Simple additive weighting - A metamodel for multiple criteria decision analysis methods

We interpret rankings provided by any MCDA method in terms of the Simple Additive Weighting.Weights of SAW which preserve rankings produced by a given MCDA method are identified.Ranges of weights resulting with the same rankings as by a given MCDA method are identified as well.An alternative explanatory framework for MCDA methods is offered. Multiple Criteria Decision Analysis (MCDA) methods, such as ELECTRE, PROMETEE, AHP, TOPSIS, VIKOR, have been applied to solving numerous real-life decision making problems in business and management. However, the mechanics of those methods is not easily understandable and it is often seen by users without much formal training as a kind of "scientific witchcraft".In order to make those popular MCDA methods more transparent, we provide a simple framework for interpretations of rankings they produce. The framework builds on the classical results of MCDA, in particular on the preference capture mechanism proposed by Zionts and Wallenius in seventies of the last century, based on Simple Additive Weighting.The essence and the potential impact of our contribution is that given a ranking produced by an MCDA method, we show how to derive weights for the Simple Additive Weighting which yield the same ranking as the given method. In that way we establish a common framework for almost no-cost posterior analysis, interpretation and comparison of rankings produced by MCDA methods in the expert systems environment. We show the working of the concept taking the TOPSIS method in focus, but it applies in the same way to any other MCDM method.We illustrate our reasoning with numerical examples taken from literature.