Journal
INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH
Volume 28, Issue 6, Pages 3513-3535Publisher
WILEY
DOI: 10.1111/itor.12704
Keywords
interactive; strict total order; discrete alternative; convex cone; multiple criteria; transitivity; linear value function; quasiconcave value function
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The study introduces interactive algorithms to find a strict total order for a set of discrete alternatives based on linear and quasiconcave value functions. The algorithms iteratively update preference matrix to elicit preference information from the decision maker until termination conditions are met, showing efficient convergence to the exact total order for both value functions.
We develop interactive algorithms to find a strict total order for a set of discrete alternatives for two different value functions: linear and quasiconcave. The algorithms first construct a preference matrix and then find a strict total order. Based on the ordering, they select a meaningful pair of alternatives to present the decision maker (DM) for comparison. We employ methods to find all implied preferences of the DM, after he or she makes a preference. Considering all the preferences of the DM, the preference matrix is updated and a new strict total order is obtained until the termination conditions are met. We test the algorithms on several instances. The algorithms show fast convergence to the exact total order for both value functions, and eliciting preference information progressively proves to be efficient.
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