Weight stability intervals in multicriteria decision aid. (English) Zbl 0634.90074

Mareschal, Bertrand

Eur. J. Oper. Res. 33, 54-64 (1988).

Summary: We study the stability of the results given by a wide class of MCDA methods to changes of the weights of the criteria. Three aspects of stability are discussed. In each case we propose to construct stability intervals for the weights of either single criteria or groups of criteria. A necessary and sufficient condition for stability is also considered. The use of these instruments is demonstrated with a numerical example.

MSC:

90C31	Sensitivity, stability, parametric optimization
90B50	Management decision making, including multiple objectives

Keywords:

multiple criteria programming; changes of the weights; stability

References:

[1]	Belton, V., A comparison of the analytic hierarchy process and a simple multi-attribute value function, European journal of operational research, 26, 1, 7-21, (1986)
[2]	Brans, J.P.; Mareschal, B.; Vincke, Ph., {\scpromethee}: A new family of outranking methods in multicriteria analysis, (), 477-490 · Zbl 0571.90042
[3]	Eckenrode, R.T., Weighting multiple criteria, Management science, 12, 3, 180-192, (1965)
[4]	Leclerq, J.P., Propositions d’extension de la notion de dominance en présence de relations d’ordre sur LES pseudo-critères: la méthode {\scmelchior}, Revue belge de statistique, d’informatique et de recherche opérationelle, 24, 1, (1984) · Zbl 0553.90011
[5]	Roubens, M., Agrégation des préférences en prénces de préordres totaux sur l’ensemble des actions et d’une relation de préférence du type (I, P, Q) sur LES points de vue, (1979), FAPOM Mons.,
[6]	Roy, B.; Brans, J.P.; Vincke, Ph., Aide à la décision multicritère, Revue belge de statistique, d’informatique et de recherche opérationnelle, 15, 4, (1975)
[7]	Roy, B.; Hugonnard, J.C., Classement des prolongements de lignes de métro en banlieue parisienne—un cas type d’application de l’analyse multicritère, Cahiers scientifiques de la revue transport, 6, (1982)
[8]	Roy, B.; Present, M.; Sihol, D., A programming method for determining which Paris metro stations should be renovated, European journal of operational research, 24, 2, 318-334, (1986)
[9]	Solymosi, T.; Dombi, J., A method for determining the weights of the criteria: the centralized weights, European journal of operational research, 26, 1, 35-41, (1986)
[10]	Vansnick, J.C., On the problem of weights in multiple criteria decision making (the noncompensatory approach), European journal of operational research, 24, 2, 288-294, (1986) · Zbl 0579.90059