A Multiple Criteria Decision Analysis Model Based on ELECTRE TRI-C for Erosion Risk Assessment in Agricultural Areas

Abstract

This paper deals with a real-world decision-aiding problem for zoning the risk of erosion, total suspended solids emissions, and ecological consequences of their transfers towards the streams. One of these consequences is the decrease of fishes into the streams in agricultural watersheds, because of the clogging of spawning areas. Given the multiple criteria nature of the problem, the originality of our research is to adapt a new decision-aiding sorting method, ELECTRE TRI-C, for identifying risk zones in rural areas, where measures must be taken. The developed model was applied in a small watershed (Low Normandy, France) where the objective was to assess the most appropriate intervention for protecting the reproduction habitat of the salmonid fishes. Agricultural parcels were evaluated on multiple criteria for grouping them into four risk categories, which are related to risk levels as well as priorities on the improvement works. The decision-aiding sorting model is co-constructed, within a constructive approach, through an interaction process between decision-aiding analysts, environmental experts, and local actors for improving transparency and communication on the results. This model is linked with a geographical information system (GIS) for assessing a set of criteria and the visualization of the farming parcels along with their type of intervention they should be submitted to best practices. The assignment results were validated by the environmental experts. These results have a strong impact on the agricultural practices of the farmers into the watersheds. The model proposed in this paper can be considered as a useful decision aid tool in any regions for implementing public agricultural and environmental policies for protecting the ecological areas.

Appendices

Appendix 1: Definition of the Outranking Credibility Index

Let us assume, without loss of generality, that all the criteria g _j ∈ F are to be maximized, which means that the preferences increase when the criteria performances increase too. Consider two farming parcels, denoted a and a′. When using the discriminating thresholds defined in Section 2.6, the following binary relations can be derived for each criterion [30]:

• 1. If | g _j (a) − g _j (a′) | ⩽ q _j , then a is indifferent to a′according to g _j , denoted a I _j a′. Let C(a I a′) be the subset of criteria such that a I _j a′.

• 2. If g _j (a) − g _j (a′) > p _j , then a is strictly preferred to a′according to g _j , denoted a P _j a′. Let C(a P a′) be the subset of criteria such that a P _j a′.

• 3. If q _j < g _j (a) − g _j (a′) ⩽ p _j , then a is weakly preferred to a′ (a hesitation between indifference and strict preference), denoted a Q _j a′. Let C(a Q a′) be the subset of criteria such that a Q _j a′.

The credibility of the comprehensive outranking of a over a′, denoted σ(a, a′), which reflects the strength of the statement “a outranks a′” (a is at least as good as a′) when taking all the criteria from F into account, is defined as follows:

$$ \sigma(a,a^{\prime}) = \left\{ \begin{array}{rcl} c(a,a^{\prime}) \prod_{j=1}^{n} \; \frac{1\;- \; d_{j}(a,a^{\prime})}{1 \; - \; c(a,a^{\prime})} & \text{if}\,\, d_{j}(a,a^{\prime}) > c(a,a^{\prime}),\\ c(a,a^{\prime}) & \textrm{otherwise,} \end{array} \right. $$

(1)

where,

$$ d_{j}(a,a^{\prime}) = \left\{ \begin{array}{rcl} 1 & \text{if}\,\,g_{j}(a) - g_{j}(a^{\prime}) < - v_{j},\\ \frac{g_{j}(a) - g_{j}(a^{\prime}) \; + \; p_{j}}{p_{j} \; - \; v_{j}} & \text{if}\,\, -v_{j} \leqslant g_{j}(a) - g_{j}(a^{\prime}) < - p_{j},\\ 0 & \text{if}\,g_{j}(a) - g_{j}(a^{\prime}) \geqslant - p_j. \end{array}\right. $$

(2)

$$\begin{array}{@{}rcl@{}}c(a,a^{\prime}) &=& \displaystyle\sum\limits_{j \;\in\; C(aPa^{\prime})} w_{j} + \sum\limits_{j \;\in\; C(aQa^{\prime})} w_{j}\\ &&+\sum\limits_{j \;\in\; C(aIa^{\prime})} w_{j} + \sum\limits_{j \;\in\; C(a^{\prime}Qa)} w_{j} \varphi_{j}, \end{array} $$

(3)

$$ \varphi_{j} = \frac{g_{j}(a) - g_{j}(a^{\prime}) + p_{j}}{p_{j} - q_{j}} \in [0,1]. $$

(4)

Therefore, σ(a, a′) is obtained from an overall aggregating function, which is based on a concordance and nondiscordance principle. This credibility index represents the sum of the voting power of the criteria, which is concordant with the assertion “a is at least as good as a′,” while taking into account the reducing effect by the criteria which are discordant with such an assertion. As presented above, this aggregation procedure requires the performances of each farming parcel on each criterion, denoted g _j (a), j = 1, … , n; the weights of the criteria, denoted w _j (we assume, without loss of generality, that $\sum_{j=1}^{n}$ = 1); the indifference, the preference, and, possibly, the veto thresholds, denoted q _j , p _j , and v _j , respectively, such that v _j ⩾ p _j ⩾ q _j ⩾ 0.

Appendix 2: Performances of the Farming Parcels from Violettes

Table 7 Performances of the farming parcels

Appendix 3: Assignment Results

Table 8 ELECTRE TRI-C versus environmental expert’s assignment results