×

Simple procedures of choice in multicriteria problems without precise information about the alternatives’ values. (English) Zbl 1231.90242

Summary: The additive model of multiattribute value theory is widely used in multicriteria choice problems. But often it is not easy to obtain precise values for the scaling weights or the alternatives’ value in each function. Several decision rules which require weaker information, such as ordinal information, have been proposed to select an alternative under these circumstances. We propose new decision rules and test them using Monte-Carlo simulation, considering that there is ordinal information both on the scaling weights and on the alternatives’ values. Results show the new rules constitute a good approximation. We provide guidelines about how to use these rules in a context of selecting a subset of the most promising alternatives, considering the contradictory objectives of keeping a low number of alternatives yet not excluding the best one.

MSC:

90B50 Management decision making, including multiple objectives

References:

[1] Ahn, B., Extending Malakooti’s model for ranking multicriteria alternatives with preference strength and partial information, IEEE Transactions on Systems Man and Cybernetics Part A: Systems and Humans, 33, 3, 281-287 (2003)
[2] Ahn, B.; Park, K., Comparing methods for multiattribute decision making with ordinal weights, Computers and Operations Research, 35, 1660-1670 (2008) · Zbl 1211.90098
[3] Bana e. Costa, C.; De Corte, J.; Vansnick, J., On the mathematical foundation of MACBETH, (Figueira, J.; Greco, S.; Ehrgott, M., Multiple criteria decision analysis: state of the art surveys (2005), Springer Verlag: Springer Verlag Boston, Dordrecht, London), 409-443 · Zbl 1072.90525
[4] Barron, F.; Barrett, B., Decision quality using ranked attribute weights, Management Science, 42, 11, 1515-1523 (1996) · Zbl 0879.90002
[5] Belton, V.; Stewart, T., Multiple criteria decision analysis: an integrated approach (2002), Kluwer Academic: Kluwer Academic Dordrecht
[6] Bisdorff, R., Concordant outranking with multiple criteria of ordinal significance—a contribution to robust multicriteria aid for decision, 4OR, 2, 293-308 (2004) · Zbl 1112.90343
[7] Bouyssou D, Pirlot M. Ordinal aggregation and strict preferences for multi-attributed alternatives, Technical Report, cahiers du LAMSADE, No. 212, 2003.; Bouyssou D, Pirlot M. Ordinal aggregation and strict preferences for multi-attributed alternatives, Technical Report, cahiers du LAMSADE, No. 212, 2003. · Zbl 1115.91020
[8] Butler, J.; Jia, J.; Dyer, J., Simulation techniques for the sensitivity analysis of multi-criteria decision models, European Journal of Operational Research, 103, 3, 531-546 (1997) · Zbl 0921.90100
[9] Butler, J.; Olson, D., Comparison of centroid and simulation approaches for selection sensitivity analysis, Journal of Multi-Criteria Decision Analysis, 8, 146-161 (1999) · Zbl 0945.90024
[10] Contreras, I.; Marmol, A., A lexicographical compromise method for multiple criteria group decision problems with imprecise information, European Journal of Operational Research, 181, 3, 1530-1539 (2007) · Zbl 1123.90320
[11] Cook, W.; Kress, M.; Seiford, L., A general framework for distance-based consensus in ordinal ranking model, European Journal of Operational Research, 92, 392-397 (1996) · Zbl 0917.90023
[12] Dias, L., A note on the role of robustness analysis in decision-aiding processes, (Roy, B.; Aloulou, M.; Kalai, R., Robustness in OR-DA Lamsade (2007)), 53-70, annales du Lamsade no 7
[13] Dias, L.; Clímaco, J., Additive aggregation with variable interdependent parameters: the VIP analysis software, Journal of the Operational Research Society, 51, 9, 1070-1082 (2000) · Zbl 1107.90368
[14] Edwards, W.; Hutton Barron, F., SMART and SMARTER: improved simple methods for multiattribute utility measurement, Organizational Behavior and Human Decision Processes, 60, 306-325 (1994)
[15] Eum, Y.; Park, K.; Kim, H., Establishing dominance and potential optimality in multi-criteria analysis with imprecise weights and value, Computers & Operations Research, 28, 5, 397-409 (2001) · Zbl 1080.90526
[16] Figueira J, Greco S, Ehrgott M, editors. Multiple criteria decision analysis: state of the art surveys. Boston, Dordrecht, London: Springer; 2005.; Figueira J, Greco S, Ehrgott M, editors. Multiple criteria decision analysis: state of the art surveys. Boston, Dordrecht, London: Springer; 2005. · Zbl 1060.90002
[17] Figueira J, Greco S, Slowinski R. Building a set of additive value functions representing a reference preorder and intensities of preference: grip method. Technical Report, cahiers du LAMSADE, No. 253, 2007.; Figueira J, Greco S, Slowinski R. Building a set of additive value functions representing a reference preorder and intensities of preference: grip method. Technical Report, cahiers du LAMSADE, No. 253, 2007. · Zbl 1159.91341
[18] Gonzalez-Pachon, J.; Romero, C., Aggregation of partial ordinal rankings: an interval goal programming approach, Computers and Operations Research, 28, 8, 827-834 (2001) · Zbl 1017.90056
[19] Greco, S.; Matarazzo, B.; Slowinski, R., Decision rule approach, (Figueira, J.; Greco, S.; Ehrgott, M., Multiple criteria decision analysis: state of the art surveys (2005), Springer Verlag: Springer Verlag Boston, Dordrecht, London), 507-562 · Zbl 1072.90534
[20] Hazen, G., Partial information, dominance, and potential optimality in multiattribute utility theory, Operations Research, 34, 2, 296-310 (1986) · Zbl 0625.90048
[21] Iyer, N., A family of dominance rules for multiattribute decision making under uncertainty, IEEE Transactions on Systems Man and Cybernetics Part A: Systems and Humans, 33, 441-450 (2003)
[22] Jacquet-Lagrèze, E.; Siskos, Y., Assessing a set of additive utility functions for multicriteria decision making: the UTA method, European Journal of Operational Research, 10, 151-164 (1982) · Zbl 0481.90078
[23] Keeney, R.; Raiffa, H., Decisions with multiple objectives: preferences and value tradeoffs (1976), John Wiley & sons: John Wiley & sons New York · Zbl 0488.90001
[24] Lahdelma, R.; Hokkanen, J.; Salminen, P., SMAA—stochastic multiobjective acceptability analysis, European Journal of Operational Research, 106, 1, 137-143 (1998)
[25] Lahdelma, R.; Miettinen, K.; Salminen, P., Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA), European Journal of Operational Research, 147, 1, 117-127 (2003) · Zbl 1011.90026
[26] Larichev O, Moshkovich H. Zapros: a method and system for ordering multiattribute alternatives on the base of a decision-maker’s preferences. Moscow: All-Union Research Institute for Systems Studies, 1991.; Larichev O, Moshkovich H. Zapros: a method and system for ordering multiattribute alternatives on the base of a decision-maker’s preferences. Moscow: All-Union Research Institute for Systems Studies, 1991.
[27] Larichev, O.; Moskovich, H., An approach to ordinal classification problems, International Transactions in Operational Research, 1, 3, 375-385 (1994) · Zbl 0854.90086
[28] Larichev, O.; Olson, D.; Moshkovich, H.; Mechitov, A., Numeric vs. cardinal measurements in multiattribute decision making: how exact is enough?, Organizational Behavior and Human Decision Processes, 64, 9-21 (1995)
[29] Lee, K.; Park, K.; Kim, S., Dominance, potential optimality, imprecise information, and hierarchical structure in multi-criteria analysis, Computers and Operations Research, 29, 1267-1281 (2002) · Zbl 0994.90094
[30] Malakooti, B., Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences, IEEE Transactions on Systems Man and Cybernetics: Part A, 30, 3, 787-801 (2000)
[31] Marichal, J.; Meyer, P.; Roubens, M., Sorting multi-attribute alternatives: the TOMASO method, Computers and Operations Research, 32, 4, 861-877 (2005) · Zbl 1071.90550
[32] Mateos, A.; Rios-Insua, S.; Jiménez, A., Dominance, potential optimality and alternative ranking in imprecise decision making, Journal of Operational Research Society, 58, 3, 326-336 (2007) · Zbl 1192.90094
[33] Moshkovich, H.; Mechitov, A.; Olson, D., Verbal decision analysis, (Figueira, J.; Greco, S.; Ehrgott, M., Multiple criteria decision analysis: state of the art surveys (2005), Springer Verlag: Springer Verlag Boston, Dordrecht, London), 609-640 · Zbl 1072.90541
[34] Paelinck, J., Qualiflex: a flexible multiple-criteria decision method, Economic Letters, 1, 193-197 (1978)
[35] Park, K., Mathematical programming models for characterizing dominance and potential optimality when multicriteria alternative values and weights are simultaneously incomplete, IEEE Transactions on Systems Man and Cybernetics Part A: Systems and Humans, 34, 601-614 (2004)
[36] Pitz G. DECAID Computer Program, Carbondale, University of Southern Illinois, 1987.; Pitz G. DECAID Computer Program, Carbondale, University of Southern Illinois, 1987.
[37] Roubens, M., Preference relation on actions and criteria in multicriteria decision making, European Journal of Operational Research, 10, 51-55 (1982) · Zbl 0481.90080
[38] Roy, B.; Mousseau, V., A theoretical framework for analysing the notion of relative importance of criteria, Journal of Multi-Criteria Decision Analysis, 5, 145-159 (1996) · Zbl 0847.90002
[39] Sage, A.; White, C., Ariadne: a knowledge-based interactive system for planning and decision support, IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 14, 35-47 (1984)
[40] Salo, A.; Hämäläinen, R., Preference ratio in multiattribute evaluation PRIME—elicitation and decision procedures under incomplete information, IEEE Transactions on Systems Man and Cybernetics: Part A, 31, 6, 533-545 (2001)
[41] Salo, A.; Punkka, A., Rank inclusion in criteria hierarchies, European Journal of Operational Research, 163, 2, 338-356 (2005) · Zbl 1104.91017
[42] Sarabando P, Dias L. Multi-attribute choice with ordinal information: a comparison of different decision rules. IEEE Transactions on Systems, Man, and Cybernetics: Part A 2009,39(3):545-54; Sarabando P, Dias L. Multi-attribute choice with ordinal information: a comparison of different decision rules. IEEE Transactions on Systems, Man, and Cybernetics: Part A 2009,39(3):545-54
[43] Solymosi, T.; Dombi, J., A method for determining the weights of criteria: the centralized weights, European Journal of Operational Research, 26, 35-41 (1986)
[44] von Winterfeldt, D.; Edwards, W., Decision analysis and behaviorial research (1986), Cambridge University Press: Cambridge University Press Cambridge
[45] Wakker, P., Additive representations of preferences: a new foundation of decision analysis (1989), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, Boston, London · Zbl 0668.90001
[46] Weber, M., Decision making with incomplete information, European Journal of Operational Research, 28, 44-57 (1987) · Zbl 0604.90004
[47] White, C.; Holloway, H., Resolvability for imprecise multiattribute alternative selection, IEEE Transactions on Systems, Man, and Cybernetics, Part A, 38, 1, 162-169 (2008)
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.