Pareto set reduction based on an axiomatic approach with application of some metrics
V. D. Nogin
St. Petersburg State University, St. Petersburg, Russia
A multicriteria choice problem involving a decision-maker’s binary preference relation is considered. Several two-stage methods are proposed for its solution. First, the Pareto set is reduced by applying an axiomatic approach. Then the problem is scalarized on the resulting set by using the Chebyshev or Euclidean metric. The methods proposed are substantiated with the help of well-known and new techniques for characterizing weakly efficient and proper efficient points. Illustrative examples are given.
multicriteria choice, Edgeworth–Pareto principle, Pareto set reduction, Chebyshev metric, Euclidean metric, scalarization, axiomatic approach.
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Computational Mathematics and Mathematical Physics, 2017, 57:4, 645–652
V. D. Nogin, “Pareto set reduction based on an axiomatic approach with application of some metrics”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 645–653; Comput. Math. Math. Phys., 57:4 (2017), 645–652
Citation in format AMSBIB
\paper Pareto set reduction based on an axiomatic approach with application of some metrics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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