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Theory of convex cones in multicriteria decision making. (English) Zbl 0692.90095
Multi-attribute decision making via O.R.-based expert systems, Proc. Int. Conf., Passau/FRG 1986, Ann. Oper. Res. 16, No. 1-4, 131-147 (1988).
Summary: [For the entire collection see Zbl 0689.00017.]
We develop the theory of convex polyhedral cones in the objective- function space of a multicriteria decision problem. The convex cones are obtained from the decision-maker’s pairwise judgements of decision alternatives and are applicable to any quasiconcave utility function. Therefore, the cones can be used in any progressively articulated solution procedure that employs pairwise comparisons. The cones represent convex sets of solutions that are inferior to known solutions to a multicriteria problem. Therefore, these convex sets can be eliminated from consideration while solving the problem. We develop the underlying theory and a framework for representing knowledge about the decision- maker’s preference structure using convex cones. This framework can be adopted in the interactive solution of any multicriteria problem after taking into account the characteristics of the problem and the solution procedure. Our computational experience with different multicriteria problems shows that this approach is both viable and efficient in solving practical problems of moderate size.

MSC:
90C31 Sensitivity, stability, parametric optimization
52Bxx Polytopes and polyhedra