## 2 Background
Many of the compensatory methods used weighted averages and thus assume that the \"value\" the decision maker places on a certain level of any criterion is independent of the levels of the other criteria. This is an essential requirement for the method justifying adding together the individual, scaled, impacts of all criteria. However, a human decision maker does not always make a decision in this way, [23]. Of the compensatory methods, MAUT is an exception to direct weighted sums as it uses a multi-dimensional utility function in which the level of one criterion can influence the impact of other criteria. However, the complexity of forming this multidimensional function and the information required to implement in practice limits the number of criteria that can be reasonably managed, although there are techniques for mitigating this limitation [24]. Compensatory methods also imply that a very good performance in one criterion can compensate for a very poor performance in another and the weights used should be interpreted as trade-off coefficients. On the other hand, non-compensatory methods do not make this assumption, and most will take account of the criteria for which an option performs poorly as well as those for which it performs well. The weights used can be interpreted as importance indicators, [25]. Non-compensatory methods often involve thresholds of acceptability and building an outranking relationship, see Figure 1. \begin{table}
\begin{tabular}{c c c c} \hline
**Abbreviation** & **Name** & **Citation** & **Category** \\ \hline \hline \multicolumn{1}{c}{AHP} & Analytic Hierarchy Process & [6] & compensatory \\ \hline \multicolumn{1}{c}{ANP} & Analytic Network Process & [14] & compensatory \\ \hline \multicolumn{1}{c}{CBA} & Cost Benefit Analysis & [15] & compensatory \\ \hline \multicolumn{1}{c}{COPRAS} & Complex Proportional Assessment & [16] & compensatory \\ \hline \multicolumn{1}{c}{CRITIC} & Objective assessment of weights & [17] & weights only \\ \hline \multicolumn{1}{c}{ELECTRE} & \multicolumn{1}{c}{ELimination Et Choix} & non-compensatory \\ \multicolumn{1}{c}{Traduisant la REalite} & [10] & \multicolumn{1}{c}{outranking} \\ \hline \multicolumn{1}{c}{MACBETH} & \multicolumn{1}{c}{Measuring Attractiveness by a} & \multicolumn{1}{c}{[18]} & compensatory \\ \multicolumn{1}{c}{Categorical Based Evaluation Technique} & & & \\ \hline \multicolumn{1}{c}{MAUT} & Multi-Attribute Utility Theory & [5] & multi-dimensional function \\ \hline \multicolumn{1}{c}{MAVT} & Multi-Attribute Value Theory & [19] & multi-dimensional function \\ \hline \multicolumn{1}{c}{MOORA} & \multicolumn{1}{c}{Multi-Objective optimization on the basis} & \multicolumn{1}{c}{[20]} & compensatory \\ \multicolumn{1}{c}{} & of ratio analysis & & \\ \hline \multicolumn{1}{c}{PROMETHEE} & \multicolumn{1}{c}{Preference Ranking Organization Method} & \multicolumn{1}{c}{[11]} & non-compensatory \\ \multicolumn{1}{c}{} & for Enrichment Evaluation & & \\ \hline \multicolumn{1}{c}{SAW or WAS} & Simple Additive Weighting & [4] & compensatory \\ \hline \multicolumn{1}{c}{Simos\({}^{\prime}\) cards} & \multicolumn{1}{c}{Method for eliciting cardinal information} & \multicolumn{1}{c}{[21]} & weights only \\ \multicolumn{1}{c}{} & on preferences from stakeholders & & \\ \hline \multicolumn{1}{c}{TOPSIS} & \multicolumn{1}{c}{Technique for Order Preference by} & \multicolumn{1}{c}{[7]} & compensatory \\ \multicolumn{1}{c}{} & similarity to Ideal Solution & & \\ \hline \multicolumn{1}{c}{VIKOR} & \multicolumn{1}{c}{Visekriterijumsko Kompromisino} & \multicolumn{1}{c}{[22]} & compensatory \\ \hline \end{tabular}
\end{table} 
Table 1: Key methods discussed in this paper (with abbreviations). Most engineering design or decision problems require either ranking or choosing from a range of feasible options and so can be addressed by either method, depending on the supporting information available [26].