This article is cited in 6 papers

Pareto set reduction based on an axiomatic approach with application of some metrics

V. D. Nogin

St. Petersburg State University, St. Petersburg, Russia

Abstract: 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.

Key words: multicriteria choice, Edgeworth–Pareto principle, Pareto set reduction, Chebyshev metric, Euclidean metric, scalarization, axiomatic approach.

UDC: 519.658

Received: 19.02.2016
Revised: 14.06.2016

DOI: 10.7868/S0044466917040093

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:4, 645–652

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