Use of Piecewise Linear Value Functions in Interactive Multicriteria Decision Support: A Monte Carlo Study

This paper describes a Monte Carlo study conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice MCDM problem, based on explicit value function models. The purpose of the study is to identify those assumptions and parameters which lead to the most efficient use of preference judgements made by the decision maker, and to the greatest robustness to judgmental errors. It is concluded that nonlinearities in the value function need to be modelled, achieved here by use of a piecewise linear form. It was also found that search for indifference points, rather than using simple preference judgements alone, is of great advantage, best realized by expressing judgements in terms of pairwise trade-offs. Methods incorporating these features are highly robust to judgmental errors. Interactive methods of this class are compared with a priori fitting of similar value functions, and found to give a very similar quality of solution.