Support Syst 43(4):1464–1475 DOI: 10.1016/j.dss.2006.06.002
de Morais Bezerra F, Melo P, Costa JP (2017) Reaching consensus with VICA-ELECTRE TRI: a case study. Group Decis Negot 26(6):1145–1171 DOI: 10.1007/s10726-017-9539-5
De Smet Y (2019) Beyond multicriteria ranking problems: the case of PROMETHEE. In: Multiple criteria decision making. Springer International Publishing, pp 95–114
De Smet Y, Montano Guzmán L (2004) Towards multicriteria clustering: an extension of the k -means algorithm. Eur J Oper Res 158(2):390–398 DOI: 10.1016/j.ejor.2003.06.012
De Smet Y, Nemery P, Selvaraj R (2012) An exact algorithm for the multicriteria ordered clustering problem. Omega 40(6):861–869 DOI: 10.1016/j.omega.2012.01.007
Dembczyński K, Kotlowski W, Słowiński R (2006) Additive preference model with piecewise linear components resulting from dominance-based rough set approximations. In: Rutkowski L, Tadeusiewicz R, Zadeh LA, Zurada JM (eds) ICAISC, volume 4029 of Lecture Notes in Computer Science, pages 499–508. Springer, ISBN 3-540-35748-3
Demir L, Akpınar ME, Araz C, Ilgın MA (2018) A green supplier evaluation system based on a new multi-criteria sorting method: Vikorsort. Expert Syst Appl 114:479–487 DOI: 10.1016/j.eswa.2018.07.071
Dias L, Mousseau V, Figueira JR, Clímaco J (2002) An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI. Eur J Oper Res 138(1):332–348 DOI: 10.1016/S0377-2217(01)00250-8
Doumpos M, Zopounidis C (2002) Multicriteria decision aid classification methods. Kluwer Academic Publishers, Dordrecht, Boston
Doumpos M, Zopounidis C (2007) Regularized estimation for preference disaggregation in multiple criteria decision making. Comput Optim Appl 38(1):61–80 DOI: 10.1007/s10589-007-9037-9
Doumpos M, Zopounidis C (2011) Preference disaggregation and statistical learning for multicriteria decision support: a review. Eur J Oper Res 209(3):203–214 DOI: 10.1016/j.ejor.2010.05.029
Doumpos M, Marinakis Y, Marinaki M, Zopounidis C (2009) An evolutionary approach to construction of outranking models for multicriteria classification: the case of the ELECTRE TRI method. Eur J Oper Res 199(2):496–505 DOI: 10.1016/j.ejor.2008.11.035
Doumpos M, Zopounidis C, Galariotis E (2014) Inferring robust decision models in multicriteria classification problems: an experimental analysis. Eur J Oper Res 236(2):601–611 DOI: 10.1016/j.ejor.2013.12.034
Duckstein L, Opricovic S (1980) Multiobjective optimization in river basin development. Water Resour Res 16(1):14–20 DOI: 10.1029/WR016i001p00014
Dyer JS (1990) Remarks on the analytic hierarchy process. Manage Sci 36(3):249–258 DOI: 10.1287/mnsc.36.3.249
Eppe S, Roland J, De Smet Y (2014) On the use of valued action profiles for relational multi-criteria clustering. Int J Multicrit Decis Making 4
Ersek Uyanık E, Sobrie O, Mousseau V, Pirlot M (2017) Enumerating and categorizing positive Boolean functions separable by a k -additive capacity. Discret Appl Math 229:17–30 DOI: 10.1016/j.dam.2017.04.010
Fernández E, Navarro J (2011) A new approach to multi-criteria sorting based on fuzzy outranking relations: the THESEUS method. Eur J Oper Res 213(2):405–413 DOI: 10.1016/j.ejor.2011.03.036
Fernández E, Figueira JR, Navarro J, Roy B (2017) ELECTRE TRI-nB: a new multiple criteria ordinal classification method. Eur J Oper Res 263(1):214–224 DOI: 10.1016/j.ejor.2017.04.048
Fernández E, Figueira JR, Navarro J (2019) An indirect elicitation method for the parameters of the ELECTRE TRI-nB model using genetic algorithms. Appl Soft Comput 77:723–733 DOI: 10.1016/j.asoc.2019.01.050
Fernández E, Figueira JR, Navarro J (2019) An interval extension of the outranking approach and its application to multiple-criteria ordinal classification. Omega 84:189–198 DOI: 10.1016/j.omega.2018.05.003
Fernández E, Figueira JR, Navarro J (2020) Interval-based extensions of two outranking methods for multi-criteria ordinal classification. Omega 95:102065 DOI: 10.1016/j.omega.2019.05.001
Fernández E, Navarro J, Solares E (2022) A hierarchical interval outranking approach with interacting criteria. Eur J Oper Res 298(1):293–307 DOI: 10.1016/j.ejor.2021.06.065
Figueira J, De Smet Y, Brans J-P (2004) MCDA methods for sorting and clustering problems: PROMETHEE TRI and PROMETHEE CLUSTER. Research report, SMG - ULB
Figueira JR, Greco S, Roy B (2009) ELECTRE methods with interaction between criteria: an extension of the concordance index. Eur J Oper Res 199(2):478–495 DOI: 10.1016/j.ejor.2008.11.025
Flores BE, Whybark DC (1986) Multiple criteria ABC analysis. Int J Oper Prod Manag 6:38–46 DOI: 10.1108/eb054765
Fürnkranz J, Hüllermeier E (2010) Preference learning: an introduction. In: Fürnkranz J, Hüllermeier E (eds) Preference learning. Springer, pp 1–17
Grabisch M (2016) Set functions, games and capacities in decision making. Theory and Decision Library C. Springer, Basel, Switzerland DOI: 10.1007/978-3-319-30690-2
Greco S, Matarazzo B, Słowiński R (2002) Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur J Oper Res 138(2):247–259 DOI: 10.1016/S0377-2217(01)00244-2
Greco S, Mousseau V, Słowiński R (2008) Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. Eur J Oper Res 191(2):416–436 DOI: 10.1016/j.ejor.2007.08.013
Greco S, Mousseau V, Słowiński R (2010) Multiple criteria sorting with a set of additive value functions. Eur J Oper Res 207(3):1455–1470 DOI: 10.1016/j.ejor.2010.05.021
Greco S, Kadziński M, Słowiński R (2011) Selection of a representative value function in robust multiple criteria sorting. Comput Oper Res 38(11):1620–1637 DOI: 10.1016/j.cor.2011.02.003
Greco S, Kadziński M, Mousseau V, Słowiński R (2012) Robust ordinal regression for multiple criteria group decision: UTAGMS-GROUP and UTADISGMS-GROUP. Decis Support Syst 52(3):549–561 DOI: 10.1016/j.dss.2011.10.005
Greco S, Mousseau V, Słowiński R (2014) Robust ordinal regression for value functions handling interacting criteria. Eur J Oper Res 239(3):711–730 DOI: 10.1016/j.ejor.2014.05.022
Greco S, Matarazzo B, Słowiński R (2016) Decision rule approach. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: State of the Art Surveys, number 233 in International Series in Operations Research & Management Science. Springer New York. Second Edition: 2016, pp 497–552
Guo M, Liao X, Liu J (2019) A progressive sorting approach for multiple criteria decision aiding in the presence of non-monotonic preferences. Expert Syst Appl 123:1–17 DOI: 10.1016/j.eswa.2019.01.033
Harker PT, Vargas LG (1990) Reply to “Remarks on the Analytic Hierarchy Process” by. J. S. Dyer. Management Science 36(3):269–273
Ishizaka A, Gordon M (2017) MACBETHSort: a multiple criteria decision aid procedure for sorting strategic products. J Oper Res Soc 68(1):53–61 DOI: 10.1057/s41274-016-0002-9
Ishizaka A, Pearman C, Nemery P (2012) AHPSort: an AHP-based method for sorting problems. Int J Prod Res 50(17):4767–4784 DOI: 10.1080/00207543.2012.657966
Ishizaka A, Lolli F, Balugani E, Cavallieri R, Gamberini R (2018) DEASort: assigning items with data envelopment analysis in ABC classes. Int J Prod Econ 199:7–15 DOI: 10.1016/j.ijpe.2018.02.007
Jacquet-Lagrèze E, Siskos Y (1982) Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur J Oper Res 10:151–164 DOI: 10.1016/0377-2217(82)90155-2
Jacquet-Lagrèze E, Siskos Y (2001) Preference disaggregation: 20 years of MCDA experience. Eur J Oper Res 130(2):233–245 DOI: 10.1016/S0377-2217(00)00035-7
Kadziński M, Ciomek K (2016) Integrated framework for preference modeling and robustness analysis for outranking-based multiple criteria sorting with ELECTRE and PROMETHEE. Inf Sci 352–353:167–187 DOI: 10.1016/j.ins.2016.02.059
Kadziński M, Słowiński R (2013) DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality. J Global Optim 56(3):1143–1166 DOI: 10.1007/s10898-012-9945-9
Kadziński M, Tervonen T (2013) Stochastic ordinal regression for multiple criteria sorting problems. Decis Support Syst 55(1):55–66 DOI: 10.1016/j.dss.2012.12.030
Kadziński M, Greco S, Słowiński R (2014) Robust ordinal regression for dominance-based rough set approach to multiple criteria sorting. Inf Sci 283:211–228 DOI: 10.1016/j.ins.2014.06.038
Kadziński M, Ciomek K, Słowiński R (2015) Modeling assignment-based pairwise comparisons within integrated framework for value-driven multiple criteria sorting. Eur J Oper Res 241(3):830–841 DOI: 10.1016/j.ejor.2014.09.050
Kadziński M, Tervonen T, Figueira JR (2015) Robust multi-criteria sorting with the outranking preference model and characteristic profiles. Omega 55:126–140 DOI: 10.1016/j.omega.2014.06.004
Kadziński M, Ciomek K (2021) Active learning strategies for interactive elicitation of assignment examples for threshold-based multiple criteria sorting. Eur J Oper Res 293(2):658–680 DOI: 10.1016/j.ejor.2020.12.055
Kadziński M, Martyn M (2021) Enriched preference modeling and robustness analysis for the ELECTRE Tri-B method. Ann Oper Res 306(1):173–207 DOI: 10.1007/s10479-020-03833-z
Karasakal E, Aker P (2017) A multicriteria sorting approach based on data envelopment analysis for R &D project selection problem. Omega 73:79–92 DOI: 10.1016/j.omega.2016.12.006
Keeney RL, Raiffa H (1976) Decisions with multiple objectives: preferences and value tradeoffs. Wiley, New York
Kheybari S, Ali Naji S, Rezaie FM, Salehpour R (2019) ABC classification according to Pareto’s principle: a hybrid methodology. Opsearch 56(2):539–562 DOI: 10.1007/s12597-019-00365-4
Köksalan M, Mousseau V, Özpeynirci Ö, Özpeynirci SB (2009) A new outranking-based approach for assigning alternatives to ordered classes. Naval Res Logist 74–85
Köksalan M, Mousseau V, Özpeynirci S (2017) Multi-criteria sorting with category size restrictions. Int J Inform Technol Decis Making 16(01):5–23 DOI: 10.1142/S0219622016500061
Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement, volume 1: additive and polynomial representations. Academic Press, New York
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
Lahdelma R, Hokkanen J, Salminen P (1998) SMAA - stochastic multiobjective acceptability analysis. Eur J Oper Res 106(1):137–143 DOI: 10.1016/S0377-2217(97)00163-X
Leroy A, Mousseau V, Pirlot M (2011) Learning the parameters of a multiple criteria sorting method. In: Brafman RI, Roberts FS, Tsoukiàs A (eds) Algorithmic decision theory, volume 6992 of Lecture Notes in Artificial Intelligence. Springer, pp 219–233
Léger J, Martel J-M (2002) A multicriteria assignment procedure for a nominal sorting problematic. Eur J Oper Res 138(2):349–364 DOI: 10.1016/S0377-2217(01)00251-X
Liu J, Liao X, Zhao W, Yang N (2016) A classification approach based on the outranking model for multiple criteria ABC analysis. Omega 61:19–34 DOI: 10.1016/j.omega.2015.07.004
Liu J, Liao X, Kadziński M, Słowiński R (2019) Preference disaggregation within the regularization framework for sorting problems with multiple potentially non-monotonic criteria. Eur J Oper Res 276(3):1071–1089 DOI: 10.1016/j.ejor.2019.01.058
Liu J, Kadziński M, Liao X, Mao X, Wang Y (2020) A preference learning framework for multiple criteria sorting with diverse additive value models and valued assignment examples. Eur J Oper Res 286(3):963–985 DOI: 10.1016/j.ejor.2020.04.013
Madhooshiarzanagh P, Abi-Zeid I (2021) A disaggregation approach for indirect preference elicitation in electre TRI-nC: application and validation. J Multi-Criteria Decis Anal 28(3–4):144–159 DOI: 10.1002/mcda.1730
Marichal J-L, Meyer P, Roubens M (2005) Sorting multi-attribute alternatives: the TOMASO method. Comput Oper Res 32(4):861–877 DOI: 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
Minoungou P, Mousseau V, Ouerdane W, Scotton P (2022) A MIP-based approach to learn MR-Sort models with single-peaked preferences. Annals Oper Res
Moscarola J, Roy B (1977) Procédure automatique d’examen de dossiers fondée sur une segmentation trichotomique en présence de critères multiples. RAIRO/Oper Res 11(2):145–173
Mousseau V, Słowiński R (1998) Inferring an ELECTRE TRI model from assignment examples. J Glob Optim 12(1):157–174 DOI: 10.1023/A:1008210427517
Mousseau V, Figueira JR, Naux J-Ph (2001) Using assignment examples to infer weights for ELECTRE TRI method: some experimental results. Eur J Oper Res 130(1):263–275 DOI: 10.1016/S0377-2217(00)00041-2
Nemery P, Lamboray C (2008) F low S ort: a flow-based sorting method with limiting or central profiles. TOP 16(1):90–113 DOI: 10.1007/s11750-007-0036-x
Ngo The A, Mousseau V (2002) Using assignment examples to infer category limits for the electre tri method. J Multi-criteria Decis Anal 11(1):29–43 DOI: 10.1002/mcda.314
Opricovic S, Tzeng G-H (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455 DOI: 10.1016/S0377-2217(03)00020-1
Özpeynirci S, Özpeynirci Ö, Mousseau V (2018) An interactive algorithm for multiple criteria constrained sorting problem. Ann Oper Res 267(1):447–466 DOI: 10.1007/s10479-017-2418-2
Pelegrina GD, Duarte LT, Grabisch M, Travassos Romano JM (2020) The multilinear model in multicriteria decision making: the case of 2-additive capacities and contributions to parameter identification. Eur J Oper Res 282(3):945–956 DOI: 10.1016/j.ejor.2019.10.005
Pelissari R, Oliveira MC, Ben Amor S, Kandakoglu A, Helleno AL (2020) SMAA methods and their applications: a literature review and future research directions. Ann Oper Res 293(2):433–493 DOI: 10.1007/s10479-019-03151-z
Perny P (1998) Multicriteria filtering methods based on concordance and non-discordance principles. Ann Oper Res 80:137–165 DOI: 10.1023/A:1018907729570
Rocha C, Dias LC (2008) An algorithm for ordinal sorting based on ELECTRE with categories defined by examples. J Global Optim 42(2):255–277 DOI: 10.1007/s10898-007-9240-3
Rocha C, Dias LC, Dimas I (jun 2012) Multicriteria classification with unknown categories: a clustering-sorting approach and an application to conflict management. J Multi-Criteria Decis Anal 20
Rosenfeld J, De Smet Y, Debeir O, Decaestecker C (2021) Assessing partially ordered clustering in a multicriteria comparative context. Pattern Recogn 114:107850 DOI: 10.1016/j.patcog.2021.107850
Roy B (1981) A multicriteria analysis for trichotomic segmentation problems. In: Nijkamp P, Spronk J (eds) Multiple criteria analysis: operational methods. Gower Publishing Company, Aldershot, pp 245–257
Roy B, Bouyssou D (1993) Aide multicritère à la décision: méthodes et cas. Economica Paris
Roy B, Mousseau V (1996) A theoretical framework for analysing the notion of relative importance of criteria. J Multi-Criteria Decis Anal 5:145–159 DOI: 10.1002/(SICI)1099-1360(199606)5:2<145::AID-MCDA99>3.0.CO;2-5
Roy B, Słowiński R (2008) Handling effects of reinforced preference and counter-veto in credibility of outranking. Eur J Oper Res 188(1):185–190 DOI: 10.1016/j.ejor.2007.04.005
Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15(3):234–281 DOI: 10.1016/0022-2496(77)90033-5
Saaty TL (1980) The analytic hierarchy process: planning, priority setting, resource allocation. McGraw-Hill International Book Company
Sabokbar HF, Hosseini A, Banaitis A, Banaitiene N (2016) A novel sorting method TOPSIS-sort: an application for Tehran environmental quality evaluation. E+M Ekonomie Manag 19(2):87–104 DOI: 10.15240/tul/001/2016-2-006
Siskos Y, Yannacopoulos D (1985) Utastar: An ordinal regression method for building additive value functions. Investigaçao Operacional 5(1):39–53
Słowínski R, Greco S, Matarazzo B (2002) Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle. Control Cybern 31(4):1005–1035
Sobrie O, Lazouni MEA, Mahmoudi S, Mousseau V, Pirlot M (2016) A new decision support model for preanesthetic evaluation. Comput Methods Programs Biomed 133:183–193 DOI: 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 MM, 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, pages 575–589. Springer
Sobrie O, Mousseau V, Pirlot M (2019) Learning monotone preferences using a majority rule sorting model. Int Trans Oper Res 26(5):1786–1809 DOI: 10.1111/itor.12512
Sokolovska N, Chevaleyre Y, Zucker J-D (2018) A provable algorithm for learning interpretable scoring systems. In: Storkey A, Pérez-Cruz F (eds) International Conference on Artificial Intelligence and Statistics, AISTATS 2018,, volume 84 of Proceedings of Machine Learning Research, pages 566–574. PMLR
Tehrani AF, Hüllermeier E (2013) Ordinal Choquistic regression. In: Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology. Atlantis Press
Tehrani AF, Cheng W, Dembczyński K, Hüllermeier E (2012) Learning monotone nonlinear models using the Choquet integral. Mach Learn 89(1–2):183–211
Tervonen T, Figueira JR (2008) A survey on stochastic multicriteria acceptability analysis methods. J Multi-Criteria Decis Anal 15(1–2):1–14
Tervonen T, Figueira J, Lahdelma R, Dias JA, Salminen P (2009) A stochastic method for robustness analysis in sorting problems. Eur J Oper Res 192(1):236–242 DOI: 10.1016/j.ejor.2007.09.008
Tlili A, Belahcène K, Khaled O, Mousseau V, Ouerdane W (2022) Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations. Eur J Oper Res 298(3):979–1006 DOI: 10.1016/j.ejor.2021.08.017
Ustun B, Rudin C (2016) Supersparse linear integer models for optimized medical scoring systems. Mach Learn 102(3):349–391 DOI: 10.1007/s10994-015-5528-6
Ustun B, Rudin C (2019) Learning optimized risk scores. J Mach Learn Res 20:150:1-150:75
Wei Y (1992) Aide multicritère à la décision dans le cadre de la problématique du tri: concepts, méthodes et applications. Thèse de doctorat, Université Paris Dauphine, Paris, France (in French)
von Winterfeldt D, Edwards W (1986) Decision analysis and behavioral research. Cambridge University Press, Cambridge
Zeleny M (1973) Compromise programming. In: Cochrane J, Zeleny M (eds) Multiple Criteria Decision Making. University of South Carolina Press, Columbia, pp 262–301
Zopounidis C, Doumpos M (2000) Building additive utilities for multi-group hierarchical discrimination: the M.H.DIS method. Optim Methods Software 14(3):219–240 DOI: 10.1080/10556780008805801
Zopounidis C, Doumpos M (2002) Multicriteria classification and sorting methods: a literature review. Eur J Oper Res 138(2):229–246 DOI: 10.1016/S0377-2217(01)00243-0
