**1. Background and Methodology**

sophisticated decision support methodologies, e.g. in terms of multicriteria analysis techni‐ ques [3, 6], and are therefore suitable to manage sustainable development of urban areas.

Although the development of multicriteria analysis began mainly in the '70s (the first scien‐ tific meeting devoted entirely to decisionmaking was held in 1972 in South Carolina) its ori‐ gins can be dated back to the eighteenth century [4]. Reflections on French policies in the action of judges and their translation into policy (social choice), led people like Condorcet to

In the last two decades of the twentieth century there was an increased trend of integration of Multicriteria Evaluation techniques (MCE) and Geographic Information Systems (GIS), trying to solve some of the analytical shortcomings of GIS "For example see [4, 7, 15]". Wal‐ lenius et al. [16], made a study of the evolution in the use of MCE techniques from 1992 to 2006, showing that the use of multiattribute techniques has increased 4.2 times during this period. In recent years, there has also been a great effort in the integration of MCE and GIS

Since we consider land-use decision making in general as an intrinsic multicriteria decision problem, in our opinion these are valid methodologies to support the land-use decision

Land-use suitability analysis aims to identify the most appropriate spatial pattern for future land uses according to specified requirements or preferences [3, 21, 22]. GIS-based land-use suitability analyses have been applied in a wide variety of situations, including ecological and geological approaches, suitability for agricultural activities, environmental impact as‐

Different attempts to classify Multicriteria Decision Making (MCDM) methods by diverse authors exist in the literature [4, 6, 7, 11, 26, 29]. The majority of them agree that additive decision rules are the best known and most widely used Multiattribute Decision Making (MADM) methods in GIS based decision making. Some of the techniques more commonly described in literature are: Simple Additive Weighting (SAW), Ordered Weighting Averag‐ ing (OWA) technique, the Analytical Hierarchy Process (AHP), ideal point methods (e.g. TOPSIS), concordance methods or outranking techniques (e.g. PROMETHEE, Electre).

Nevertheless, the integration of these techniques continues to pose certain problems or diffi‐ culties at the time of developing specific applications. Among the most notable drawbacks

**•** The impracticality of applying pairwise comparison techniques as PROMETHEE with

**•** The difficulty on the implementation of some MCE methods, thereby leading to a difficult analysis of the results, as well as an ignorance of the internal procedure of the methods by

**•** The need to generate data processing software attached to the GIS, based on algorithms that describe MCE methods, which naturally implies that many users of these systems

long series of data due to limitations posed by existing informatics systems.

sessment, site selection for facilities, and regional planning [3, 6, 11, 17, 21,23, 28].

deepen in decision taken supported in several criteria [4].

techniques on the Internet "For example see [17, 20]".

process by means of a land-use suitability analysis.

are [4]:

198 Decision Support Systems

non-specialist users.

cannot access these methods.

#### **1.1. Study area and project background**

Zaragoza city and its surroundings are located in the Ebro corridor, a highly dynamic eco‐ nomic area within the Iberian Peninsula. The climate in this area is semi-arid with mean an‐ nual precipitation of about 350 mm and a mean annual temperature of about 15° C.This city is crossed by the cited Ebro river and two of its main tributaries, the Gállego and Huerva rivers (Figure 1). Geologically, Quaternary alluvial terraces of the Ebro river were deposited above Tertiary gypsum formations, forming a covered karst area with intense karstification processes. The Quaternary materials are an important source of sand and gravel which are needed for civil engineering purposes. In addition, it hosts important groundwater reser‐ voirs, used for domestic, industrial and agricultural purposes.

The availability of these resources has been one of the reasons of the fast development of the city in the last decades. But this fast development has also led to negative interactions with the environment and man-made infrastructure. Intense irrigation triggered land subsidence which in turn caused costly damage and/or destruction of infrastructure such as roads, buildings, gas and water supply networks [36]. Many infrastructures that have been built occupy areas where soils of high fertility had naturally developed, making these areas inac‐ cessible to agriculture. Also, many ecologically important areas have been harmed and an increased contamination of the aquifer has been observed [37].

**1.2. Methodology**

see [24, 25, 30, 33, 35, 36].

**Figure 2.** Workflow of the land-use suitability analysis.

These included (Figure 2):

It is important to differentiate between the site selection problem and the site search prob‐ lem. The aim of site selection analysis is to identify the best location for a particular activity from a given set of potential (feasible) sites. Where there is no predetermined set of candi‐

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In terms of the MCE methods applied, the main advantage of the SAW approach can be con‐ sidered its low degree of complexity as which made it attractive to be used for the site search analysis in this project. It is precisely this simplicity that makes weighted summation

The site selection analysis has been performed by the implementation of PROMETHEE-2 which belongs to the 'family' of outranking techniques. Since the mentioned techniques re‐ quire pairwise or global comparisons among alternatives, these methods become impractical for applications where the number of alternatives ranges in the tens or hundreds of thou‐ sands (Pereira and Duckstein, 1993). For a more detailed description of both methodologies

In order to perform both site search and site selection, several steps needed to be covered.

**•** Definition of alternatives (decision options): feasible location areas.

date sites, the problem is referred to as site search analysis [3].

actually quite widely applied in real-world settings [8, 40, 42].

**Figure 1.** Location and geomorphology of study area.

Based on the above, the area surrounding Zaragoza, which represents a rapidly growing ur‐ ban area, merits closer investigation in terms of geoscientific factors. Thus, a research project was initiated to develop a methodological workflow which will facilitate the sustainable de‐ velopment in the surroundings of a growing city. Our main objective was to perform a landuse suitability analysis to identify the most appropriate future land-use patterns. Therefore a variety of tasks needed to be performed such as:


Here, we report on the land-use suitability analysis to find most suitable locations for indus‐ trial facilities. As mentioned above, we compare the results obtained by the application of two distinctive multicriteria analysis techniques for environmental decision making on in‐ dustrial location. For more details on the general project workflow and geo-resources and geo-hazards modellingsee [24, 25, 30, 31, 33, 37, 39].

#### **1.2. Methodology**

**Figure 1.** Location and geomorphology of study area.

variety of tasks needed to be performed such as:

**•** Land-use suitability analysis by means of SDSS.

geo-hazards modellingsee [24, 25, 30, 31, 33, 37, 39].

and 3D techniques.

200 Decision Support Systems

information for its introduction into a GIS environment.

Based on the above, the area surrounding Zaragoza, which represents a rapidly growing ur‐ ban area, merits closer investigation in terms of geoscientific factors. Thus, a research project was initiated to develop a methodological workflow which will facilitate the sustainable de‐ velopment in the surroundings of a growing city. Our main objective was to perform a landuse suitability analysis to identify the most appropriate future land-use patterns. Therefore a

**•** Characterization of the study area and collection, analysis and processing of the available

**•** Geo-hazards and geo-resources detection, description and modelling with the help of GIS

Here, we report on the land-use suitability analysis to find most suitable locations for indus‐ trial facilities. As mentioned above, we compare the results obtained by the application of two distinctive multicriteria analysis techniques for environmental decision making on in‐ dustrial location. For more details on the general project workflow and geo-resources and

It is important to differentiate between the site selection problem and the site search prob‐ lem. The aim of site selection analysis is to identify the best location for a particular activity from a given set of potential (feasible) sites. Where there is no predetermined set of candi‐ date sites, the problem is referred to as site search analysis [3].

In terms of the MCE methods applied, the main advantage of the SAW approach can be con‐ sidered its low degree of complexity as which made it attractive to be used for the site search analysis in this project. It is precisely this simplicity that makes weighted summation actually quite widely applied in real-world settings [8, 40, 42].

The site selection analysis has been performed by the implementation of PROMETHEE-2 which belongs to the 'family' of outranking techniques. Since the mentioned techniques re‐ quire pairwise or global comparisons among alternatives, these methods become impractical for applications where the number of alternatives ranges in the tens or hundreds of thou‐ sands (Pereira and Duckstein, 1993). For a more detailed description of both methodologies see [24, 25, 30, 33, 35, 36].

**Figure 2.** Workflow of the land-use suitability analysis.

In order to perform both site search and site selection, several steps needed to be covered. These included (Figure 2):

**•** Definition of alternatives (decision options): feasible location areas.


The criteria weights were determined with the AHP. This technique represents another MCE method and involves pairwise comparison of criteria where preferences between crite‐ ria are expressed on a numerical scale usually ranging from 1 (equal importance) to 9 (strongly more important). This preference information is used to compute the weights by means of an eigenvalue computation where the normalized eigenvector of the maximum ei‐ genvalue characterizes the vector of weights. Empirical applications suggest that this pair‐ wise comparison method is one of the most effective techniques for spatial decisionmaking approaches based on GIS [15, 43]. There exist many well-documented examples of applica‐ tion of this method with success [44, 46].

**•** Urbanized areas: obtained from the topographic map scale 1:25,000 from the National Geographical Institute (IGN, *Instituto Geográfico Nacional*), imported to ArcGIS and updat‐

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**•** Infrastructures (roads, rail roads, canals) and their area of protection: also extracted from the topographic maps. The area of protection of roads and train rails was delineated as defined by the Spanish Roads Law and according to the Spanish Railway Sector Law, re‐

**•** Other restrictive planning: Zaragoza Land Management Planning (PGOUZ, *Plan General de Ordenación Urbana de Zaragoza*), mapping provided by Zaragoza Council, and natural resources planning of the thickets and oxbows of the Ebro river, provided by the Aragon

**•** Cattle tracks: tracks traditionally used by the seasonal migration of livestock which are

**•** Industrial areas where no space is left for new industries. Provided by the Aragon Insti‐ tute of Public Works (IAF,*Instituto Aragonés de Fomento*) from the Aragon Government.

A variety of social, economic and environmental factors were taken into consideration. Fig‐ ure 4 shows the mapping of all the variables that were considered relevant for industrial de‐ velopment. Areas considered less suitable are kept in red while a higher suitability is shown

protected by law, provided by the Aragon Government.

ed.

spectively.

Government.

**Figure 3.** Industrial restrictions.

in green.These variables are:

It is well known that the input data to the GIS multicriteria evaluation procedures usually present the property of inaccuracy, imprecision, and ambiguity. In spite of this knowledge, the methods typically assume that the input data are precise and accurate. Some efforts have been made to deal with this problem by combining the GIS multicriteria procedures with sensitivity analysis [47] and error propagation analysis [48]. Another approach is to use methods based upon fuzzy logic [3].

In many situations it is hard to choose the input values for multicriteria analysis procedures, since the criteria values for the different alternatives usually do not have a single realization, but can obtain a range of possible values [5]. Performing a multicriteria analysis with the mean values produces some kind of mean result, but the uncertainty in either the input val‐ ues or the result cannot be quantified. A solution to this dead-end is a stochastic approach, which utilizes probability distributions for the input parameters instead of single values. A stochastic multicriteria analysis implies that the analysis is performed multiple times with varying input values for the criteria involved. These criteria input values (or performance scores) are drawn from probability distributions that are inferred from empirical criteria populations (e.g pixels on a map, expert knowledge). Such an approach uses the whole range of possible criteria value outcomes and extreme events are according to their low out‐ come probabilities realistically represented as rare events. In a last step we explored the in‐ fluence of criteria weightsby conducting a sensitivity analysis.

#### *1.2.1. Site search analysis*

Within the site search analysis, every pixel was considered a decision alternative. Con‐ straints depict the areas where industry is and will not be allowed. These restrictions are generally characterized by the existence of other land uses (e.g. urbanareas), the protection of natural areas and land management planning. These restrictions are (Figure 3):

**•** Natura 2000 network areas: natural reserve of the oxbows in La Cartuja (map provided by the Aragon Government).


**Figure 3.** Industrial restrictions.

**•** Definition of constraints: areas with land-use restrictions.

**•** Determination of criteria weights

202 Decision Support Systems

tion of this method with success [44, 46].

methods based upon fuzzy logic [3].

*1.2.1. Site search analysis*

the Aragon Government).

fluence of criteria weightsby conducting a sensitivity analysis.

**•** Definition of important factors in the decision process: identification of criteria.

The criteria weights were determined with the AHP. This technique represents another MCE method and involves pairwise comparison of criteria where preferences between crite‐ ria are expressed on a numerical scale usually ranging from 1 (equal importance) to 9 (strongly more important). This preference information is used to compute the weights by means of an eigenvalue computation where the normalized eigenvector of the maximum ei‐ genvalue characterizes the vector of weights. Empirical applications suggest that this pair‐ wise comparison method is one of the most effective techniques for spatial decisionmaking approaches based on GIS [15, 43]. There exist many well-documented examples of applica‐

It is well known that the input data to the GIS multicriteria evaluation procedures usually present the property of inaccuracy, imprecision, and ambiguity. In spite of this knowledge, the methods typically assume that the input data are precise and accurate. Some efforts have been made to deal with this problem by combining the GIS multicriteria procedures with sensitivity analysis [47] and error propagation analysis [48]. Another approach is to use

In many situations it is hard to choose the input values for multicriteria analysis procedures, since the criteria values for the different alternatives usually do not have a single realization, but can obtain a range of possible values [5]. Performing a multicriteria analysis with the mean values produces some kind of mean result, but the uncertainty in either the input val‐ ues or the result cannot be quantified. A solution to this dead-end is a stochastic approach, which utilizes probability distributions for the input parameters instead of single values. A stochastic multicriteria analysis implies that the analysis is performed multiple times with varying input values for the criteria involved. These criteria input values (or performance scores) are drawn from probability distributions that are inferred from empirical criteria populations (e.g pixels on a map, expert knowledge). Such an approach uses the whole range of possible criteria value outcomes and extreme events are according to their low out‐ come probabilities realistically represented as rare events. In a last step we explored the in‐

Within the site search analysis, every pixel was considered a decision alternative. Con‐ straints depict the areas where industry is and will not be allowed. These restrictions are generally characterized by the existence of other land uses (e.g. urbanareas), the protection

**•** Natura 2000 network areas: natural reserve of the oxbows in La Cartuja (map provided by

of natural areas and land management planning. These restrictions are (Figure 3):

A variety of social, economic and environmental factors were taken into consideration. Fig‐ ure 4 shows the mapping of all the variables that were considered relevant for industrial de‐ velopment. Areas considered less suitable are kept in red while a higher suitability is shown in green.These variables are:

**•** Important areas from the environment point of view: natural areas included in the Natura network 2000 as SPAs (Special Protection Areas for birds), and the SACs (Special Conser‐ vation Areas), habitats, points of geological interest and other areas which mapping has been provided mainly by the Aragon Government.

Many multicriteria methods, as the SAW methodology, require criteria standardization to bring all of them to a common scale. The classification ensures that the weights properly re‐ flect the importance of a criterion.The standardization method used here may be classified as a subjective scales approach [26] since the variables are classified in subjective ranges. These ranges can be selected following standards, legal requirements, or the classes already determined in the geo-resources and geo-hazards models used as criteria in the decision process. Six categories were selected considering the adaptation of these classes to the varia‐ bles to be introduced. For more details on the standardization approach see [25, 30, 31].

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Weights for criteria are assigned with the help of the AHP. An AHP extension was specifi‐ cally developed for the ArcGIS environment at the Institute of Applied Geosciences of the Technische Universität Darmstadt [34]. This tool can be downloaded from the ESRI web page (http://arcscripts.esri.com/). For more details on the AHP performance see [25, 30, 31]. In a last step all classified raster files (criteria) are multiplied by its corresponding weight

The main objective of a site selection analysis is the ranking of feasible alternatives. General‐ ly, outranking methods, such as PROMETHEE-2, require pairwise or global comparisons among alternatives. Here location alternatives are represented by industrial areas, as de‐ fined in the Aragon Institute of Public Works (IAF) database, which signify spaces for the establishment of new industries. Geometrically, these alternatives represent a polygon each.

As alternatives are directly compared along their criteria values, the application of outrank‐ ing methods does not require a transformation or standardization of criteria values. The re‐ strictions (constraints) and criteria are the same used for the site search analysis. Alternatives located completely in restrictions areas were eliminated from the analysis. However, there exist some industrial polygons, representing one alternative, located partial‐ ly in restricted areas, as these polygons are partially occupied or crossed by a road or a cattle track. It has implied the inclusion of the constraints as an additional criterion in the decision process. The criterion representative of use restrictions was then reclassified into two differ‐ ent values; zero in the area where industry is forbidden or not possible due to the presence

It is important to define whether a higher value of a particular criterion leads to an improve‐ ment or to a decrease in land-use suitability. In the case of industrial development, an increase in the value of all criteria, with the exception of groundwater protection and geotechnical char‐ acteristics, implies a suitability decrease. For example, a higher groundwater protection value implies an increase in suitability to industrial use location while an increase in doline develop‐

Geometrically, every alternative is a polygon so that within each polygon a variety of crite‐ ria values (pixels in the criteria layers) are to be found. The question then arises which of the multiple criteria realization to use for the multicriteria analysis evaluation. Therefore, a mul‐

A total of twenty seven industrial areas were evaluated for the site selection analysis.

of other uses, and one in areas where this use is permitted or feasible.

ment susceptibility implies a decrease in industrial use location suitability.

and summed up.

*1.2.2. Site selection analyst*


**Figure 4.** Variable mapping. 1) natural protected areas, 2) doline susceptibility, 3) groundwater protection, 4) flooding hazard, 5) agricultural capability of the soils, 6) slope percentage, 7) geotechnical characteristics.

Many multicriteria methods, as the SAW methodology, require criteria standardization to bring all of them to a common scale. The classification ensures that the weights properly re‐ flect the importance of a criterion.The standardization method used here may be classified as a subjective scales approach [26] since the variables are classified in subjective ranges. These ranges can be selected following standards, legal requirements, or the classes already determined in the geo-resources and geo-hazards models used as criteria in the decision process. Six categories were selected considering the adaptation of these classes to the varia‐ bles to be introduced. For more details on the standardization approach see [25, 30, 31].

Weights for criteria are assigned with the help of the AHP. An AHP extension was specifi‐ cally developed for the ArcGIS environment at the Institute of Applied Geosciences of the Technische Universität Darmstadt [34]. This tool can be downloaded from the ESRI web page (http://arcscripts.esri.com/). For more details on the AHP performance see [25, 30, 31]. In a last step all classified raster files (criteria) are multiplied by its corresponding weight and summed up.

#### *1.2.2. Site selection analyst*

**•** Important areas from the environment point of view: natural areas included in the Natura network 2000 as SPAs (Special Protection Areas for birds), and the SACs (Special Conser‐ vation Areas), habitats, points of geological interest and other areas which mapping has

**•** Doline (sinkhole) susceptibility: model developed within the project using a quantitative

**•** Groundwater protection: a model developed also within the project, performed with Go‐

**•** Flooding hazard: a flooding hazard mapping developed along the Ebro river [50] was digitised and introduced in the land-use suitability analysis. This model shows the differ‐

**•** Agricultural capability of the soils: mapping developed within the project [39] applying

**•** Slope of the terrain: developed from the DEM (resolution 20x20 m) from the Ministry of

**•** Geotechnical characteristics of the subsoil: different geomorphological units with better or worse geotechnical characteristics, described according to the PGOUZ. This classification has been applied to the geomorphological units derived from the geological map, scale 1:50,000, from National Geological Survey (IGME, *Instituto Geológico y Minero de España*).

**Figure 4.** Variable mapping. 1) natural protected areas, 2) doline susceptibility, 3) groundwater protection, 4) flooding

hazard, 5) agricultural capability of the soils, 6) slope percentage, 7) geotechnical characteristics.

cad [37] and applying a methodology by the German Geological Survey [49].

been provided mainly by the Aragon Government.

method, a logistic regression technique [38].

ent periods of return of flood events.

the Cervatana Model [51].

204 Decision Support Systems

Agriculture (*SIG oleícola*).

The main objective of a site selection analysis is the ranking of feasible alternatives. General‐ ly, outranking methods, such as PROMETHEE-2, require pairwise or global comparisons among alternatives. Here location alternatives are represented by industrial areas, as de‐ fined in the Aragon Institute of Public Works (IAF) database, which signify spaces for the establishment of new industries. Geometrically, these alternatives represent a polygon each. A total of twenty seven industrial areas were evaluated for the site selection analysis.

As alternatives are directly compared along their criteria values, the application of outrank‐ ing methods does not require a transformation or standardization of criteria values. The re‐ strictions (constraints) and criteria are the same used for the site search analysis. Alternatives located completely in restrictions areas were eliminated from the analysis. However, there exist some industrial polygons, representing one alternative, located partial‐ ly in restricted areas, as these polygons are partially occupied or crossed by a road or a cattle track. It has implied the inclusion of the constraints as an additional criterion in the decision process. The criterion representative of use restrictions was then reclassified into two differ‐ ent values; zero in the area where industry is forbidden or not possible due to the presence of other uses, and one in areas where this use is permitted or feasible.

It is important to define whether a higher value of a particular criterion leads to an improve‐ ment or to a decrease in land-use suitability. In the case of industrial development, an increase in the value of all criteria, with the exception of groundwater protection and geotechnical char‐ acteristics, implies a suitability decrease. For example, a higher groundwater protection value implies an increase in suitability to industrial use location while an increase in doline develop‐ ment susceptibility implies a decrease in industrial use location suitability.

Geometrically, every alternative is a polygon so that within each polygon a variety of crite‐ ria values (pixels in the criteria layers) are to be found. The question then arises which of the multiple criteria realization to use for the multicriteria analysis evaluation. Therefore, a mul‐ ticriteria GIS extension was developed to draw site specific values (minimum, maximum, mean etc.) for raster cell populations that lie within the polygonal outline of a location alter‐ native. For our analysis the mean value was used for all criteria since, in our opinion, this value better symbolizes all alternative values. Minimum and maximum values are usually rare events with a low probability of occurrence.

*1.2.3. Stochastic PROMETHEE-2*

**Φ-(ax)** 1 0.5 1.5

modified after [5].

where:

Aj

Ri

MSR for every alternative.

m: number of iterations

n: number of available alternatives

: rank count for the ith rank

: jth alternative

The stochastic PROMETHEE-2 approach requires the assignment of theoretical distribution types to every criterion of the available alternatives. Distribution models were inferred based upon the criteria value populations (pixel values) within each location alternative (polygon) along all criteria. The software used to fit distribution types and to perform distri‐ bution fitting test was @Risk [52]. In a next step the distribution models were used within a

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Starting a MCS with *n* iterations for the specified distributions produces *n* realizations for every cell of the input matrix [5]. Figure 6 shows the principle of one iteration cycle.Values are randomly drawn between 0 and 1 and input values (criteria performance scores) are de‐ termined using the inferred theoretical model distribution. With *n* being 5000, the multicrite‐ ria analysis is repeated 5000 times. The results may then be used to establish a rank distribution for a specific alternative or a distribution of alternatives for a specific rank (see

**Table 1.** Example of possible preference indices, leaving, entering and net flow calculations and final ranking.Slightly

However, the alternative possessing the highestnumber of first ranks may not necessarily be the best [5]. Therefore, it was suggested calculating a dimensionless mean stochastic rank

In order to compare mean stochastic ranks of simulations with different iteration counts, the

MSR value must be standardized which leads to the stochastic rank index SI [5]:

(*Ri* \**i*)∀ *j* =1,…, *n* (1)

Monte Carlo Simulation (MCS). The number of iterations *n* was set to 5000.

Figure 7 for a four hypothetical scenarios demonstration).

*MSR Aj*, *<sup>m</sup>*<sup>=</sup> <sup>1</sup>

*<sup>n</sup>* <sup>∑</sup> *<sup>n</sup> i* =1

**Π a1 a2 a3 Φ+(ax) Φ(ax) Rank a1** - 0.25 0.75 1.0 0 2 **a2** 0.75 - 0.75 1.5 1 1 **a3** 0.25 0.25 - 0.5 -1 3

PROMETHEE-2 methodology uses preference function, which is a function of the difference between two alternatives for any criterion [32]. Six types of functions based on the notions of criteria, are proposed. For more details on preference functions see [5, 30, 32].

We exclusively used the "usual criterion" preference function that is based on the simple difference of values between alternatives as this function helps to discriminate best between available alternatives which we wanted to achieve.

The pair comparison of alternatives produces a preference matrix for each criterion (Figure 5). Having calculated the preference matrices along each criterion, a first aggregation is per‐ formed by multiplying each preference value by a weighting factor w (expressing the weight or importance of a criterion), and building the sum of these products [5]. This results in a preference index, Π (see Figure 5). The AHP has also been integrated in this tool and used for criteria weighting.

**Figure 5.** Schematic calculation of the preference index Π. Source [5].

The final ranking of alternatives is performed by calculating the net flow Φ (a1) for every alternative, a, which is a subtraction between the leaving flow and the entering flow. The higher the net flow is, the higher is the preference of an alternative over the others (Table 1).The leaving flow Φ+ (a1) represents a measure of the outranking character of a1 (how a1 is outranking all the other alternatives). Symmetrically, the entering flow Φ- (a1) is giving the outranked character of a1 (how a1 is dominated by all the other actions).

#### *1.2.3. Stochastic PROMETHEE-2*

ticriteria GIS extension was developed to draw site specific values (minimum, maximum, mean etc.) for raster cell populations that lie within the polygonal outline of a location alter‐ native. For our analysis the mean value was used for all criteria since, in our opinion, this value better symbolizes all alternative values. Minimum and maximum values are usually

PROMETHEE-2 methodology uses preference function, which is a function of the difference between two alternatives for any criterion [32]. Six types of functions based on the notions of

We exclusively used the "usual criterion" preference function that is based on the simple difference of values between alternatives as this function helps to discriminate best between

The pair comparison of alternatives produces a preference matrix for each criterion (Figure 5). Having calculated the preference matrices along each criterion, a first aggregation is per‐ formed by multiplying each preference value by a weighting factor w (expressing the weight or importance of a criterion), and building the sum of these products [5]. This results in a preference index, Π (see Figure 5). The AHP has also been integrated in this tool and

The final ranking of alternatives is performed by calculating the net flow Φ (a1) for every alternative, a, which is a subtraction between the leaving flow and the entering flow. The higher the net flow is, the higher is the preference of an alternative over the others (Table 1).The leaving flow Φ+ (a1) represents a measure of the outranking character of a1 (how a1 is outranking all the other alternatives). Symmetrically, the entering flow Φ- (a1) is giving the

outranked character of a1 (how a1 is dominated by all the other actions).

criteria, are proposed. For more details on preference functions see [5, 30, 32].

rare events with a low probability of occurrence.

available alternatives which we wanted to achieve.

**Figure 5.** Schematic calculation of the preference index Π. Source [5].

used for criteria weighting.

206 Decision Support Systems

The stochastic PROMETHEE-2 approach requires the assignment of theoretical distribution types to every criterion of the available alternatives. Distribution models were inferred based upon the criteria value populations (pixel values) within each location alternative (polygon) along all criteria. The software used to fit distribution types and to perform distri‐ bution fitting test was @Risk [52]. In a next step the distribution models were used within a Monte Carlo Simulation (MCS). The number of iterations *n* was set to 5000.

Starting a MCS with *n* iterations for the specified distributions produces *n* realizations for every cell of the input matrix [5]. Figure 6 shows the principle of one iteration cycle.Values are randomly drawn between 0 and 1 and input values (criteria performance scores) are de‐ termined using the inferred theoretical model distribution. With *n* being 5000, the multicrite‐ ria analysis is repeated 5000 times. The results may then be used to establish a rank distribution for a specific alternative or a distribution of alternatives for a specific rank (see Figure 7 for a four hypothetical scenarios demonstration).


**Table 1.** Example of possible preference indices, leaving, entering and net flow calculations and final ranking.Slightly modified after [5].

However, the alternative possessing the highestnumber of first ranks may not necessarily be the best [5]. Therefore, it was suggested calculating a dimensionless mean stochastic rank MSR for every alternative.

$$\text{MSR } A \mathbf{j}\_i \text{ } m = \frac{1}{n} \sum\_{\mathbf{i}=1}^{n} \text{(Ri } ^\ast \text{i)} \forall \text{ } j = 1 \text{ } \dots \text{ } m \tag{1}$$

where:

m: number of iterations

Aj : jth alternative

n: number of available alternatives

Ri : rank count for the ith rank

In order to compare mean stochastic ranks of simulations with different iteration counts, the MSR value must be standardized which leads to the stochastic rank index SI [5]:

$$\begin{array}{l}\text{SI} \quad A\text{j.} \quad m = \frac{\text{MSR} \quad A\text{j.} \quad m - \text{MSR} \text{ min.} \; m}{\text{MSR} \; \text{max.} \; , \; m - \text{MSR} \; \text{min.} \; m} \end{array} \tag{2}$$

**2. Results and validation**

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.

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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

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

**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)

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.

**A** 1.00 2.00 3.00 1.00 5.00 8.00 6.00 0.2288 **B** 0.50 1.00 2.00 0.50 3.00 7.00 4.00 0.1736 **C** 0.33 0.50 1.00 0.33 2.00 6.00 3.00 0.1131 **D** 1.00 2.00 3.00 1.00 5.00 8.00 6.00 0.2288 **E** 0.20 0.33 0.50 0.20 1.00 4.00 2.00 0.0678 **F** 0.13 0.14 0.17 0.13 0.25 1.00 0.50 0.0251 **G** 0.17 0.25 0.33 0.17 0.50 2.00 1.00 0.0427

the preferences in the assignation of the weights to the criteria.

**2.1. Site search analysis**

Geotechnical characteristics.

where:

m: number of iterations

SIAj: stochastic rank index for the jth alternative

MSRAj: MSR for the jth alternative

MSRmin: the lowest possible MSR value

MSRmax: the largest possible MSR value

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: [5].
