Abstract
The principle of concordance/discordance was introduced by B. Roy in his very early work on Multiple Criteria Decision Analysis. Although such a principle is grounded by strong evidence from real life decision situations, the way in which it has been implemented in existing MCDA methods allows only for its partial and limited use. Indeed, the principle lacks a theoretical frame enabling a more general use in decision analysis. The paper presents a possible generalisation of this principle under the concepts of positive and negative reasons. For this purpose, a new formalism, (a four valued logic) is suggested. Under such a formalism the concordance test is seen as the evaluation of the existence of positive reasons supporting the sentence “x is at least as good as y”, while the discordance test can be viewed as the evaluation of the existence of negative reasons against the same sentence. A number of results obtained in preference modelling and aggregation shows the potentiality of this approach.
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References
Belnap N.D., (1977), “A useful four-valued logic”, in G. Epstein, J. Dumm, (eds.), Modern uses of multiple valued logics, D. Reidel, Dordrecht, 8–37.
Bouyssou D., (1992a), “On some properties of outranking relations based on a concordance — discordance principle”, in A. Goicoechea, L. Duckstein and S. Zionts, (eds.), Multiple criteria decision making, Springer-Verlag, Berlin, 93–106.
Bouyssou D., (1992b), “Ranking methods based on valued preference relations: A characterization of the net flow network”, European Journal of Operational Research, vol. 60, 61–67.
Bouyssou D., (1996), “Outranking relations: do they have special properties?”, Journal of Multi-Criteria Decision Analysis, vol. 5, 99–111.
Bouyssou D., Perny, P., (1992), “Ranking method for valued preference relations: A characterization of a method based on leaving and entering flows”, European Journal of Operational Research, vol. 61, 186–194.
Bouyssou D., Pirlot M., (1997), “Choosing and ranking on the basis of fuzzy preference relations with the’Min in Favor”, in G. Fandel, T. Gal, (eds.), Multiple criteria decision making, Springer Verlag, Berlin, 115–127.
Bouyssou D., Pirlot M., (1999), “Conjoint measurement without additivity and transitivity”, in N. Meskens, M. Roubens, (eds.), Advances in Decision Analysis, Kluwer Academic, Dordrecht, 13–29.
Bouyssou D., Vincke Ph., (1997), “Ranking alternatives on the basis of preference relations: a progress report with special emphasis on outranking relations”, Journal of Multiple Criteria Decision Analysis, vol. 6, 77–85.
Bouyssou D., Pirlot M., Vincke Ph., (1997), “A general model of preference aggregation”, in M.H. Karwan, J. Spronk, J. Wallenius, (eds.), Essays in decision making, Springer Verlag, Berlin, 120–134.
Bouyssou D., Marchant Th., Perny P., Pirlot M., Tsoukiàs A., Vincke Ph., (2000), Evaluation and Decision Models: a critical perspective, Kluwer Academic, Dordrecht.
Brans J.P., Vincke Ph., (1985), “A preference ranking organization method”, Management Science, vol. 31, 647–656.
Dubois D., Prade H., (1988), Possibility Theory, Plenum Press, New York.
Fargier H., Perny P., (2001), “Modélisation des préférences par une règle de concordance généralisée”, in A. Colorni, M. Parruccini, B. Roy (eds.), Selected Papers from 49 th and 50 th meetings of the EURO Working Group on MCDA, EUR-Report, to appear.
Fitting M.C., (1991), “Bilattices and the semantics of Logic Programming”, Journal of Logic Programming, vol. 11, 91–116.
Fortemps Ph., Słowiński R., (2001), “A graded quadrivalent logic for ordinal preference modelling”, Fuzzy Optimization and Decision Making, vol. 1, no. 1.
Grabisch M., Perny P., (2001), “Agrégation Multicritère”, in B. Bouchon-Meunier, C. Marsala (eds.). Utilisation de la logique floue, Hermès, Paris, to appear.
Ginsberg M., (1988), “Multivalued logics: A uniform approach to reasoning in artificial intelligence”, Computational Intelligence, vol. 4, 265–316.
Greco S., Matarazzo B., Słowiński R., Tsoukiàs A., (1998), “Exploitation of a rough approximation of the outranking relation in Multi-Criteria Choice and Ranking”, in T.J. Stewart and R.C. van der Honert (eds.), Trends in Multi-Criteria Decision Making, Springer Verlag, LNEMS 465, Berlin, 45–60.
Greco S., Matarazzo B., Słowiński R., (2001), “Conjoint measurement and rough set approach for multicriteria sorting problems in presence of ordinal criteria”, in A. Colorni, M. Paruccini, B. Roy, (eds.), AMCDA: Selected papers from the 49 th and 50 th meetings of the EURO MCDA Working Group, EUR-report, Ispra, 114–141.
Marchant Th., (1996), “Valued relations aggregation with the Borda method”, Journal of Multiple Criteria Decision Analysis, vol. 5, 127–132.
Ngo The A., Tsoukiàs A., Vincke Ph., (2000), “A polynomial time algorithm to detect PQI interval orders”, International Transactions of Operations Research, vol. 7, 609–623.
Ngo The A., Tsoukiàs A., (2001), “A new axiomatisation of PQI interval orders”, submitted.
Ostanello A., (1985), “Outranking relations”, in G. Fandel, J. Spronk, Multiple Criteria Decision Methods and Applications, Springer Verlag, Berlin, 41–60.
Perny P., (1998), “Multicriteria filtering methods based on concordance and non-discordance principles”, Annals of Operations Research, vol. 80, 137–165.
Perny P., Roubens M., (1998), “Preference Modelling”, in Handbook of Fuzzy Sets and Possibility Theory, Operations Research and Statistics, R. Słowiński (ed.), D. Dubois et H. Prade (series eds.), Kluwer Academic Publishers, 3–30.
Perny P., Roy B., (1992), “The use of fuzzy Outranking Relations in Preference Modelling”, in Fuzzy sets and Systems, vol. 49, 33–53.
Perny P., Tsoukiàs A., (1998), “On the continuous extension of a four valued logic for preference modelling”, in Proceedings of the IPMU 1998 conference, 302–309.
Pirlot M., (1995), “A characterization of ‘min’ as a procedure for exploiting valued preference relations and related results”, Journal of Multiple Criteria Decision Analysis, vol. 4, 37–56.
Pirlot M., (1997), “A common framework for describing some outranking methods”, Journal of Multiple Criteria Decision Analysis, vol. 6, 86–92.
Roy B., (1968), “Classement et choix en présence de points de vue multiples (Le méthode ELECTRE)”, Revue Française d’Informatique et de Recherche Opérationnelle, vol. 8, 57–75.
Roy B., (1978), ELECTRE III: Un algorithme de classement fondé sur une représentation floue des préférences en présence de critères multiples, Cahiers du CERO, vol. 20, 1, 3–24.
Roy B., (1991), “The outranking approach and the foundations of ELECTRE methods”, Theory and Decision, vol. 31, 49–73.
Roy B., Bouyssou D., (1993), Aide Multicritère à la Décision: Methodes et cas, Economica, Paris.
Roy B., Mousseau V., (1996), “A theoretical framework for analysing the notion of relative importance of criteria”, Journal of Multi-criteria Decision Analysis, vol. 5, 145–159.
Roy B., Skalka J.-M., (1984), „ELECTRE IS: Aspects méthodologiques et guide d’utilisation“, Technical Report, Document du LAMSADE N°30, Université Paris Dauphine, Paris.
Roy B., Vincke Ph., (1984), “Relational systems of preferences with one or more pseudo-criteria: some new concepts and results”, Management Science, vol. 30, 1323–1335.
Roy B., Vincke Ph., (1987), “Pseudo-orders: definition, properties and numerical representation”, Mathematical Social Sciences, vol. 14, 263–274.
Tsoukiàs A., (1996), “A first-order, four valued, weakly paraconsistent logic”, Cahier du LAMSADE n. 139.
Tsoukiàs A., (1997), “Sur la généralisation des concepts de concordance et discordance en aide multicrite à la décision”, Mémoire présenté pour l’obtention de l’habilitation à diriger des recherches, Université Paris Dauphine, appeared also as Document du LAMSADE. n. 117.
Tsoukiàs A., Vincke Ph., (1995), “A new axiomatic foundation of partial comparability”, Theory and Decision, vol. 39, 79–114.
Tsoukiàs A., Vincke Ph., (1997), “Extended preference structures in MCDA”, in J. Clímaco (ed.), Multi-criteria Analysis, Springer Verlag, Berlin, 37–50.
Tsoukiàs A., Vincke Ph., (1998), “Double Threshold Orders: a new axiomatisation”, Journal of Multiple Criteria Decision Analysis, vol. 7, 285–301.
Tsoukiàs A., Vincke Ph., (2001), “A characterization of PQI interval orders”, to appear in Discrete Applied Mathematics.
Vanderpooten, D., (1990), “The construction of prescriptions in outranking methods”, in Bana e Costa CA., (ed.), Readings in Multiple Criteria Decision Aid, Springer-Verlag, Berlin, 184–215.
Vincke Ph., (1982), “Aggregation of preferences: a review”, European Journal of Operational Research, vol. 9, 17–22.
Vincke Ph., (1988), “P,Q,I preference structures”, in J. Kacprzyk, M. Roubens, eds., Non conventional preference relations in decision making, LNEMS 301, Springer Verlag, Berlin, 72–81.
Vincke Ph., (1992a), “Exploitation of a crisp relation in a ranking problem”, Theory and Decision, vol. 32, 221–240.
Vincke Ph., (1992b), Multicriteria Decision Aid, J. Wiley, New York.
Vincke Ph., (1999), “The Outranking Approach”, in T. Gal, Th. Stewart, Th. Hanne, (eds.), Multicriteria Decision Making; Advances in MCDM Models, Algorithms, Theory and Applications, Kluwer Academic, Dordrecht.
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Tsoukiàs, A., Perny, P., Vincke, P. (2002). From Concordance / Discordance to the Modelling of Positive and Negative Reasons in Decision Aiding. In: Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Słowiński, R., Vanderpooten, D., Vincke, P. (eds) Aiding Decisions with Multiple Criteria. International Series in Operations Research & Management Science, vol 44. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0843-4_7
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DOI: https://doi.org/10.1007/978-1-4615-0843-4_7
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