A Robustness Study of State-of-the-Art Surrogate Weights for MCDM

Abstract

A vast number of methods for solving multi-criteria decision problems have been suggested for assessing criteria weights requiring more exact input data than users normally are able to provide. In particular, the selection of adequate criteria weights is difficult and in order to be realistic, other methods must be introduced. One class of such methods is to introduce so called surrogate weights, where numerical weights are assigned to each criterion based on a cardinal or ordinal rank ordering, assumed to represent the information extracted from the user. One essential problem is the robustness of such methods. In this article, we compare state-of-the-art methods based on surrogate weights from the literature and, utilising a simulation approach, discuss underlying assumptions and robustness properties. This results in a quantitative measurement of these weighting methods and a methodology applicable also to forthcoming methods.

Supporting multiattribute decisions in scenario planning using a simple method based on ranks

“…ROC and RR and weights perform better when this assumption is valid (Danielson & Ekenberg, 2017). In the direct rating method, decision makers assign a weight of 100 to the attribute offering the most desired swing and lower weights to less preferable swings, but there is no constraint on what the weights sum to.…”

“…This assumption favors RS weights. Danielson and Ekenberg (2017) suggest the use of cardinal counterparts to RR, RS, and ROC weights in order to reflect, not only the ranks of attribute swings, but the strengths of preference between them. While these weights may be appropriate to many multiattribute decision problems, by also requiring elicitations of strength of preference, they would add to the already large number of judgments required in scenario planning-based decisions.…”

“…For each of these decision sizes 10,000 simulated decisions were generated. As Danielson and Ekenberg (2017) point out, the results of such simulations are heavily dependent on the assumptions that underpin the mechanism that generates the simulations. For example, the assumptions underlying the simulations conducted by Edwards and Barron (1994) favored the use of ROC weights.…”

Evaluating Partnerships to Enhance Disaster Risk Management using Multi-Criteria Analysis: An Application at the Pan-European Level

“…While the evaluation of multiple criteria by a single decision maker is rather straightforward, the comparison of many stakeholder evaluations is far from obvious and a plethora of suggestions on how this could be done can be found in the literature (Danielson and Ekenberg 2016 ). Recent analyzes in this field suggest that cardinal ranking methods are superior in a number of ways when compared to other ranking methods (Danielson and Ekenberg 2017 ). We therefore adopt this approach for our case too.…”

“…A review of current quantitative multi-criteria decision aid methods can be found in Danielson and Ekenberg ( 2016 ). The cardinal ranking method and its mathematical representation are discussed in detail in Danielson and Ekenberg ( 2017 ). This method was selected because it is superior to other MCA approaches in a number of ways (see again the simulation tests by Danielson and Ekenberg 2016 , 2017 ) and could be implemented within the scope of the criteria introduced above.…”