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Outranking Methods Y. Ilker TOPCU, Ph.D. ilkertopcu yoneylem.itu.tr

Dominance vs. MAVT. Dominance of a over b translates a sort of agreement for all points of view in favor of a: vj(a)>vj(b) where at least one of the inequalities is strict Methods based on multi attribute value theory lead to a function allowing the ranking of all alternatives from best to worstDo

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Outranking Methods Y. Ilker TOPCU, Ph.D. ilkertopcu yoneylem.itu.tr

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    1. Outranking Methods Y. Ilker TOPCU, Ph.D. www.ilkertopcu.info www.yoneylem.itu.edu.tr

    2. Dominance vs. MAVT Dominance of a over b translates a sort of agreement for all points of view in favor of a: vj(a)>vj(b) where at least one of the inequalities is strict Methods based on multi attribute value theory lead to a function allowing the ranking of all alternatives from best to worst Dominance relation is quite poor because very few pairs of alternatives verify it – Multi attribute value function is very rich because it introduces very strong mathematical hypotheses and necessitates very complicated questions to be asked to the decision maker (DM)

    3. Development of Outranking Methods One may wonder whether it is always necessary to go that far for constructing a function in the frame of decision aid The underlying idea for the development of the outranking methods is to reveal a relation in between the dominance relation (too poor to be useful) and the multi attribute value function (too rich to really be reliable) What is attempted in outranking methods is to enrich the dominance relation by some elements

    4. Incomparability When a DM must compare two alternatives, s/he will react in one of the three following ways: preference for one of them indifference between them refusal or inability to compare them Two alternatives can perfectly remain incomparable without endangering the decision aid procedure A conclusion of incomparability between some alternatives may also be quite helpful since it puts forward some aspects of the problem which would perhaps deserve a more thorough study

    5. Outranking Relation A binary relation S is defined in the set of alternatives such that aSb if there are enough arguments to decide that a is at least as good as b, while there is no essential reason to refute that statement (given what is known about the DM’s preferences and given the quality of the valuations of the alternatives and the nature of the problem)

    6. Main Steps of Outranking Methods 1. Building the outranking relation 2. Exploitating the outranking relation with regard to the chosen statement of the problem

    7. PROMETHEE Preference Ranking Organization METHod for Enrichment Evaluation (Brans & Vincke, 1985) PROMETHEE I yields a partial preorder PROMETHEE II yields a unique complete preorder

    8. Main Steps 1. Building the outranking relation DM chooses a generalized criterion and fixes the necessary parameters related to the selected criterion: a preference function is defined for each attribute Multicriteria preference index is defined as the weighted average of the preference functions This preference index determines a valued outranking relation on the set of alternatives.

    9. Main Steps 2. Exploitating the outranking relation with regard to the chosen statement of the problem For each alternative, a leaving and an entering flow are defined. A net flow is also considered A partial preorder (PROMETHEE I) or a complete preorder (PROMETHEE II) can be proposed to the DM

    10. Usual Criterion Pk(ai,aj) = Quasi Criterion Pk(ai,aj) = Crit. with Linear Pref. Pk(ai,aj) = Level Criterion Pk(ai,aj) = Crit. With Indifference Area. Pk(ai,aj) = Gaussian Criterion Pk(ai,aj) =

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