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Preference programming with incomplete ordinal information. (English) Zbl 1317.91028

Summary: This paper extends possibilities for analyzing incomplete ordinal information about the parameters of an additive value function. Such information is modeled through preference statements which associate sets of alternatives or attributes with corresponding sets of rankings. These preference statements can be particularly helpful in developing a joint preference representation for a group of decision-makers who may find difficulties in agreeing on numerical parameter values. Because these statements can lead to a non-convex set of feasible parameters, a mixed integer linear formulation is developed to establish a linear model for the computation of decision recommendations. This makes it possible to complete incomplete ordinal information with other forms of incomplete information.

MSC:

91B06 Decision theory
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[1] Barron, F. H.; Barrett, B. E., Decision quality using ranked attribute weights, Management Science, 42, 1515-1523 (1996) · Zbl 0879.90002
[2] Corner, J. L.; Kirkwood, C. W., Decision analysis applications in the operations research literature, 1970-1989, Operations Research, 39, 206-219 (1991)
[3] Dyer, J. S.; Sarin, R. K., Measurable multiattribute value functions, Operations Research, 27, 810-822 (1979) · Zbl 0423.90004
[5] Grushka-Cockayne, Y.; De Reyck, B.; Degraeve, Z., An integrated decision-making approach for improving european air traffic management, Management Science, 54, 1395-1409 (2008) · Zbl 1232.90277
[6] Guo, M.; Yang, Y.-B.; Chin, K.-S.; Wang, H., Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty, European Journal of Operational Research, 182, 1294-1312 (2007) · Zbl 1127.90363
[7] Hazen, G. B., Partial information, dominance, and potential optimality in multiattribute utility theory, Operations Research, 34, 296-310 (1986) · Zbl 0625.90048
[8] Kangaspunta, J.; Liesiö, J.; Salo, A., Cost-efficiency analysis of weapon system portfolios, European Journal of Operational Research, 223, 264-275 (2012) · Zbl 1253.90146
[9] Keeney, R. L.; Raiffa, H., Decisions with Multiple Objectives: Preferences and Value Trade-Offs (1976), John Wiley: John Wiley New York, USA · Zbl 0488.90001
[10] Kirkwood, C. W.; Sarin, R. K., Ranking with partial information: a method and an application, Operations Research, 33, 38-48 (1985) · Zbl 0569.90052
[11] Könnölä, T.; Brummer, V.; Salo, A., Diversity in foresight: insights from the fostering of innovation ideas, Technological Forecasting and Social Change, 74, 608-626 (2007)
[12] Larichev, O. I., Cognitive validity in design of decision-aiding techniques, Journal of Multi-Criteria Decision Analysis, 1, 127-138 (1992) · Zbl 0838.90071
[13] Liesiö, J.; Mild, P.; Salo, A., Preference Programming for robust portfolio modeling and project selection, European Journal of Operational Research, 181, 1488-1505 (2007) · Zbl 1123.90327
[14] Liesiö, J.; Salo, A., Scenario-based portfolio selection of investment projects with incomplete probability and utility information, European Journal of Operational Research, 217, 162-172 (2012) · Zbl 1244.91111
[15] Lindstedt, M.; Liesiö, J.; Salo, A., Participatory development of a strategic product portfolio in a telecommunication company, International Journal of Technology Management, 42, 250-266 (2007)
[16] Mild, P.; Salo, A., Combining a multiattribute value function with an optimization model: an application to dynamic resource allocation for infrastructure maintenance, Decision Analysis, 6, 139-152 (2009)
[17] Moshkovich, H. M.; Mechitov, A. I.; Olson, D. L., Ordinal judgments in multiattribute decision analysis, European Journal of Operational Research, 137, 625-641 (2002) · Zbl 1030.90503
[18] Ojanen, O.; Makkonen, S.; Salo, A., A multi-criteria framework for the selection of risk analysis methods at energy utilities, International Journal of Risk Assessment and Management, 5, 16-35 (2005)
[19] Park, K. S.; Kim, S. H.; Yoon, C. Y., An extended model for establishing dominance in multiattribute decisionmaking, Journal of the Operational Research Society, 47, 1415-1420 (1996) · Zbl 0863.90099
[20] Pearman, A. D., Establishing dominance in multiattribute decision making using an ordered metric method, Journal of the Operational Research Society, 44, 461-469 (1993) · Zbl 0774.90052
[21] Sage, A. P.; White, C. C., ARIADNE: a knowledge-based interactive system for planning and decision support, IEEE Transactions on System, Man, and Cybernetics, 14, 35-47 (1984)
[22] Salo, A.; Hämäläinen, R. P., Preference assessment by imprecise ratio statements, Operations Research, 40, 1053-1061 (1992) · Zbl 0765.90059
[23] Salo, A.; Hämäläinen, R. P., Preference ratios in multiattribute evaluation (PRIME) - elicitation and decision procedures under incomplete information, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 31, 533-545 (2001)
[24] Salo, A.; Hämäläinen, R. P., Preference programming - multicriteria weighting models under incomplete information, (Zopounidis, C.; Pardalos, P. M., Handbook of Multicriteria Analysis (2010), Springer: Springer New York)
[25] Salo, A.; Liesiö, J., A case study in participatory priority-setting for a Scandinavian research program, International Journal of Information Technology & Decision Making, 5, 65-88 (2006)
[26] Salo, A.; Punkka, A., Rank inclusion in criteria hierarchies, European Journal of Operational Research, 163, 338-356 (2005) · Zbl 1104.91017
[27] Sarabando, P.; Dias, L. C., Simple procedures of choice in multicriteria problems without precise information about the alternatives’ value, Computers & Operations Research, 37, 2239-2247 (2010) · Zbl 1231.90242
[28] Weber, M., Decision making with incomplete information, European Journal of Operational Research, 28, 44-57 (1987) · Zbl 0604.90004
[29] White, C. C.; Sage, A. P.; Dozono, S., A model of multiattribute decisionmaking and trade-off weight determination under uncertainty, IEEE Transactions on Systems, Man, and Cybernetics, 14, 223-229 (1984)
[30] White, C. C.; Sage, A. P.; Scherer, W. T., Decision support with partially identified parameters, Large Scale Systems, 3, 177-189 (1982) · Zbl 0527.90051
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