Categorization of the Potential Impact of Italian Quarries on Water Resources through a Multi-Criteria Decision Aiding-Based Model

By inergency On Mar 27, 2024

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2.3. Multi-Criteria Decision Aiding (MCDA)

Several approaches and methods have been proposed in the literature for vulnerability and risk assessment when complex problems involve human activities and environmental protection in the context of sustainable development [49,50,51,52,53,54]. Considering that the aim of this study is to obtain an initial categorization of the Italian quarries based on their potential impact on water resources, as a tool for a future broader analysis of the sustainability of mining, a simplified approach using Multi-Criteria Decision Aiding (MCDA) [55,56,57,58,59,60] has been adopted. We deal with a large number of alternatives (i.e., the number of quarries being a few thousand), compared based on specific hydrological and hydrogeological criteria. These criteria include selected parameters for surface water and groundwater, sometimes interdependent or interconnected, expressed both in numerical and ordinal scales. The solution to the problem is certainly not easy when relying on the simple maximization or minimization of an objective function. It must be approached with the use of more flexible tools capable of contextualizing the decision-making process in a global inter-system context, also taking into account the data currently available for Italian quarries.

The large number of alternatives made the choice fall on the ELECTRE models [61,62,63]. These models can incorporate a vast range of data and are related to criteria, weights, indifference, weak preference, strong-preference thresholds and even veto thresholds. The objective of sorting the quarries from the most impactful to the least impactful, giving their considerable number, cannot be pursued by solving a ranking type problem (γ problematic) through the ELECTRE III. Instead, it requires the application of a sorting type problem (β problematic), involving the division of quarries into categories based on different levels of impact; this is accomplished through the application of the ELECTRE TRI model [64,65,66]. The software chosen to apply this decision analysis procedure was MCDA-ULaval v0.6.28, developed at the Université Laval of Quebec [67].

Before initiating the sorting process among all the quarries, it is essential to establish gradual levels of criticality within the evaluation scales of each criterion. These levels serve as the basis for formulating judgments for each quarry. Therefore, for each criterion, five levels of criticality have been defined, which are determined by the minimum and maximum values of the related judgment scale, along with four separating values, appropriately identified through specific technical parameters. The impact degree of a quarry is then summarized through the various levels of criticality that combine the different judgment criteria. Quarries which, on average, across various criteria, receive evaluations falling into the highest levels of criticality, will be categorize with the highest impact. Conversely, those falling into the lowest levels of criticality will be considered as having lower impact. Within the set of quarries identified with the highest impact, considering their potentially reduced number compared with the total, a refinement of the results can be performed. This involves a further evaluation of the quarries, in this case strictly ordinal, ranging from those with the most critical impact to those with the least critical impact.

The mathematical algorithm used for the quarry categorization can be summarized as follows.

Given a set G of m criteria, for each criterion g_j, where j = 1, 2, …, m, the preference and indifference thresholds (q_j and p_j, respectively) and potentially a veto threshold (v_j) must be set. Subsequently, to each pair of alternatives, a and b, the classification algorithm associates a restricted outranking relation aS_jb. The latter relation is based on the premise that sufficiently strong reasons converge for the truth of the statement “a, with respect to criterion j, is at least as good as b (not worse than)”. From all m restricted outranking relations, a complete outranking relation “aSb” is derived.

For each j-criterion and for each pair of alternatives (a,b), the construction of relation aS_jb involves three subsequent phases:

1.

The calculation of a concordance index c_j(a,b), so if

g_j(b) − g_j(a) ≤ q_j is c_j(a,b) = 1, there is no contradiction with the statement “aSb”;
q_j < g_j(b) − g_j(a) ≤ p_j, is 0 < c_j(a,b) < 1, there is weak contradiction with the statement “aSb”;
g_j(b) − g_j(a) ≥ p_j, is c_j(a,b) = 0, there is a total contradiction with the statement “aSb”.

Once the indices c_j(a,b) have been computed and the weights w_j associated with each j-criterion (g_j) have been considered, the global concordance index c(a,b) is constructed as follows:

$c (a, b) = \sum_{j} w_{j} c_{j} (a, b)$

The global concordance indices are summarized in a global concordance matrix C(a,b).

2.

The calculation of a discordance index d_j(a,b), such as to indicate the extent to which the relation between the a and b on j-criterion disagrees with the statement “aSb” and its effect on the relation aSb, so if

g_j(b) − g_j(a) ≤ p_j[g_j(a)] is d_j(a,b) = 0, there is no contradiction with the statement “aSb”;
p_j[g_j(a)] < g_j(b)-g_j(a) ≤ v_j[g_j(a)], is 0 < d_j(a,b) < 1, there is weak contradiction with the statement “aSb”;
g_j(b) − g_j(a) ≥ v_j[g_j(a)], is d_j(a,b) = 1, this prohibits any outranking of a over b, regardless of the evaluations on all the remaining criteria.

3.

The construction of the outranking relation is completed by establishing the degree of credibility σ(a,b), a value between 0 and 1. This value, considering both the concordance and discordance indices, summarizes the strength of the “aSb” relation.

The calculation of σ(a,b) starts from the concordance index c(a,b), weakened through the discordance indices d_j(a,b) if and only if its value is sufficiently high, and that is if the condition d_j(a,b) > c(a,b) is true.

In general, let G(a,b) be the set of criteria for which the discordance index is greater than the concordance index:

$G (a, b) = [j / j \in G, d_{j} (a, b) > c (a, b)]$

we have the following:

if G(a,b) = 0, an absence of discordant criteria, then σ(a,b) = c(a,b);

if G(a,b) ≠ 0, then $σ (a, b) = c (a, b) \prod_{j \in G} \frac{1 - d_{j} (a, b)}{1 - c (a, b)}$ .

The classification algorithm, summarizing the outranking relation, provides a partial ordering of the alternatives. Two orders are constructed: the first by selecting the alternatives from best to worst (descending distillation), the second by starting from the worst alternatives to arrive at the best (ascending distillation). To construct the two orders, we proceed through the cutting algorithm with specific characteristics [68]. The intersection between the ascending and descending orders highlights the relationships between alternatives and underlines some incomparability. In particular, alternative a is considered as the following:

Better than alternative b, if, in at least one classification (ascending or descending), a is positioned better than b, and in the other a is classified at least as well as b;
Equivalent to alternative b, if the two belong to the same class in both systems;
Incomparable with alternative b, if there is a contradiction in the two classifications; for example, a is in a better position than b in the ascending classification, but b is positioned ahead of a according to the descending distillation.

All selected data of the quarries, exported from GIS, have been summarized in a matrix with the number of rows equal to the number of quarries and eight columns, corresponding to the selected criteria, specifically four for surface water (SW) and four for groundwater (GW) (Figure 3).

Three criteria refer to qualitative evaluations (T for SW and T and C for GW); they were transferred and summarized on an ordinal scale (Figure 3). As mentioned earlier, to apply the ELECTRE TRI, five predefined levels of critical impact on water resources were established within the evaluation scales of each criterion (Table 1). The levels were identified through four separating values, chosen based on technical considerations (Figure 3). These values, for each criterion, categorize an alternative into different bands of more- or less-accentuated potential impact. For each criterion, indifference and preference thresholds were inserted, representing evaluations within which there is indifference or dominance of one over another in a pairwise comparison. These thresholds must be proportionally related to the evaluations being compared.

Finally, weights were assigned to the criteria, initially to the two macro-criteria (SW and GW), and then to the micro-criteria into which each of the two macros has been divided (Figure 3). The choice of weights w_j for the various criteria plays a crucial role. Initially, the AHP (Analytic Hierarchy Process) method of pairwise comparisons [69] was applied, considering the eigenvector associated with the pairwise comparison matrix obtained from the particular value judgments made on each possible pair of criteria, as well as the different criteria deemed to have weight within the final categorization by the conceptual model. A second application involved the determination of weights through the ordinal method of the cards [70,71], in which the set of criteria is divided into several possible subsets of decreasing importance relative to the conceptual model, each of which is assigned the corresponding rank. A third application refers exclusively to expert judgements which consider a gradually decreasing weight for the micro-criteria to be deemed less influential on the potential impact of the quarries.

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