Abstract
In this paper we present the foundations of the multiple reference points and reference set method of solving multicriteria decision problems and discuss its properties. To select a compromise solution to the multicriteria optimization problem, the decision-maker is requested to provide the additional information consisting of several families of reference points representing the values of criteria being of a special importance for the problem solution. The supplementary information concerning the preferences in the criteria space is aggregated in such a manner, so that the problem is reduced to the bicriteria trade-off between the proximity measures to the sets of desired and avoidable values of criteria. The solution process is interactive, the decision-maker may define at each step new reference points, trade-offs, and search directions.
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References
Górecki H., Skulimowski A.M.J. (1988). Safety Principle in Multiobjective Decision Support in the Decision Space Defined by Availability of Resources. Arch. Automatyki i Telem., 32, 339–353.
Jacquet-Lagrèze E., Meziani R., Slowinski R. (1987). MOLP with an interactive assessment of a piecewise linear utility function. EJOR, 31, 350–357.
Michalowski W., Szapiro T. (1992). A Bi-Reference Procedure for Interactive Multiple Criteria Programming. Operations Research, 40, No. 2, 247–258.
Skulimowski A.M.J. (1988). A Sufficient Condition for 0-Optimality of Distance Scalarization Procedures. Found. Contr. Engrg., 13, No. 1, 27–41.
Skulimowski A.M.J. (1990). Classification and Properties of Dominating Points in Vector Optimization. Methods of Operations Research, 58, 99–112.
Skulimowski A.M.J. (1996). Decision Support Systems Based on Reference Sets, UMM Publishers: Monographs, No. 40, Kraków,p. 165.
Weistroffer H.R. (1984). A combined over-and under-achievement programming approach to multiple objectives decision-making. LSS, 7, 47–58.
Wierzbicki A.P. (1986). On the Completeness and Constructiveness of Parametric Characterizations to Vector Optimization Problems. OR Spektrum, 8, 73–87.
Yu P.-L., Leitmann G. (1974a). Compromise Solutions, Domination Structures and Salukvadze’s Solution. JOTA, 13, No. 3, 362–378.
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© 1997 Springer-Verlag Berlin Heidelberg
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Skulimowski, A.M.J. (1997). Methods of Multicriteria Decision Support Based on Reference Sets. In: Caballero, R., Ruiz, F., Steuer, R. (eds) Advances in Multiple Objective and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46854-4_31
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DOI: https://doi.org/10.1007/978-3-642-46854-4_31
Publisher Name: Springer, Berlin, Heidelberg
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