Title: Reducing the Pareto optimal set in MCDM using imprecise probabilities

Authors: Lev V. Utkin

Addresses: Department of Industrial Control and Automation, St. Petersburg State Forest Technical University, Institutsky per. 5, 194021 St. Petersburg, Russia

Abstract: An approach for reducing a set of Pareto optimal solutions on the basis of specific information about importance of criteria is proposed in the paper. The DM's judgments about criteria have a clear behaviour interpretation and can be used in various decision problems. It is shown that the imprecise probability theory can be successfully applied for formalising the available information which is represented by means of a set of probability measures. Simple explicit expressions instead of linear programming problems are derived for dealing with three decision rules: maximality, interval dominance and interval bound dominance rules. Numerical examples illustrate the proposed approach.

Keywords: multicriteria decision making; MCDM; imprecise probabilities; desirable gambles; probability measures; judgments; preferences; Pareto sets; optimal sets; maximality; interval dominance; interval bound dominance rules.

DOI: 10.1504/IJOR.2014.057840

International Journal of Operational Research, 2014 Vol.19 No.1, pp.21 - 39

Received: 20 Feb 2012
Accepted: 23 Jul 2012
Published online: 17 Jun 2014 *

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