Interactive group decision making procedure under incomplete information. (English) Zbl 1009.90519

Summary: This paper deals with multiple criteria decision making problem with incomplete information when multiple decision makers are involved. Usually decision makers are willing or able to provide only incomplete information, because of time pressure, lack of knowledge or data, and their limited expertise related with problem domain. There have been just a few studies considering incomplete information in group settings. This incompletely specified information constructs region of linear constraints and therefore, pairwise dominance relationship between alternatives reduces to intractable nonlinear programmings. Hence, to handle this difficulty, we suggest a method, utilizing individual decision results to form group consensus. Final group consensus ranking toward more agreement of participants can be built through solving a series of linear programmings, using individual decision results under group members’ possibly different weight constraints.


90B50 Management decision making, including multiple objectives
91B06 Decision theory


Full Text: DOI


[1] Anandaligam, G., A multiagent multiattribute approach for conflict resolution in acid rain impact mitigation, IEEE transactions on systems, management and cybernetics, 19, 1142-1153, (1989)
[2] Brans, J.P.; Vincke, Ph.; Mareschal, B., How to select and how to rank projects: the PROMETHEE method, European journal of operational research, 24, 228-238, (1986) · Zbl 0576.90056
[3] Chinneck, J.W., MINOS (IIS): infeasibility analysis using MINOS, Computers & operations research, 21, 1-9, (1994) · Zbl 0800.90688
[4] Cook, W.; Seiford, L., Priority ranking and consensus formation, Management science, 24, 1721-1732, (1978) · Zbl 0491.90006
[5] Goicoechea, A., Hansen, D.R., Duckstein, L., 1982. Multiobjective Decision Analysis with Engineering and Business Application. Wiley, New York · Zbl 0584.90045
[6] Hannan, E.L., Obtaining nondominated priority vectors for multiple objective decision making problems with different combination of cardinal and ordinal information, IEEE transactions on systems, management and cybernetics, 11, 538-543, (1981) · Zbl 0465.90001
[7] Hazen, G.B., Partial information, dominance and potential optimality in multiattribute utility theory, Operations research, 34, 296-310, (1986) · Zbl 0625.90048
[8] Islei, G.; Lockett, G., Group decision making: supposition and practice, Socio-economic planning science, 25, 67-81, (1991)
[9] Jacquet-Lagreze, E.; Siskos, J., 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
[10] Kahneman, D., Slovic, P., Tversky, A., 1982. Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge
[11] Keeney, R.L., Raiffa, H., 1976. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York · Zbl 0488.90001
[12] Kim, S.H.; Ahn, B.S., Group decision making procedure considering preference strength under incomplete information, Computers & operations research, 24, 1101-1112, (1997) · Zbl 0883.90069
[13] Kirkwood, C.W.; Sarin, R.K., Ranking with partial information: A method and an application, Operations research, 33, 38-48, (1985) · Zbl 0569.90052
[14] Kmietowicz, Z.W.; Pearman, A.D., Decision theory, linear partial information and statistical dominance, Omega, 12, 391-399, (1984) · Zbl 0549.90056
[15] Park, K.S.; Kim, S.H., Tools for interactive multiattribute decision making with incompletely identified information, European journal of operational research, 98, 111-123, (1997) · Zbl 0920.90085
[16] Pekelman, D.; Sen, S.K., Mathematical programming models for the determination of attributes weights, Management science, 20, 8, 1217-1229, (1974) · Zbl 0303.90006
[17] Ramanathan, R.; Ganesh, L.S., Group preference aggregation methods employed in AHP: an evaluation and an intrinsic process for deriving members weightages, European journal of operational research, 79, 249-265, (1994) · Zbl 0815.90003
[18] Roy, B.; Vincke, P., Multicriteria analysis: survey and new directions, European journal of operational research, 8, 207-218, (1981) · Zbl 0464.90068
[19] Salo, A.A., Interactive decision aiding for group decision support, European journal of operational research, 84, 134-149, (1995) · Zbl 0910.90191
[20] Srinivasan, V.; Shocker, A.D., Linear programming techniques for multidimensional analysis of preferences, Psychometrika, 38, 3, 337-369, (1973) · Zbl 0316.92024
[21] Tamiz, M.; Mardle, S.J.; Jones, D.F., Detecting IIS in infeasible linear programmes using techniques from goal programming, Computers & operations research, 23, 113-119, (1996) · Zbl 0868.90080
[22] Van Loon, J.N.M., Irreducibly inconsistent systems of linear inequalities, European journal of operational research, 8, 283-288, (1981) · Zbl 0468.90041
[23] Weber, M., A method of multiattribute decision making with incomplete information, Management science, 31, 11, 1365-1371, (1985) · Zbl 0594.90046
[24] Weber, M., Decision making with incomplete information, European journal of operational research, 28, 44-57, (1987) · Zbl 0604.90004
[25] White, C.C.; Sage, A.P.; Dozono, S., A model of multiattribute decisionmaking and trade-off weight determination under uncertainty, IEEE transactions on systems, management and cybernetics, 14, 2, 223-229, (1984)
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