×

About the applicability of MCDA to some robustness problems. (English) Zbl 1116.90051

Summary: Coping with uncertainties or ignorance in decision problems may lead to the idea that several scenarios can occur or that several sets of data can constitute a good representation of the reality. In consequence, numerous authors have focused on the robust aspect of these problems. In such a context, one can consider that a scenario (or a particular instance of the data) permits to partially qualify the solutions, just as a criterion does. In other words, the evaluation of a specific solution for a given scenario could be perceived as the evaluation of this solution according to one particular criterion. With this in mind, the applicability of classic multicriteria concepts to the robustness framework, in the context of optimization problems, is explored. We achieve this by studying their similarities and differences. The distinguishing characteristics bring us to introduce a new problematic: the multicriteria evaluation of robustness.

MSC:

90B50 Management decision making, including multiple objectives
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gupta, S.; Rosenhead, J., Robustness in sequential investment decisions, Management Science, 15, 2, 18-29 (1968)
[2] Rosenhead, J.; Elton, M.; Gupta, S., Robustness and optimality as criteria for strategic decisions, Operational Research Quarterly, 23, 4, 413-430 (1972)
[3] F. Hampel, Robust statistics: A brief introduction and overview, Tech. Rep. 94, Seminar für Statistik, Eidgenössische Technische Hochschule, 2001.; F. Hampel, Robust statistics: A brief introduction and overview, Tech. Rep. 94, Seminar für Statistik, Eidgenössische Technische Hochschule, 2001.
[4] Roy, B., A missing link in or-da: Robustness analysis, Foundations of Computing and Decision Sciences, 23, 3, 141-160 (1998) · Zbl 0967.90077
[5] B. Roy, Robustesse de quoi et vis-À-vis de quoi mais aussi robustesse pourquoi en aide à la décision, in: J. Figueira, C. Hengeller-Antunes, J. Climaco (Eds.), Proceedings of the 56th Meeting of the European Working Group, Multiple Criteria Decision Aid, CCRC, Coimbra, 2004.; B. Roy, Robustesse de quoi et vis-À-vis de quoi mais aussi robustesse pourquoi en aide à la décision, in: J. Figueira, C. Hengeller-Antunes, J. Climaco (Eds.), Proceedings of the 56th Meeting of the European Working Group, Multiple Criteria Decision Aid, CCRC, Coimbra, 2004.
[6] Vincke, P., Robust and neutral methods for aggregating preferences into an outranking relation, European Journal of Operational Research, 112, 405-412 (1999) · Zbl 0944.91015
[7] Vincke, P., Robust solutions and methods in decision-aid, Journal of Multicriteria Decision Analysis, 8, 181-187 (1999) · Zbl 0946.90042
[8] Kouvelis, P.; Yu, G., Robust discrete optimization and Its applications (1997), Kluwer Academic Publishers · Zbl 0873.90071
[9] R. Hites, The aggregation of preferences method for solving combinatorial problems with uncertainty, in: J. Figueira, C. Hengeller-Antunes, J. Climaco (Eds.), Proceedings of the 56th Meeting of the European Working Group, “Multiple Criteria Decision Aid, Coimbra, 2004.; R. Hites, The aggregation of preferences method for solving combinatorial problems with uncertainty, in: J. Figueira, C. Hengeller-Antunes, J. Climaco (Eds.), Proceedings of the 56th Meeting of the European Working Group, “Multiple Criteria Decision Aid, Coimbra, 2004.
[10] B. Roy, Flexibilité et Robustesse en Ordonnancement, Hermès, A propos de robustesse en Recherche Opérationnelle et Aide à la Décision, 2004, pp. 33-48.; B. Roy, Flexibilité et Robustesse en Ordonnancement, Hermès, A propos de robustesse en Recherche Opérationnelle et Aide à la Décision, 2004, pp. 33-48.
[11] B. Roy, D. Bouyssou, Aide Multicritèreà la Décision: Méthodes et Cas, Economica, 1993.; B. Roy, D. Bouyssou, Aide Multicritèreà la Décision: Méthodes et Cas, Economica, 1993.
[12] Vincke, P., Multicriteria decision-aid (1992), John Wiley and Sons
[13] B. Roy, French-English decision aiding glossary, Newsletter of the European Working Group Multicriteria Aid for Decisions, Series 3, no. 1, Spring 2000.; B. Roy, French-English decision aiding glossary, Newsletter of the European Working Group Multicriteria Aid for Decisions, Series 3, no. 1, Spring 2000.
[14] Rousseeuw, P.; Leroy, A., Robust regression and outlier detection (1987), Wiley · Zbl 0711.62030
[15] D. Donoho, P. Huber, A Festschift for Erich L. Lehmann, Wadsworth, The Notion of Breakdown Point, 1983, pp. 157-184.; D. Donoho, P. Huber, A Festschift for Erich L. Lehmann, Wadsworth, The Notion of Breakdown Point, 1983, pp. 157-184.
[16] Huber, P., Robust statistics (1981), Wiley · Zbl 0536.62025
[17] K. Sorensen, Tabu searching for robust solutions, in: 4th Metaheuristics International Conference, Porto, Portugal, 16-20 July 2001, pp. 707-712.; K. Sorensen, Tabu searching for robust solutions, in: 4th Metaheuristics International Conference, Porto, Portugal, 16-20 July 2001, pp. 707-712.
[18] Kozina, G.; Perepelitsa, V., Interval spanning trees problem: Solvability and computational complexity, Interval Computations, 1, 42-50 (1994) · Zbl 0833.68097
[19] Perepelitsa, V.; Kozina, G., Interval discrete models and multiobjectivity complexity estimates, Interval Computations, 1, 51-59 (1993) · Zbl 0833.90119
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.