**2. Methodology**

#### *2.1. The Multi-Attribute Utility Theory (MAUT)*

Implicit in any decision-making process is the need to construct either directly or indirectly, the preference order, so that alternatives can be ranked and the best alternative can be selected. For some decision-making problems, this may be easily accomplished. For example, in case of a decision based on a cost-minimization rule (where the lowest cost alternative is chosen), the preference order is adequately represented by the natural order of real numbers, representing costs. Hence, in such a case, the preference order need not be constructed explicitly [18].

Multi-criteria decision-making (MCDM) provides a systematic approach to evaluate multiple conflicting attributes in decision-making. Conflicting attributes usually arise when evaluating options, for example, minimizing costs while maximizing performance. MCDM is used to identify and quantify decision-makers' and stakeholders' considerations about various (mostly) non-monetary factors, in order to compare alternative courses of action [19]. The multiple performance attribute can be combined into a so-called utility function, in which all the attributes are brought into a single scale [20]. One of the decision-making techniques that attempts to construct the preference order by directly eliciting the decision maker's preference and using multiple attributes is known as the multi-attribute utility theory (MAUT). The assumption is that a decision maker, who must select one alternative from a recognized set of decision alternatives, will be governed by preferences. In order to build a model which will represent the decision maker's preference and implement different attributes, a real-valued function called the utility function has to be determined for each attribute [19,20]. Once the functions are constructed, the selection of the appropriate alternative can be done using an optimization method. This technique involves several steps [21], including the definition of objectives and constraints, followed by the definition of attributes and by the development of a single utility function for each of the selected attributes. By assigning relative weights to the multiple attributes, an amalgamation step follows, which includes combining the single criterion utility functions using the relative weights into one measure based on mathematical assumptions about the decision maker's preference structure. Ceri´c [22] states that MAUT is used in cases when the best alternative solution must be chosen, i.e., for compiling a ranking list of the alternatives offered.

MAUT has been widely used in decision-making processes in the transportation infrastructure domain. Several papers consider the application of theory in the transport sector for the multi-objective optimization of multi-alternative decisions [23], the assessment of quality in bridge construction [24], road bridge managemen<sup>t</sup> [25], or the development of a rating model that incorporates a wide range of factors affecting flexible pavements [26]. Several publications also address the implementation of MAUT in the railway sector for selecting transportation corridors linked to a traffic simulation model [27], selecting railway lines for reconstruction [28], or railway route planning and design [29]. Additional papers consider civil engineering infrastructure assets, where MAUT is incorporated in maintenance decision-making [21,30,31]. In order to implement MAUT for the categorization of railway embankments, a selection of proper attributes and alternatives shall be conducted.
