## 2 Materials and Methods
Approximate techniques assign an approximate weight to each attribute, strictly according to their ranking relative to other attributes with respect to importance. Approximate techniques appeal to principles of order statistics to justify weights in the absence of additional information on relative preference. As observed in the literature over the past three decades, there are several important pitfalls to be aware of when assigning attribute weights as described below:  
* Objective and attribute structure. The structure of the objectives and the selection of weighting methods affect results and should be aligned to avoid bias;
* Attribute definitions affect weighting. The detail with which certain attributes are specified affects the weight assigned to them; that is, the division of an attribute can increase or decrease the weight of an attribute. For example, weighing price, service level, and distance separately as criteria for a mechanic selection led to different results than weighing shop characteristics (comprised of price and service level) and distance did [62];  
Figure 1: Taxonomy of Multi-Criteria Decision Analysis techniques. * Number of attributes affects method choice. It is very difficult to directly or indirectly weight when one has to consider many attributes (e.g., double digits or more), owing to the greater difficulty associated with answering all the questions needed for developing attribute weights; [PERSON] [63] advocates the use of five to nine attributes to avoid cognitive overburden;
* More attributes are not necessarily better. As the number of attributes increases, there is a tendency for the weights to equalize, meaning that it becomes harder to distinguish the difference between attributes in terms of importance as the number of significant attributes increases [64];
* Attribute dominance. If one attribute is weighted heavier than all other attributes combined, the correlation between the individual attribute score and the total preference score approaches one;
* Weights compared within but not among decision frameworks. The interpretation of an attribute weight within a particular modeling framework should be the same regardless of the method used to obtain weights [65]; however, the same consistency in attribute weighting cannot be said to be present across all multi-criteria decision analysis frameworks [66];
* Consider the ranges of attributes. People tend to neglect accounting for attribute ranges when assigning weights using weighting methods that do not stress them [56,67]; rather, these individuals seem to apply some intuitive interpretation of weights as a very generic degree of importance of attributes, as opposed to explicitly stating ranges, which is preferred [68, 69, 70]. This problem could occur when evaluating job opportunities. People may assume that salary is the most important factor, however, if the salary range is very narrow (e.g., a few hundred dollars), then other factors such as vacation days or available benefits may in fact be more important in the decision maker's happiness. There is no superior method for eliciting attribute weights, independent of a problem's context. Consequently, users should be aware of how each method works, its drawbacks and advantages, the types of questions asked by the method, how these answers are used to generate weights, and how different the weights might be if other methods are used. Peer reviewers should be mindful of how each of these methods for eliciting attribute weights are used in practice and how users of these methods interpret the results. The specific method for eliciting attribute weights itself is not the only ingredient in stimulating the discussion. The weighting methods are only tools used in the analysis, and one should focus on the process for how the weights are used [65]. Using the defined taxonomy from Figure 1, we next evaluate the characteristics of each of the specified MCDA classifications.