**2. Results and validation**

#### **2.1. Site search analysis**

*SI Aj*, *<sup>m</sup>*<sup>=</sup> *MSR Aj*, *<sup>m</sup>* <sup>−</sup> *MSR min*, *<sup>m</sup>*

where:

208 Decision Support Systems

[5].

m: number of iterations

MSRAj: MSR for the jth alternative

MSRmin: the lowest possible MSR value

MSRmax: the largest possible MSR value

SIAj: stochastic rank index for the jth alternative

The more the SI value approaches 0, the better the alternative.

**Figure 6.** PROMETHEE input value determination for one iteration cycle. Source: [5].

**Figure 7.** Left: example distribution of 4 scenarios (s1,..., s4) for rank 1. Right: rank distribution for scenario 1. Source:

*MSR max*, *<sup>m</sup>* <sup>−</sup> *MSR min*, *<sup>m</sup>* (2)

The criteria preference values have been assigned by the authors after discussions with ex‐ perts from different stakeholder groups from the Zaragoza City Council and the Ebro River Authority (CHE, *Confederación Hidrográfica del Ebro*). The highest preference values (and therefore the highest weights) were given to the groundwater protection and environmen‐ tally high value areas (Table 2). Hazard criteria were considered less important as some of the encountered geological hazards (land subsidence and sinkhole development) can be mi‐ tigated or avoided by applying more suitable (but more costly) construction techniques.

The validation of a model consists in checking whether the structure of the model is suitable for the purpose and if it achieves an acceptable level of accuracy in predictions. In the case of explanatory or predictive models, validation is usually carried out by checking the degree of agreement between the data produced by the model and data from the real world [4]. In the case of our project in order to validate the model has been verified that the result follows the preferences in the assignation of the weights to the criteria.


**Table 2.** Pairwise comparison matrix, criteria weights for site searchanalysis.A) Groundwater protection, B) Doline susceptibility, C)Flooding hazard, D)Location of natural areas, E) Agricultural capability of soils, F) Slope percentage, G) Geotechnical characteristics.

Figure 8 shows the final results of the land-use suitability analysis for new industrial devel‐ opment. The lefthand side of figure 8 shows the suitability map under sustainability. The grey sections indicate the areas where industrial locationis not possible due to the con‐ straints. Although the suitability analysis sometimes presents good values, the constraints imply that these areas cannot be exploited due to any restriction.The most suitable locations for industrial development are on the pediments or glacis (Figure 1) and Tertiary materials outside environmental protected areas where the groundwater vulnerability and flood risk is lower. The least suitable locations are the floodplains with high groundwater vulnerabili‐ ty and flood risk, environmentally protected areas around the river bed and other areas in the higher terraces which present more susceptibility to doline development.

To test the robustness of the results, a sensitivity analysis of the model has been performed where higher weights were given to economic aspects. The highest weights were assigned to doline susceptibility and flooding hazard, which might cause the destruction of future in‐ dustrial sites (Table 3). Slope and geotechnical characteristics of the soils were also assigned high values as a more technically difficult terrain will increase the construction budget. Fig‐ ure 8 shows the results of this last approach where the best locations for industry were iden‐ tified to be the pediments and slopes in Tertiary sediments. The least favorable locations are on the flood plain and low river terraces, where sinkhole susceptibility shows higher values. In fact, in order to measure the correlation between both results the Pearson coefficient of correlation between both raster images has been calculated giving a value of 0.874, signifi‐ cant at a 0.01 level, implying a high agreement between both results.

Zaragoza city, outside the alluvial sector (i.e. alternatives 25, 26 and 27). In contrast, the worst locations are the alluvial areas in the surroundings of El Burgo de Ebro (i.e. alterna‐ tives 4 and 18), the industrial areas in the north of Zaragoza city (i.e. alternatives 16 and 17),

Comparison of Multicriteria Analysis Techniques for Environmental Decision Making on Industrial Location

http://dx.doi.org/10.5772/51222

211

**Preference matrix A B C D E F G Weight**

**Table 3.** Pairwise comparison matrix, criteria weights for site search analysis under economic aspects.A) Groundwater protection, B) Doline susceptibility, C)Flooding hazard, D)Location of natural areas, E) Agricultural capability of soils, F)

**Preference matrix A B C D E F G H Weight**

**Table 4.** Pairwise comparison matrix, criteria weights for site selection analysis.A) Groundwater protection, B) Doline susceptibility, C)Flooding hazard, D)Location of natural areas, E) Agricultural capability of soils, F) Slope percentage, G)

In the stochastic approach, distribution types have to be assigned to every alterna‐ tive and criterion and a MCS is performed over a MCE method (here PROME‐ THEE-2) meaning that the multicriteria analysis is performed a specified number of times (here: 5000; hence stochastic PROMETHEE-2). It should be noted that, due to local/regional variability, the local distributions of a criterion are highly likely to be different for each location alternative. Thus, although it seems reasonable, at first

**A** 1.00 2.00 3.00 1.00 5.00 8.00 6.00 0.50 0.197 **B** 0.50 1.00 2.00 0.50 3.00 7.00 4.00 0.33 0.121 **C** 0.33 0.50 1.00 0.33 2.00 6.00 3.00 0.25 0.087 **D** 1.00 2.00 3.00 1.00 5.00 8.00 6.00 0.50 0.197 **E** 0.20 0.33 0.50 0.20 1.00 4.00 2.00 0.17 0.048 **F** 0.13 0.14 0.17 0.13 0.25 1.00 0.50 0.11 0.020 **G** 0.17 0.25 0.20 0.17 0.50 2.00 1.00 0.14 0.030 **H** 2.00 3.00 4.00 2.00 6.00 9.00 7.00 1.00 0.300

**A** 1.00 0.25 0.33 2.00 5.00 0.33 0.33 0.0735 **B** 4.00 1.00 4.00 5.00 8.00 2.00 3.00 0.3492 **C** 3.00 0.25 1.00 4.00 7.00 1.00 2.00 0.1774 **D** 0.50 0.20 0.25 1.00 4.00 0.25 0.25 0.0505 **E** 0.20 0.13 0.14 0.25 1.00 0.14 0.14 0.0224 **F** 3.00 0.50 1.00 4.00 7.00 1.00 2.00 0.1892 **G** 3.00 0.33 0.50 4.00 7.00 0.50 1.00 0.1378

and the Logroño Road Corridor, upstream of Zaragoza (i.e. alternative 8).

Slope percentage, G) Geotechnical characteristics.

Geotechnical characteristics, H) Constraints.

**2.3. Stochastic PROMETHEE-2**

**Figure 8.** Result of a) site search analysis under sustainability and b) sensitivity analysis for industrial development site search analysis (objective economic development).

#### **2.2. Site selection analysis**

As a consequence of the introduction of a new criterion depicting restriction of use or con‐ straints as explained in section 2.2.2., the criteria weights used for the site search analysis are not valid implying a new calculation of them using the AHP. Table 4 shows the preference matrix and criteria weights of the site selection analysis for industrial development. The cri‐ teria preference values are the same as for the site search analysis (Table 2) under the sus‐ tainability scenario, however the constraints obtained the highest preference values and as a consequence the highest weight, in order to avoid the outranking of alternatives located par‐ tially in forbidden areas.

The preference indices and the leaving and entering flow generated after the application of PROMETHEE-2 methodology are presented in Table 5. Figure 9 shows the location of the alternatives of the site selection analysis. The best alternatives are generally located south of Zaragoza city, outside the alluvial sector (i.e. alternatives 25, 26 and 27). In contrast, the worst locations are the alluvial areas in the surroundings of El Burgo de Ebro (i.e. alterna‐ tives 4 and 18), the industrial areas in the north of Zaragoza city (i.e. alternatives 16 and 17), and the Logroño Road Corridor, upstream of Zaragoza (i.e. alternative 8).


**Table 3.** Pairwise comparison matrix, criteria weights for site search analysis under economic aspects.A) Groundwater protection, B) Doline susceptibility, C)Flooding hazard, D)Location of natural areas, E) Agricultural capability of soils, F) Slope percentage, G) Geotechnical characteristics.


**Table 4.** Pairwise comparison matrix, criteria weights for site selection analysis.A) Groundwater protection, B) Doline susceptibility, C)Flooding hazard, D)Location of natural areas, E) Agricultural capability of soils, F) Slope percentage, G) Geotechnical characteristics, H) Constraints.

#### **2.3. Stochastic PROMETHEE-2**

To test the robustness of the results, a sensitivity analysis of the model has been performed where higher weights were given to economic aspects. The highest weights were assigned to doline susceptibility and flooding hazard, which might cause the destruction of future in‐ dustrial sites (Table 3). Slope and geotechnical characteristics of the soils were also assigned high values as a more technically difficult terrain will increase the construction budget. Fig‐ ure 8 shows the results of this last approach where the best locations for industry were iden‐ tified to be the pediments and slopes in Tertiary sediments. The least favorable locations are on the flood plain and low river terraces, where sinkhole susceptibility shows higher values. In fact, in order to measure the correlation between both results the Pearson coefficient of correlation between both raster images has been calculated giving a value of 0.874, signifi‐

**Figure 8.** Result of a) site search analysis under sustainability and b) sensitivity analysis for industrial development site

As a consequence of the introduction of a new criterion depicting restriction of use or con‐ straints as explained in section 2.2.2., the criteria weights used for the site search analysis are not valid implying a new calculation of them using the AHP. Table 4 shows the preference matrix and criteria weights of the site selection analysis for industrial development. The cri‐ teria preference values are the same as for the site search analysis (Table 2) under the sus‐ tainability scenario, however the constraints obtained the highest preference values and as a consequence the highest weight, in order to avoid the outranking of alternatives located par‐

The preference indices and the leaving and entering flow generated after the application of PROMETHEE-2 methodology are presented in Table 5. Figure 9 shows the location of the alternatives of the site selection analysis. The best alternatives are generally located south of

cant at a 0.01 level, implying a high agreement between both results.

search analysis (objective economic development).

**2.2. Site selection analysis**

210 Decision Support Systems

tially in forbidden areas.

In the stochastic approach, distribution types have to be assigned to every alterna‐ tive and criterion and a MCS is performed over a MCE method (here PROME‐ THEE-2) meaning that the multicriteria analysis is performed a specified number of times (here: 5000; hence stochastic PROMETHEE-2). It should be noted that, due to local/regional variability, the local distributions of a criterion are highly likely to be different for each location alternative. Thus, although it seems reasonable, at first

sight, to determine one distribution type for one criterion, if location dependent stat‐ istical analyses indicate varying distribution types, then varying types should be as‐ signed to one criterion.

Table 6 show the distribution types assigned to every alternative and criterion for the suita‐ bility analyses. Distribution fitting tests were performed to confirm/reject a modeled distri‐ bution type. The software used was @Risk [52]. If physical properties can only have nonnegative values distribution types can (and should) be selected such that this feature is

Comparison of Multicriteria Analysis Techniques for Environmental Decision Making on Industrial Location

http://dx.doi.org/10.5772/51222

213

The more commonly used distributions for continuous variables (i.e. slope percentage) are normal and lognormal, but also logistic and exponential distributions are present in some

A binomial distribution was selected for categorical variables having two possible out‐ comes.If there are more than two categories (possible outcomes) the use of a categorical dis‐ tribution can be problematic, implying the inclusion in the decision process of categories not present in the alternative. For example, if one alternative presented values 1 and 4 in agri‐ cultural capability criterion, the distribution selected by the fitting test would have given values 2 and 3 to this alternative, which are not present in the real world. Thus, instead of assigning a distribution, the percentage of cases (p value in Table 6) in every category was calculated and used as the probability of occurrence of every category. This was also the case for some continuous variables, which presented few different values, thus complicating the distribution selection (i.e. alternative 3 in doline susceptibility criterion). In these cases, the percentage or probability of occurrence of every value was introduced in the analysis.

reflected, for example by choosing an exponential distribution.

**Figure 9.** Location of alternatives for site selection analysis.

variable (i.e. groundwater protection and/or doline susceptibility).


**Table 5.** Leaving floe, entering flow, net flow and rank for site selection analysis, stochastic rank index and final rank for stochastic approach, and mean value in SAW methodology for every alternative of location.

Table 6 show the distribution types assigned to every alternative and criterion for the suita‐ bility analyses. Distribution fitting tests were performed to confirm/reject a modeled distri‐ bution type. The software used was @Risk [52]. If physical properties can only have nonnegative values distribution types can (and should) be selected such that this feature is reflected, for example by choosing an exponential distribution.

**Figure 9.** Location of alternatives for site selection analysis.

sight, to determine one distribution type for one criterion, if location dependent stat‐ istical analyses indicate varying distribution types, then varying types should be as‐

 13.69 12.22 -1.48 14 0.41 10 3.95 13.41 8.74 -4.67 20 0.75 22 3.09 13.65 8.62 -5.03 22 0.65 19 3.26 15.76 8.50 -7.25 25 0.50 13 3.95 12.77 9.28 -3.49 16 0.70 21 3.25 7.48 12.93 5.45 8 0.27 7 4.60 6.42 17.08 10.66 4 0.06 1 5.38 13.31 6.91 -6.40 24 0.69 20 3.55 11.97 8.25 -3.72 17 0.56 14 3.75 12.30 8.11 -4.18 18 0.63 17 3.32 9.49 10.92 1.44 10 0.42 11 3.69 13.30 8.96 -4.34 19 0.63 18 3.79 8.99 11.42 2.44 9 0.56 15 3.57 8.61 15.29 6.69 7 0.19 5 4.66 10.74 9.97 -0.77 12 0.60 16 4.76 15.17 4.93 -10.25 26 0.95 27 3.61 13.40 7.00 -6.40 23 0.88 26 3.75 19.37 6.63 -12.75 27 0.86 25 2.55 11.97 8.74 -3.24 15 0.45 12 4.32 12.74 7.78 -4.96 21 0.76 24 3.9 10.83 9.58 -1.25 13 0.76 23 3.83 5.25 15.16 9.91 5 0.33 8 4.68 4.90 15.82 10.92 3 0.21 6 5.68 10.13 9.98 -0.15 11 0.39 9 5.61 5.78 17.63 11.85 1 0.11 4 4.88 6.18 17.32 11.14 2 0.10 3 4.80 7.22 17.04 9.83 6 0.07 2 5.32

**Table 5.** Leaving floe, entering flow, net flow and rank for site selection analysis, stochastic rank index and final rank

for stochastic approach, and mean value in SAW methodology for every alternative of location.

SAW Mean value

**Alt Φ- Φ+ Φ Rank PROMETHEE SI Rank stochastic**

signed to one criterion.

212 Decision Support Systems

The more commonly used distributions for continuous variables (i.e. slope percentage) are normal and lognormal, but also logistic and exponential distributions are present in some variable (i.e. groundwater protection and/or doline susceptibility).

A binomial distribution was selected for categorical variables having two possible out‐ comes.If there are more than two categories (possible outcomes) the use of a categorical dis‐ tribution can be problematic, implying the inclusion in the decision process of categories not present in the alternative. For example, if one alternative presented values 1 and 4 in agri‐ cultural capability criterion, the distribution selected by the fitting test would have given values 2 and 3 to this alternative, which are not present in the real world. Thus, instead of assigning a distribution, the percentage of cases (p value in Table 6) in every category was calculated and used as the probability of occurrence of every category. This was also the case for some continuous variables, which presented few different values, thus complicating the distribution selection (i.e. alternative 3 in doline susceptibility criterion). In these cases, the percentage or probability of occurrence of every value was introduced in the analysis.

In the case of the criterion "susceptibility to doline development", difficulties were experi‐ enced as some alternatives showed continuous values close to value 0 (see Figure 10). Since it was not possible to apply the percentage of values in these cases, a decision was made to apply an exponential distribution in order to avoid the introduction of negative values in the suitability analysis, even though the adopted solution was not absolutely satisfactory. Fi‐ nally, some alternatives presented the same value for the whole alternative (unique value in the tables). Some representative examples of the selected distribution types can be seen in Figures 10. The bars symbolize the original (empirical) values retrieved from the pixels with‐ in each location alternative; the solid line the fitted theoretical distribution model.

factor in PROMETHEE-2 and the stochastic approach it was not enough to rank this alterna‐ tive in the last positions. Besides, the first rank changes from alternative number 25 to alter‐ native number 7, in the PROMETHEE-2 and the stochastic approach, respectively. This is the consequence of assigning a unique mean value in the PROMETHEE-2 approach to the alternatives. Figure 11 saws the values of the SAW methodology for both alternatives. It can be observed how, although both alternatives present similar mean value, alternative 7 present homogeneous high values, implying more percentage of high values in its distribu‐ tion, while alternative 25 present a variety of suitability values, implying a less percentage of high suitability values. The stochastic approach overcomes this handicap by simulating val‐ ues along the whole range of values inside the distribution assigned to the alternatives.

Comparison of Multicriteria Analysis Techniques for Environmental Decision Making on Industrial Location

http://dx.doi.org/10.5772/51222

215

The industrial use suitability map developed with the SAW and AHP methods integrated in a GIS for the surroundings of Zaragoza, is a substantial aid in the land-use management of this city. Besides, an additional benefit is achieved by integrating geoscientific aspects in the

**Figure 10.** Examples of distributions assigned to alternatives.

land-use decision process, as demanded by Agenda 21.

**3. Discussion and conclusions**


**Table 6.** Distribution types for every alternative and criterion for industrial settlements suitability analysis. Al.) Alternative, A) Groundwater protection, B) Doline susceptibility, C) Flooding hazard, D) Location of natural areas, E) Agricultural capability of soils, F) Slope percentage, G) Geotechnical characteristics, H) Constraints. p) percentage, ln) lognormal, u) unique value, b) binomial, l) logistic, n) normal, e)exponential, iu) Intuniform

The results of the site selection suitability analysis based on stochastic PROMETHEE-2 can be seen in Table 5. In general, there are few differences in the SI values and total flows be‐ tween the first rankings: alternatives 7, 25, 23, 26 and 27 (Figure 9). In addition, all these al‐ ternatives are located in the areas with higher suitability values in the site search analysis (SAW mean value in Table 5). Nevertheless, alternative 24 presents a high mean value in the SAW methodology but is ranked 11 and 9 in the PROMETHEE-2 and the stochastic ap‐ proach. This is due to the fact that the major part of this polygon is located in a restricted area. In fact, the worst rankings, alternative 16, 17 and 18, are located partially inside re‐ stricted areas. However, in the case of alternative 24 the weight assigned to the constraint factor in PROMETHEE-2 and the stochastic approach it was not enough to rank this alterna‐ tive in the last positions. Besides, the first rank changes from alternative number 25 to alter‐ native number 7, in the PROMETHEE-2 and the stochastic approach, respectively. This is the consequence of assigning a unique mean value in the PROMETHEE-2 approach to the alternatives. Figure 11 saws the values of the SAW methodology for both alternatives. It can be observed how, although both alternatives present similar mean value, alternative 7 present homogeneous high values, implying more percentage of high values in its distribu‐ tion, while alternative 25 present a variety of suitability values, implying a less percentage of high suitability values. The stochastic approach overcomes this handicap by simulating val‐ ues along the whole range of values inside the distribution assigned to the alternatives.

**Figure 10.** Examples of distributions assigned to alternatives.

#### **3. Discussion and conclusions**

In the case of the criterion "susceptibility to doline development", difficulties were experi‐ enced as some alternatives showed continuous values close to value 0 (see Figure 10). Since it was not possible to apply the percentage of values in these cases, a decision was made to apply an exponential distribution in order to avoid the introduction of negative values in the suitability analysis, even though the adopted solution was not absolutely satisfactory. Fi‐ nally, some alternatives presented the same value for the whole alternative (unique value in the tables). Some representative examples of the selected distribution types can be seen in Figures 10. The bars symbolize the original (empirical) values retrieved from the pixels with‐

**Al. A B C D E F G H Al. A B C D E F G H** p ln p p p ln u b **15** p ln u u p ln p b l n p p p ln u b **16** e p u u u ln p u e p u u u n u b **17** l n u u u ln p b l n u p p ln p b **18** l ln u p p e p b l ln p u u ln u b **19** l e u u p ln p b l ln u u p ln u b **20** l ln u u u n p b u u u p iu ln p b **21** p e u u p n u b l e u u u ln u b **22** l n u u p n u b p e u u u ln u b **23** p p u u p ln p b l e u u p ln u b **24** p p u u u n u u e u u u p ln u b **25** u u u p p n u u l p u p u l u b **26** u u u p p ln p b p e u u p n u b **27** p e u p p ln p b

in each location alternative; the solid line the fitted theoretical distribution model.

**Table 6.** Distribution types for every alternative and criterion for industrial settlements suitability analysis. Al.) Alternative, A) Groundwater protection, B) Doline susceptibility, C) Flooding hazard, D) Location of natural areas, E) Agricultural capability of soils, F) Slope percentage, G) Geotechnical characteristics, H) Constraints. p) percentage, ln)

The results of the site selection suitability analysis based on stochastic PROMETHEE-2 can be seen in Table 5. In general, there are few differences in the SI values and total flows be‐ tween the first rankings: alternatives 7, 25, 23, 26 and 27 (Figure 9). In addition, all these al‐ ternatives are located in the areas with higher suitability values in the site search analysis (SAW mean value in Table 5). Nevertheless, alternative 24 presents a high mean value in the SAW methodology but is ranked 11 and 9 in the PROMETHEE-2 and the stochastic ap‐ proach. This is due to the fact that the major part of this polygon is located in a restricted area. In fact, the worst rankings, alternative 16, 17 and 18, are located partially inside re‐ stricted areas. However, in the case of alternative 24 the weight assigned to the constraint

lognormal, u) unique value, b) binomial, l) logistic, n) normal, e)exponential, iu) Intuniform

**14** p u u p p ln p b

214 Decision Support Systems

The industrial use suitability map developed with the SAW and AHP methods integrated in a GIS for the surroundings of Zaragoza, is a substantial aid in the land-use management of this city. Besides, an additional benefit is achieved by integrating geoscientific aspects in the land-use decision process, as demanded by Agenda 21.

It is important to notice the similarity of the results after applying the site search analysis and the site selection analysis. In general, the highest rank positions are present in alterna‐ tives located in areas where the site search analysis also presented the highest suitability val‐ ues. Some differences can be observed in alternatives located in areas with restrictions, as in the site selection analysis constrains are included as criteria. This is the case of alternative 24 which presented a high mean value in the SAW methodology but present a rank 11 and 9 in the PROMETHEE-2 and the stochastic approach. In this case, the weight assigned to the con‐ straint factor in PROMETHEE-2 and the stochastic approach it was not enough to rank this alternative in the last positions. Thus, a higher weight should be given to the constraint fac‐

Comparison of Multicriteria Analysis Techniques for Environmental Decision Making on Industrial Location

http://dx.doi.org/10.5772/51222

217

Performing a PROMETHEE-2 with the mean values produces a mean result, but the uncer‐ tainty in either the input values or the result cannot be quantified. The stochastic approach helps approaching this problem by using probability distributions for the input parameters, instead of single values. For spatial multicriteria analysis in a variable data environment it is our recommendation to use stochastic approaches although, in this case, the process was not

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, Ho 804/7-1+2). We also greatly acknowledge support of the Ebro River Authority (CHE), the Aragón Re‐

and A. Hoppe3

1 Department of Geography and Land Management, Faculty of Arts, University of Zarago‐

3 Institute of Applied Geosciences, Technische Universität Darmstadt, Darmstadt, Germany

absolutely integrated in the GIS, and as a consequence it is very time consuming.

, J. de la Riva1

tor in the site selection approaches.

**Acknowledgements**

**Author details**

za, Zaragoza, Spain

M.T. Lamelas1\*, O. Marinoni2

gion Authority and the Zaragoza Council.

\*Address all correspondence to: tlamelas@unizar.es

2 CSIRO Ecosystem Sciences, Brisbane, Australia

**Figure 11.** SAW values for alternatives 7 and 25.

A fundamental problem of decision theory is how to derive weights of criteria. One disad‐ vantage of the AHP method is the inherent subjectivity of assigning preference values be‐ tween criteria. The weights derived from these preference values have usually a profound effect on the results of the suitability analysis. However, in our particular case, in the indus‐ trial suitability analysis, there were no strong differences between the results of the site search analysis performed under the concept of sustainable development or the site search analysis performed under the concept of economic development, although different weights were assigned to the criteria in both approaches.

If differences are greater, a possible solution is to establish a set of suitability maps and to combine these to select the most suitable areas.

After some talks with different managers in the administration and following the approach under sustainability aspects, our results suggest that the best location for new industries is on the pediments and Tertiary sediments outside the natural protected areas, where the groundwater vulnerability and flood risk is lower, although the geotechnical characteristics of the terrain are less favorable, according to the PGOUZ. The least favorable location em‐ bodies the floodplain with high groundwater vulnerability values and the natural protected areas around the river bed, and other areas in the higher terraces which are more susceptible to doline development.

An advantage of outranking methods as PROMETHEE-2 is the fact that criteria do not need standardization or transformation processes which reduces subjectivity. However, in a spa‐ tial multicriteria analysis decisions still need to be made, as for example what characteristic value (from the population of pixels within a location alternative polygon) to use for a sub‐ sequent multicriteria analysis (e.g.maximum, minimum, mean, etc.). If using PROME‐ THEE-2 more decisions needs to be made in regards to the selection of the preference function as well as which set of criteria weights to use.

It is important to notice the similarity of the results after applying the site search analysis and the site selection analysis. In general, the highest rank positions are present in alterna‐ tives located in areas where the site search analysis also presented the highest suitability val‐ ues. Some differences can be observed in alternatives located in areas with restrictions, as in the site selection analysis constrains are included as criteria. This is the case of alternative 24 which presented a high mean value in the SAW methodology but present a rank 11 and 9 in the PROMETHEE-2 and the stochastic approach. In this case, the weight assigned to the con‐ straint factor in PROMETHEE-2 and the stochastic approach it was not enough to rank this alternative in the last positions. Thus, a higher weight should be given to the constraint fac‐ tor in the site selection approaches.

Performing a PROMETHEE-2 with the mean values produces a mean result, but the uncer‐ tainty in either the input values or the result cannot be quantified. The stochastic approach helps approaching this problem by using probability distributions for the input parameters, instead of single values. For spatial multicriteria analysis in a variable data environment it is our recommendation to use stochastic approaches although, in this case, the process was not absolutely integrated in the GIS, and as a consequence it is very time consuming.
