The Compromise Criterion in MCDM: Interpretation and Sensitivity to the p Parameter

Abstract

In this paper we discuss the application of the compromise criterion to multicriteria decisionmaking and present an application taken from the field of architecture. The L^p (Minkowski) metric is used to rank a given set of alternatives according to their generalized distance from the ideal solution. We also examine the interpretation of the parameter p and the sensitivity of the results to its value. When p = 1, the compromise solution minimizes the total regret; when p is very large, the alternative selected minimizes very low performance as regards all the objectives. However, intermediate values of p which lack a clear linguistic interpretation imply a second level of compromise between the two extreme strategies. An empirical problem is used to illustrate the model. It concerns the selection of lightweight construction systems for the enclosure of outdoor swimming pools. Fifteen construction systems were evaluated and ranked on the basis of twenty-six different criteria. The sensitivity analysis exemplifies the effect of changing the parameters.