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PROMETHEE: an extension through fuzzy mathematical programming

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  • A S Fernández-Castro

    (University of A Coruña)

  • M Jiménez

    (University of The Basque Country)

Abstract

PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.

Suggested Citation

  • A S Fernández-Castro & M Jiménez, 2005. "PROMETHEE: an extension through fuzzy mathematical programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 119-122, January.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:1:d:10.1057_palgrave.jors.2601828
    DOI: 10.1057/palgrave.jors.2601828
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    References listed on IDEAS

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    1. Bertrand Mareschal & Jean Pierre Brans, 1992. "PROMETHEE V: MCDM problems with segmentation constraints," ULB Institutional Repository 2013/9341, ULB -- Universite Libre de Bruxelles.
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    1. Halouani, N. & Chabchoub, H. & Martel, J.-M., 2009. "PROMETHEE-MD-2T method for project selection," European Journal of Operational Research, Elsevier, vol. 195(3), pages 841-849, June.

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