Abstract
In some MCDM techniques — most notably in Outranking Methods — the result of the comparison of a finite set of alternatives according to several criteria is summarized using a fuzzy preference relation. This fuzzy relation does not, in general, possess “nice properties” such as transitivity or completeness and elaborating a recommendation on the basis of such information is not an obvious task. The purpose of this paper is to study techniques exploiting fuzzy preference relations in order to choose or rank. We present a number of results concerning techniques based on the “min in Favor” score, i.e. the minimum level with which an alternative is “at least as good as” all other alternatives.
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References
Arrow, K.J. and Raynaud, H.: Social choice and multicriterion decision making, MIT Press, Cambridge, 1986.
Barrett, C.R., Pattanaik, P.K. and Salles, M: On choosing rationally when preferences are fuzzy. Fuzzy Sets and Systems 34 (1990) 197–212.
Bouyssou, D: “A note on the ‘min in favor’ ranking method for valued preference relations”. In M. Cerny, D. Glükaufova and D. Loula (eds): Multicriteria Decision Making. Methods — Algorithms — Applications, Czechoslovak Academy of Sciences, Prague, 1992, pp. 16–25.
Bouyssou, D.: A note on the sum of differences choice function for fuzzy preference relations. Fuzzy Sets and Systems 47 (1992) 197–202.
Bouyssou, D.: “A note on the ‘min in favor’ choice procedure for fuzzy preference relations”. In: P.M. Pardalos, Y. Siskos and C. Zopounidis (eds.): Advances in Multicriteria Analysis, Kluwer, Dordrecht, 1995, pp. 9–16.
Bouyssou, D.: Outranking relations: do they have special properties ?. Journal of Multiple Criteria Decision Analysis 5 (1996) 99–111.
Bouyssou, D. and Perny, P: Ranking methods for valued preference relations: a characterization of a method based on entering and leaving flows. European Journal of Operational Research 61 (1992) 186–194.
Brans J.P., Mareschal, B. and Vincke, Ph.: “PROMETHEE: a new family of outranking methods in multicriteria analysis”. In: J.P. Brans (ed.): OR’ 84, North Holland, Amsterdam, 1984, pp. 408–421.
Kitainik, L.: Fuzzy decision procedures with binary relations — Towards a unified theory, Kluwer, Dordrecht, 1993.
Ovchinnikov, S.V. and Roubens, M.: On fuzzy strict preference, indifference, and incomparability relations. Fuzzy Sets and Systems 49 (1992) 15–20.
Perny, P. and Roy, B.: The use of fuzzy outranking relations in preference modelling. Fuzzy Sets and Systems 49 (1992) 33–53.
Pirlot, M.: Ranking procedures for valued preference relations: a characterization of the ‘min’ procedure. Cahiers du CERO 34 (1992) 233–241.
Pirlot, M.: A characterization of “min” as a procedure for exploiting valued preference relations and related results. Journal of Multiple Criteria Decision Analysis 4 (1995) 37–56.
Pirlot, M.: “About ordinal procedures for exploiting valued preference relations”, Communication at ORBEL 9, Brussels, 19-20 January 1995.
Roy, B.: ELECTRE III: un algorithme de classement fondé sur une représentation floue des préférences en présence de critères multiples. Cahiers du CERO 20 (1978) 3–24.
Roy, B. and Bouyssou, D.: Aide multicritère à la décision: méthodes et cas, Economica, Paris, 1993.
Vincke, Ph.: Multicriteria decision-aid, John Wiley & Sons, Chichester, 1992.
Young, H.P.: An axiomatization of Borda’s rule. Journal of Economic Theory 9 (1974) 43–52.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bouyssou, D., Pirlot, M. (1997). Choosing and Ranking on the Basis of Fuzzy Preference Relations with the “Min in Favor”. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59132-7_13
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DOI: https://doi.org/10.1007/978-3-642-59132-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62097-6
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