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Measuring credibility of compensatory preference statements when trade-offs are interval determined

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Abstract

This paper studies how an overall fuzzy preference relation can be constructed in the compensatory context of the ‘simple additive difference model’, when imprecision on the trade-offs has to be taken into account. Three credibility indices of preferences are analysed and illustrated by a numerical example. Arguments are presented supporting the use of the third index, for which an interesting transitivity property (which was an open problem) is proved.

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Jeffrey Sanford Russell, John Hawthorne & Lara Buchak

References

  • Bana e Costa, C.A.: 1988, ‘A methodology for sensitivity analysis in three-criteria problems: a case study in municipal management’,European Journal of Operational Research 33, 159–173.

    Google Scholar 

  • Bana e Costa, C.A.: 1990a, ‘An additive value function technique with a fuzzy outranking relation for dealing with poor intercriteria preference information’, in C.A. Bana e Costa (Ed.),Readings in Multiple Criteria Decision Aid, Springer-Verlag, pp. 351–382.

  • Bana e Costa, C.A.: 1990b, ‘Une méthode pour l'aide à la décision en situations multicritères et multiacteurs’,Sistemi Urbani 3, 301–332.

    Google Scholar 

  • Bana e Costa, C.A. and Ferreira, J.A.: 1992, ‘Computing volumes of convex polyhedrons in ℜ n : the software PROBE’, working paper,CESUR, Lisbon, Portugal.

    Google Scholar 

  • Bouyssou, D.: 1986, ‘Some remarks on the notion of compensation in MCDM’,European Journal of Operational Research 26(1), 150–160.

    Google Scholar 

  • Charnetski, J.R. and Soland, R.M.: 1978, ‘Multiple-attribute decision making with partial information: the comparative hypervolume criterion’,Naval Logistics Quarterly 25, 279–288.

    Google Scholar 

  • Charnetski, J.R. and Soland, R.M.: 1979, ‘Multiple-attribute decision making with partial information: the expected value criterion’,Naval Logistics Quarterly 26, 249–256.

    Google Scholar 

  • Eiselt, H.A. and Laporte, G.: 1992, ‘The use of domains in multicriteria decision making’,European Journal of Operational Research 61, 292–298.

    Google Scholar 

  • French, S.: 1988,Decision Theory: An Introduction to the Mathematics of Rationality, Ellis Horwood Limited.

  • Hazen, G.B.: 1986, ‘Partial information, dominance, and potential optimality in multiattribute utility theory’,Operations Research 34(2), 296–310.

    Google Scholar 

  • Jacquet-Lagrèze, E.: 1975, ‘How can we use the notion of semi-orders to build outranking relations in multi-criteria decision making’, in D. Wendt and C. Vlek (Eds.),Probability and Human Decision Making, Reidel, pp. 87–112.

  • Jacquet-Lagrèze, E.: 1982, ‘Binary preference indices: a new look on multicriteria aggregation procedures’,European Journal of Operational Research 10(1), 26–32.

    Google Scholar 

  • Keeney, R.L. and Nair, K.: 1977, ‘Selecting nuclear power plant sites in the Pacific northwest using decision analysis’, in D.E. Bell, R.L. Keeney and H. Raiffa (Eds.),Conflicting Objectives in Decisions, John Wiley, pp. 298–322.

  • Kirkwood, C.W.: 1982, ‘A case history of nuclear power plant site selection’,Journal of the Operational Research Society 33, 353–363.

    Google Scholar 

  • Kirkwood, C.W. and Sarin, R.: 1985, ‘Ranking with partial information: a method and an application’,Operations Research 33, 38–48.

    Google Scholar 

  • Lasserre, J.B.: 1983, ‘An analytical expression and an algorithm for the volume of a convex polyhedron in ℜ n ’,Journal of Optimization Theory and Applications 39(3), 363–377.

    Google Scholar 

  • Mayer, M. and Reisner, S.: 1991, ‘A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces’,Geometriae Dedicata 37, 327–337.

    Google Scholar 

  • de Montgolfier, J. and Bertier, P.: (1978),Approche Multicritère des Problèmes de Décision, Editions Hommes et Techniques.

  • Roy, B.: 1971, ‘Problems and methods with multiple objective functions’,Mathematical Programming 1(2), 239–266.

    Google Scholar 

  • Roy, B.: 1973, ‘How outranking relation helps multiple criteria decision making’, in J.L. Cochrane and M. Zeleny (Eds.),Multiple Criteria Decision Making, The University of South Carolina Press, pp. 179–201.

  • Roy, B.: 1974, ‘Critères multiples et modélisation des préférences (l'apport des relations de surclassement)’,Revue d'Economie Politique 1, 1–44.

    Google Scholar 

  • Roy, B.: 1985,Méthodologie Multicritère d'Aide à la Décision, Economica.

  • Roy, B. and Bouyssou, D.: 1993,Aide Multicritère à la Décision: Méthodes et Cas, Economica.

  • Sarin, R.K.: (1977), ‘Interactive evaluation and bound procedure for selecting multi-attributed alternatives’, in M.K. Starr and M. Zeleny (Eds.),Multiple Criteria Decision Making, North-Holland, pp. 211–224.

  • Schneller, G.O. and Sphicas, G.P.: 1983, ‘Decision making under uncertainty: Starr' domain criterion’,Theory and Decision 15, 321–336.

    Google Scholar 

  • Siskos, J. Lochard, J., and Lombard, J.: 1986, ‘A multicriteria decision-making methodology under fuzziness: application to the evaluation of radiological protection in nuclear power plants’, in H.-J. Zimmermann, L.A. Zadeh and B.R. Gaines (Eds.),Fuzzy Sets and Decision Analysis, North-Holland, pp. 261–284.

  • Starr, M.K.: 1962,Product Design and Decision Theory, Prentice-Hall.

  • Starr, M.K.: 1966, ‘A discussion of some normative criteria for decision making under uncertainty’,Industrial Management Review 8, 71–78.

    Google Scholar 

  • Trejos, M.: 1991, ‘Toma de decisiones multicriterio: Método de relationes binarias de sobreclasificación que usa una familia de functiones de utilidad’,Doctoral Thesis, Facultat de Ingeniería de la Universidad Nacional Autónoma de México.

  • Tversky, A.: 1969, ‘Intransitivity of preferences’,Psychological Review 76, 31–48.

    Google Scholar 

  • Zimmermann, H.-J.: 1990, Decision making in ill-structured environments and with multiple criteria’, in C.A. Bana e Costa (Ed.),Readings in Multiple Criteria Decision Aid, Springer-Verlag, pp. 119–151.

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Bana e Costa, C.A., Vincke, P. Measuring credibility of compensatory preference statements when trade-offs are interval determined. Theor Decis 39, 127–155 (1995). https://doi.org/10.1007/BF01078981

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