## 3 Previous Work  
A taxonomy of general approaches to MCDA has been developed by [27] that includes (a) how the decision problem is formulated, (b) how criteria are established, and (c) how stakeholder preferences are determined and implemented. Here, we are concerned only with (c) the implementation methodologies. There are many reviews of these methods in the published literature, but few specifically focused on civil engineering applications, for example [28], and some on environmental decisions, e.g., [1]. However, there are few published comparisons of methods in design and management contexts, that compare more than two methods. One example is [29] that lists 33 papers describing applications in (i) architecture, (ii) urban planning and (iii) energy-efficient construction which were the keywords in her literature review. While 17 methods were mentioned in the papers reviewed, AHP was used 16 times, much more than any of the other methods. Examples of some limited comparisons are, [26] who compared PROMETHEE, TOPSIS, VIKOR and COPRA and [30] who compared AHP, TOPSIS and VIKOR and preferred VIKOR for the selection of a manufacturing process. Four methods were compared by [31] for use in Life Cycle Assessment applications, and three (AHP, TOPSIS and a fuzzy logical based method due to Mamdani) gave comparable results. The AHP, TOPSIS and SAW (simple additive weighting) methods were applied by [32] to the operation of a rubber plantation and AHP was preferred. Preferences of 40 MCDA users were explored by [33], but only with three methods, all of which had similar evaluations. In a power generation application, [34] compared SAW, AHP, TOPSIS and a multiplicative method, all of which produced similar results. Some of the issues arising in comparison of decision support methods are discussed by [35], while the most general intercomparison of MCDA methods found in the literature search was by [36] who assessed the users experience and difficulties with methods as well as comparing their results.  
Figure 1: Grouping of multi-criteria decision analysis (MCDA) techniques and components. (Note: citations for all terms in the figure are listed in Table 1. Fuzzy number versions of some of these methods have been developed).  
Thus, few recent extensive comparisons of a wide range of MCDA methods in civil engineering or related applications were found that might give guidance on the selection of suitable methods, except for [28], and none describing the software available for a wide range of applications related to civil engineering. This is understandable, given the widely different data requires of many of the methods, that would make an objective comparison difficult. However, there are substantive reviews focused on specific aspects of Civil Engineering, such as [37] in relation to sustainability in Bridge Design, or [29] in relation to energy efficient building design. Therefore, for this paper, an alternative way to explore the usefulness of MCDA methods is to assess published information on their usage in civil engineering practice to determine the most widely used methods and the application areas in which they are used. Thus, a focused review of the literature was undertaken for this paper, as described below.