# Rural Road Assessment Method for Sustainable Territorial Development
## 2 Materials and Methods  
This paper presents methodologies to assess the static and dynamic contributions of roads to sustainable territorial development. This mechanism requires the support of a multi-criteria assessment model determined by the context conditions, the characteristics of the type of infrastructure, and its location. From this model, a static (A), dynamic (B), and prioritization (C) evaluation mechanism can be derived. The static method involves a series of indicators and weighted hierarchical criteria to assess the contribution of each sustainability dimension (environmental, technical, economic, and social) at a certain moment (\(t_{0}\)). The dynamic technique accounts for the causal relationships among each of the indicators. This makes it possible to calculate the progressive effect of interactionsat each time \(k\) due to some indicators' effect on others, from static initial values and an optimized set of roads. Based on the dynamic behavior, the indicators are processed in each \(t_{k}\) to prioritize the selected roads according to their distance to an ideal and to determine their time behavior. Figure 1 illustrates the evaluation method proposed by the authors, which is consistent with steps A, B, and C.  
Figure 1 indicates that a case study is required to develop the static assessment. This case study is defined by a database that facilitates the responses to an indicator set of an evaluation framework with \"i\" roads. The database of rural road indicators for the Araucania region, as proposed by [PERSON] (37), is referenced. From this information, the normalized indicators are aggregated by criterion and dimension consistent with the weights proposed by [PERSON] et al. (13) and the multi-criteria SAW technique (38). With the contribution to each sustainability dimension, a multi-objective optimization is implemented for the set of roads in the case study. Employing the Pareto optimal technique allows for the refinement of the set of roads to those efficient infrastructures that ensure that no alternative road exists that enhances one dimension without compromising at least one other dimension (39). At this point, it is necessary to configure an FCM that arises from the indicators of the assessment model and a panel of multidisciplinary specialists. In this model, the cause-effect interrelationship between indicators is determined. FCMs are soft computing techniques that combine fuzzy logic and neural networks. This technique simplifies a complex decision environment while integrating the different stakeholders' perspectives through a semi-quantitative approach with incomplete and vague data (40). Thus, a network is represented in which each node illustrates the normalized value [0, 1] of an indicator at \(t_{0}\). The indicators are interconnected with fuzzy weights between [\(-1\) and 1], representing the strength of a causal relationship and the meaning of the impact. The weight of the relationship arises from the application of a Mamdani-type fuzzy inference system (FIS) and a triangular distribution. An FIS is an expert system with approximate reasoning that maps a vector of inputs to a single scalar output (38). With the support of Matlab R2021b software, the Fuzzy logic tool, and the center of gravity theory, the responses of 45 multidisciplinary experts are pooled to obtain diffused weights of the relationship  
Figure 1: Proposed method for static-dynamic evaluation of rural roads. between indicators. For further background on applying the FIS, see [PERSON] [41] and [PERSON] et al. [42]. From the determination of the Pareto-optimal roads for a time \(t_{0}\) and the FCM, the dynamic analysis assesses the behavior of the set of optimal roads at different times \(t_{k}\). At each time, the \(A_{r}\) value of each \(C_{r}\) indicator is calculated by aggregating the influences of all the other indicators on it and flattening the overall impact by a barrier function \(f\), according to Equation (1) [43].