{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:52:12Z","timestamp":1766137932364,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T00:00:00Z","timestamp":1645574400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T00:00:00Z","timestamp":1645574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100020451","name":"Universidad Aut\u00f3noma de Coahuila","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100020451","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"DOI":"10.13039\/501100016234","name":"Universidad Aut\u00f3noma de Sinaloa","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100016234","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s10479-022-04554-1","type":"journal-article","created":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T05:06:19Z","timestamp":1645592779000},"page":"819-843","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes"],"prefix":"10.1007","volume":"325","author":[{"given":"Eduardo","family":"Fern\u00e1ndez","sequence":"first","affiliation":[]},{"given":"Jos\u00e9 Rui","family":"Figueira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1823-2603","authenticated-orcid":false,"given":"Jorge","family":"Navarro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,23]]},"reference":[{"key":"4554_CR1","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1016\/j.ejor.2009.10.018","volume":"204","author":"J Almeida-Dias","year":"2010","unstructured":"Almeida-Dias, J., Figueira, J., & Roy, B. (2010). ELECTRE TRI-C: A multiple criteria sorting method based on characteristic reference actions. European JOurnal of Operational Research, 204, 565\u2013580.","journal-title":"European JOurnal of Operational Research"},{"issue":"3","key":"4554_CR2","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1016\/j.ejor.2011.09.047","volume":"217","author":"J Almeida-Dias","year":"2012","unstructured":"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, 217(3), 567\u2013579.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR3","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1016\/j.ijpe.2006.08.008","volume":"106","author":"C Araz","year":"2007","unstructured":"Araz, C., & Ozkarahan, I. (2007). Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure. International Journal of Production Economics, 106, 585\u2013606.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"4554_CR4","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.ejor.2006.01.027","volume":"178","author":"D Bouyssou","year":"2007","unstructured":"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\u2013245.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"4554_CR5","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.ejor.2006.01.033","volume":"178","author":"D Bouyssou","year":"2007","unstructured":"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\u2013276.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"4554_CR6","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.ejor.2014.09.057","volume":"242","author":"D Bouyssou","year":"2015","unstructured":"Bouyssou, D., & Marchant, T. (2015). 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\u2013211.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR7","unstructured":"Bouyssou, D, Marchant, T., and Pirlot, M. (2020). A theoretical look at ELECTRE TRI-nB https:\/\/arxiv.org\/abs\/2008.09484"},{"key":"4554_CR8","unstructured":"Bouyssou, D. and Pirlot, M. (2013). On the relationship between strict and non-strict outranking relations. Cahier du LAMSADE 346, LAMSADE, Universit\u00e9 Paris Dauphine. Available in http:\/\/lamsade.dauphine.fr\/~bouyssou"},{"issue":"1","key":"4554_CR9","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s10479-015-1803-y","volume":"229","author":"D Bouyssou","year":"2015","unstructured":"Bouyssou, D., & Pirlot, M. (2015a). A consolidated approach to the axiomatization of outranking relations: A survey and new results. Annals of Operations Research, 229(1), 159\u2013212. https:\/\/doi.org\/10.1007\/s10479-015-1803-y","journal-title":"Annals of Operations Research"},{"issue":"5","key":"4554_CR10","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1111\/itor.12135","volume":"22","author":"D Bouyssou","year":"2015","unstructured":"Bouyssou, D., & Pirlot, M. (2015b). A note on the asymmetric part of an outranking relation. International Transactions in Operational Research, 22(5), 883\u2013912. https:\/\/doi.org\/10.1111\/itor.12135","journal-title":"International Transactions in Operational Research"},{"key":"4554_CR11","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1287\/mnsc.31.6.647","volume":"31","author":"JP Brans","year":"1985","unstructured":"Brans, J. P., & Vincke, P. (1985). A preference ranking organization method: The PROMETHEE method for multiple criteria decision-making. Management Science, 31, 647\u2013656.","journal-title":"Management Science"},{"key":"4554_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.omega.2016.11.008","volume":"73","author":"S Corrente","year":"2017","unstructured":"Corrente, S., Figueira, J. R., Greco, S., & S\u0142owinski, R. (2017). A robust ranking method extending Electre III to hierarchy of interacting criteria, imprecise weights and stochastic analysis. Omega-International Journal of Management Science, 73, 1\u201317.","journal-title":"Omega-International Journal of Management Science"},{"key":"4554_CR13","doi-asserted-by":"publisher","first-page":"820","DOI":"10.1016\/j.omega.2012.10.009","volume":"41","author":"S Corrente","year":"2013","unstructured":"Corrente, S., Greco, S., & S\u0142owin\u0301ski, R. (2013). Multiple criteria hierarchy process with ELECTRE and PROMETHEE. Omega the International Journal of Management Science, 41, 820\u2013846.","journal-title":"Omega the International Journal of Management Science"},{"issue":"1","key":"4554_CR14","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.ejor.2015.12.053","volume":"252","author":"S Corrente","year":"2016","unstructured":"Corrente, S., Greco, S., & S\u0142owi\u0144ski, R. (2016). Multiple criteria hierarchy process for ELECTRE TRI methods. European Journal of Operational Research, 252(1), 191\u2013203.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"4554_CR15","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1016\/j.ejor.2008.11.035","volume":"199","author":"M Doumpos","year":"2009","unstructured":"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. European Journal of Operational Research, 199(2), 496\u2013505.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR16","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.omega.2018.05.003","volume":"84","author":"E Fern\u00e1ndez","year":"2019","unstructured":"Fern\u00e1ndez, E., Figueira, J., & Navarro, J. (2019). An interval extension of the outranking approach and its application to multiple-criteria ordinal classification. Omega: the International Journal of Management Science, 84, 189\u2013198.","journal-title":"Omega: the International Journal of Management Science"},{"key":"4554_CR17","doi-asserted-by":"publisher","first-page":"102065","DOI":"10.1016\/j.omega.2019.05.001","volume":"95","author":"E Fern\u00e1ndez","year":"2020","unstructured":"Fern\u00e1ndez, E., Figueira, J., & Navarro, J. (2020). Interval-based extensions of two outranking methods for multi-criteria ordinal classification. Omega: the International Journal of Management Science, 95, 102065.","journal-title":"Omega: the International Journal of Management Science"},{"issue":"1","key":"4554_CR18","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.ejor.2017.04.048","volume":"263","author":"E Fern\u00e1ndez","year":"2017","unstructured":"Fern\u00e1ndez, E., Figueira, J., Navarro, J., & Roy, B. (2017). ELECTRE TRI-nB: A new multiple criteria ordinal classification method. European Journal of Operational Research, 263(1), 214\u2013224.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR19","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.ejor.2011.03.036","volume":"213","author":"E Fernandez","year":"2011","unstructured":"Fernandez, E., & Navarro, J. (2011). A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method. European Journal of Operational Research, 213, 405\u2013413.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2021.06.065","author":"E Fern\u00e1ndez","year":"2021","unstructured":"Fern\u00e1ndez, E., Navarro, J., & Solares, E. (2021). A hierarchical interval outranking approach with interacting criteria. European Journal of Operational Research (in Press). https:\/\/doi.org\/10.1016\/j.ejor.2021.06.065","journal-title":"European Journal of Operational Research (in Press)"},{"issue":"2","key":"4554_CR21","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1016\/j.ejor.2008.11.025","volume":"199","author":"JR Figueira","year":"2009","unstructured":"Figueira, J. R., Greco, S., & Roy, B. (2009). ELECTRE methods with interaction between criteria: An extension of the concordance index. European Journal of Operational Research, 199(2), 478\u2013495.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-020-03516-9","author":"C Gaganis","year":"2020","unstructured":"Gaganis, C., Papadimitri, P., & Tasiou, M. (2020). A multicriteria decision support tool for modelling bank credit ratings. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-020-03516-9","journal-title":"Annals of Operations Research"},{"key":"4554_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2015.07.019","volume":"250","author":"K Govindan","year":"2016","unstructured":"Govindan, K., & Jepsen, M. (2016). ELECTRE: A comprehensive literature review on methodologies and applications. European Journal of Operational Research, 250, 1\u201329.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-2217(00)00167-3","volume":"129","author":"S Greco","year":"2001","unstructured":"Greco, S., Matarazzo, B., & S\u0142owi\u0144ski, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129, 1\u201347.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR25","doi-asserted-by":"publisher","first-page":"4767","DOI":"10.1080\/00207543.2012.657966","volume":"50","author":"A Ishizaka","year":"2012","unstructured":"Ishizaka, A., Nemery, P., & Pearman, C. (2012). AHPSort: An AHP based method for sorting problems. International Journal of Production Research, 50, 4767\u20134784.","journal-title":"International Journal of Production Research"},{"key":"4554_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-021-04082-4","author":"A Ishizaka","year":"2021","unstructured":"Ishizaka, A., Pereira, V., & Siraj, S. (2021). AHPSort-GAIA\u202f: A visualization tool for the sorting of alternative in AHP portrayed through a case in the food and drink industry. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-021-04082-4","journal-title":"Annals of Operations Research"},{"key":"4554_CR27","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-1-4757-2383-0_13","volume-title":"Advances in Multicriteria Analysis","author":"E Jacquet-Lagr\u00e8ze","year":"1995","unstructured":"Jacquet-Lagr\u00e8ze, E. (1995). An application of the UTA discriminant model for the evaluation of R&D projects. In P. M. Pardalos, Y. Siskos, & C. Zopounidis (Eds.), Advances in Multicriteria Analysis (pp. 203\u2013211). Kluwer Academic Publishers, Dordrecht."},{"key":"4554_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-020-03833-z","author":"M Kadzi\u0144ski","year":"2020","unstructured":"Kadzi\u0144ski, M., & Martyn, M. (2020). Enriched preference modelling and robustness analysis for the ELECTRE Tri-B method. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-020-03833-z","journal-title":"Annals of Operations Research"},{"key":"4554_CR29","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/S0377-2217(02)00138-8","volume":"144","author":"M K\u00f6ksalan","year":"2003","unstructured":"K\u00f6ksalan, M., & Ulu, C. (2003). An interactive approach for placing alternatives in preference categories. European Journal of Operational Research, 144, 429\u2013439.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR30","doi-asserted-by":"crossref","unstructured":"Leroy, A., Mousseau, V., and Pirlot, M. (2011): Learning the parameters of a multiple criteria sorting method. Proceedings of the International Conference on Algorithmic Decision Theory, ed. (R. Brafman, F.S. Roberts, A. Tsioukias), Lecture Notes in Computer Science vol. 6992, pp. 219\u2013233.","DOI":"10.1007\/978-3-642-24873-3_17"},{"key":"4554_CR31","unstructured":"Massaglia, R., and Ostanello, A. (1991). N-TOMIC: A support system for multicriteria segmentation problems. In: Korhonen, P., Lewandowski, A., and Wallenius, J. (Eds.). Multiple Criteria Decision Support. LNEMS, Volume 356, Springer-Verlag, Berlin, Germany, pp. 167\u2013174."},{"key":"4554_CR32","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.cor.2019.05.027","volume":"110","author":"P Meyer","year":"2019","unstructured":"Meyer, P., & Olteanu, A. L. (2019). Handling imprecise and missing evaluations in multi-criteria majority-rule sorting. Computers & Operations Research, 110, 135\u2013147.","journal-title":"Computers & Operations Research"},{"key":"4554_CR33","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/S0377-2217(03)00120-6","volume":"156","author":"V Mousseau","year":"2004","unstructured":"Mousseau, V., & Dias, L. (2004). Valued outranking relations in ELECTRE providing manageable disaggregation procedures. European Journal of Operational Research, 156, 467\u2013482.","journal-title":"European Journal of Operational Research"},{"key":"4554_CR34","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/s11750-007-0036-x","volume":"16","author":"P Nemery","year":"2008","unstructured":"Nemery, P., & Lamboray, C. (2008). FlowSort: A flow-based sorting method with limiting or central profiles. TOP, 16, 90\u2013113.","journal-title":"TOP"},{"key":"4554_CR35","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1023\/A:1018907729570","volume":"80","author":"P Perny","year":"1998","unstructured":"Perny, P. (1998). Multicriteria filtering methods based on concordance and non-discordance principles. Annals of Operations Research, 80, 137\u2013165.","journal-title":"Annals of Operations Research"},{"key":"4554_CR36","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/BF00134132","volume":"31","author":"B Roy","year":"1991","unstructured":"Roy, B. (1991). The outranking approach and the foundations of ELECTRE methods. Theory and Decision, 31, 49\u201373.","journal-title":"Theory and Decision"},{"key":"4554_CR37","unstructured":"Roy, B. (2002). Pr\u00e9sentation et interpr\u00e9tation de la m\u00e9thode ELECTRE TRI pour affecter des zones dans des cat\u00e9gories de risque. Document du LAMSADE 124, LAMSADE, Universit\u00e9 Paris Dauphine, Paris, France, (25 pages)."},{"key":"4554_CR38","unstructured":"Roy, B., and Bouyssou, D. (1993). Aide Multicrit\u00e8re \u00e0 la D\u00e9cision : M\u00e9thodes et Cas. Economica, Paris, France."},{"key":"4554_CR39","doi-asserted-by":"publisher","first-page":"1786","DOI":"10.1111\/itor.12512","volume":"26","author":"O Sobrie","year":"2019","unstructured":"Sobrie, O., Mousseau, V., & Pirlot, M. (2019). Learning monotone preferences using a majority rule sorting model. International Transactions in Operational Reserarch, 26, 1786\u20131809. https:\/\/doi.org\/10.1111\/itor.12512","journal-title":"International Transactions in Operational Reserarch"},{"key":"4554_CR40","unstructured":"Yu, W. (1992). ELECTRE TRI: Aspects m\u00e9thodologiques et manuel d\u2019utilisation. Document du LAMSADE N\u00ba 74, Universit\u00e9 Paris-Dauphine, Paris, France."},{"key":"4554_CR41","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.cor.2014.03.012","volume":"49","author":"J Zheng","year":"2014","unstructured":"Zheng, J., Metchebon Takougang, S. A., Mousseau, V., & Pirlot, M. (2014). Learning criteria weights of an optimistic Electre Tri sorting rule. Computers and Operations Research, 49, 28\u201340. https:\/\/doi.org\/10.1016\/j.cor.2014.03.012","journal-title":"Computers and Operations Research"},{"key":"4554_CR42","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1080\/10556780008805801","volume":"14","author":"C Zopounidis","year":"2000","unstructured":"Zopounidis, C., & Doumpos, M. (2000). Building additive utilities for multi-group hierarchical discrimination\u202f: The M.H.DIS method. Optimization Methods and Software, 14, 219\u2013240.","journal-title":"Optimization Methods and Software"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04554-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-04554-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04554-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T17:23:30Z","timestamp":1685640210000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-04554-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,23]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["4554"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-04554-1","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"type":"print","value":"0254-5330"},{"type":"electronic","value":"1572-9338"}],"subject":[],"published":{"date-parts":[[2022,2,23]]},"assertion":[{"value":"19 January 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}