COMPARISON OF MULTI-CRITERIA EVALUATION METHODS INTEGRATED IN GEOGRAPHICAL INFORMATION SYSTEMS TO ALLOCATE URBAN AREAS by José Ignacio Barredo and Joaquín Bosque-Sendra1 ABSTRACT This work compares two Multi-Criteria Evaluation (MCE) methods: weighted linear sum and precedence methods (ranking), to allocate urban areas using Geographical Information Systems (GIS). The models are applied through PC-Arc/Info software to a data base Environmental Information System of Valencia's Lake Basin (SIACLAV), kindly supplied by the Ministry of Environment and Natural Resources and the Engineering Institute of Venezuela. The purpose is to test whether using ordinal data, the results from the weighted linear sum procedure are very different from those obtained with the ranking procedure. A high spatial correspondence between optimum areas selected with both procedures is found. KEY WORDS Multi-Criteria Evaluation, GIS, Cartographic modelling, decision making, urban and regional planning, land allocation. 1. INTRODUCTION Geographical Information Systems (GIS) are important tools in territorial planning, especially when applied for generating land suitability maps. Multi-criteria evaluation (MCE) methods are used, among other techniques, to accomplish this objective. This paper discuss and compares merits and disadvantages of two techniques: weighted linear sum (WLS) and precedence methods (ranking). The weighted linear sum method has been used by several authors (Alegre, 1983; Chuvieco y Salas, 1992; Eastman and Gold, 1995; Ramos, 1979, p.??). These papers incorrectly apply the method because the location factors are measured in an ordinal or qualitative scale, which is not formally correct (Hopkins, 1977, p. 389). Voogd (1983, p. 121) recognizes this circumstance, "linear weighted sum is also often used in cases in which only ordinal information is available". For an ordinal scale, a procedure such as the precedence method should be used in order to keep the ordinal character of the data. Since the weighted linear sum method is a more convenient method, easier to be used, it is interesting to test whether the results are comparable to those obtained with the precedence method for allocating urban areas. The models are applied through PC-Arc/Info software to a 1:100.000 scale data base SIACLAV (Environmental Information System of Valencia's Lake Basin, Veenezuela). The paper is divided into five parts. It starts with an analysis of the possible relationships between GIS and MCE. Then, the urban area under study is described, followed by explanation of the two methods and analysis of the results obtained. Finally, the conclusions of the obtained models and their application close the discussion. 2. GIS AND MCE GIS are powerful tools when applied to earth sciences and land use study. GIS procedures involve managing, editing, and analyzing huge volumes of spatial data and their related thematic atributes. However, available GIS software lack in relation to spatial analysis and cartographic modelling, because they just offer deterministic analysis and overlay of maps (Openshaw, 1991; Fischer and Nijkamp, 1993). To overcome these deficiencies, GIS packages such as IDRISI and SPANS currently include MCE modules. We propose to use MCE techniques to improve managing of thematic data. MCE is a set of procedures designed to facilitate decision making. The basic purpose is "to investigate a number of choice possibilities in the light of multiple criteria and conflicting objectives" (Voogd, 1983: 21). Integration of GIS and MCE could provide a powerful tool for studying allocation of activities and spatial modelling. It allows assessing a region on the basis of multiple objectives and criteria, and supports as well decision-making in urban and regional planning (Carver, 1991; Chuvieco, 1993). In the last years, several procedures of MCE are included in GIS for urban and regional planning: a) for allocation of agricultural land use (Janssen and Rietveld, 1990), b) residential quality assessment (Can, 1993) and c) land suitability (Joerin and Musy, 1995; Pereira and Duckstein, 1993). Jankowski (1995) reviewed several MCE procedures and the possibility of integrating them in a GIS. Likewise, some GIS packages such as IDRISI (Eastman, 1993, p. ; Eastman et al., 1993; Eastman et al., 1995) included MCE procedures. This software contains a module for the WLS method to resolve multi-criteria problems with single objective, and other module to resolve multi-objective problems based on principles of the ideal point approximation. However, this package does not allow to work problems in which the factors are in ordinal scale. 3. STUDIED AREA: THE BASIN OF VALENCIA'S LAKE (VENEZUELA) The basin of Valencia's Lake is in the mountainous range of Caribe, between the states of Aragua and Carabobo, in the Central Region of Venezuela. The basin has a surface of around 3000 km2, and from North to South presents three physiographical areas: coastal mountain, plains of Valencia's Lake and inner mountain. The basin is a space characterized by intensive agrarian activities and a high agrarian dedication, with 80.000 ha. of a high agrarian potentiality. Besides this area is characterized by a very accelerate urbanization process and industrialization, that shows a rising trend nowadays. Urban development results in an intensive agriculture, in conflicting agrarian, residential and industrial land uses, and in the population's excessive concentration (Guevara, 1983). Present urban development implies urban growth, remarkable in areas near to residential and industrial urban spaces, together with loss of agrarian land, which involved a decreasing process of the agrarian surface in the basin. 1 Therefore, nowadays, the basin is a space with two different activities, that compete for the available land: urban and agrarian uses. This competition maker important the study of optimal location for new urban areas. 4. MULTI-CRITERIA PROCEDURES USED FOR URBAN GROWTH SITES We have employed two different MCE techniques to study the same area: the WLS method and the precedence method. The map overlay procedure (see figure 1) is the same in both techniques, the only difference being the treatment of the thematic information related to initial input covers. For the development of capability models for urban growth sites, we first establish a set of factors that influence the capability of urban growth. From this factors, we analyze the possibilities and constrains for urban growth in the studied area. The following factors are considered: - Geotecnical stability (Morphodinamic) - Priority land use (Land use) - Slope gradients (Slope) - Land carrying capacity (Lithology) - Proximity to urban areas (Distance to urban areas) - Ecologically sensitive areas (Natural land cover) On the other hand, the constrains are: - National parks (National Parks cover) The factor's categories were assessed using an ordinal scale that measures the capability for urban growth from a nominal scale (Tables I - VI). In the WLS method the values range from zero to 5, for minimal and maximum urban growth capability; a value of -100 was assigned for non-urbanizing areas. In the precedence method the values range from 6 to 1, for minimal and maximum urban growth capability, and a value of -1 was given to non-urbanized areas (Tables I - VI). It should be noted that the scales are reversed due to the requirements of the methods. For example, the value 4 in the precedence method corresponds to the value 2 in the WLS. 4.1 PRECEDENCE METHOD The precedence method (CEOTMA, 1994, p. 515-518) was established to evaluate a set of alternatives measured in ordinal values. This method assigns ordinal values to evaluate each factor's category, and the land is structured according to an evaluation matrix: T= P1 P2 . . . Ps = n11 ....... n1m n21 ....... n2m . . . . . . ns1 ....... nsm = (nij) 1 Where: i= 1, 2, ..., s; s= Number of alternatives j= 1, 2, ..., m; m= Number of factors nij ∈ (1, 2, ....,nj) represents the ordinal values assigned to each factor's category. In our case nj = 6 (6 is the worst value). The ordering relation is established as follows: Given two polygons (P1 and P2): P1= (n1, n2,..., nm) P2= (n'1, n'2,...n'm) P1 precedes or is superior to P2 (P1 > P2), if : ni ≤ n'i, ∀i And otherwise, P2 is superior to P1, if: n'i ≤ ni, ∀i However, if neither condition is accomplished, P1 and P2 remain disordered. To order all the alternatives (in our case 7.908 polygons), it is necessary to apply another step (iteration) to obtain two new values (N1 and N2) for each alternative. These values are calculated from the initial values assigned to each factor: First, we assume that the number of better alternatives than P1 is: N1 = n1 x n2 x...nj...x nm = Πnj Secondly, the number of alternatives less favorable than P1 is: N2 = (n + 1 - n1)(n + 1 - n2)...(n + 1 - nj) = Π (n + 1 - nj) where n is the number of ordinal classes assigned. In our case, n = 6 The relation of precedence assumes the following expression: An alternative P1 = (N1, N2) is better than/or precede P2 = (N'1, N'2) if: N1 < N'1 N2 ≥ N'2 Oppositely, if: N1 > N'1 N2 > N'2 or N1 < N'1 N2 < N'2 then, P1 and P2 are not ordered in the relation. To completely sort the alternatives, a third iteration counts the number of alternatives that precede to each one and the number of alternatives that follow to each 1 one, based on the previous relation of precedence. We obtain two new values that correspond to the number of alternatives better than P1 (N3) and less favorable than P1 (N4). 4.2 WEIGHTED LINEAR SUM For this procedure, we assign a value for each factor categories and a weight to each factor. Thus, a weighted value of a place's capability is obtained for urban areas growth: r i = ∑ w j xij [1] Where: ri is the capability value of a place i in the territory; wj is the weight of the factor j xij is the ordinal value capability of factor j in the place i To calculate factor weights (wj) of the area under study, the Analytical Hierarchy Process is used (Saaty, 1977). This procedure is based on the pairwise comparison matrix showed in table VII. This table compares the relative importance among factors that influence the capability for urban growth. Comparison is stablished in a continuous scale of preferences ranging from 1/9 (least influence) to 9 (largest influence) (1/9 1/7 1/3 1 2 4 7 9). For example, the lithology is 1/2 less important than the slope, whereas the morphodynamic and slope are of the same importance (1). The numbers in Table VII show importance off each factor. This is based on the knowledge of the evolution of the urban areas in the basin under study the last decades. From this matrix (table VII), one obtains a set of weights Wj to be used in the WLS method (Table VII). TABLE VII Analytical Hierarchy Process for obtain factors weights Factors Slope Morphod Land use Litholog Natural Distance to urban . y land cover Slope 1 1 2 2 OJOOO OOO Morphod 1 1 . Land use 1/2 1/2 1 Litholog 1/2 1/2 1/2 1 y Nat. L. 1/2 1/2 1/2 1 1 C. Distance 1/4 1/4 1/3 1/2 1/2 1 wj 0.27 0.27 0.18 0.12 0.12 0.06 1 In equation 1, the values for each category (xij) represent the ordinal preference for each class (Tables I to VI). As stated, before the inconvenient of the ordinal scale assumed for xij in the WLS method are well known. However, the use of ordinal values for xij allows to compare the result of two methods (WLS and precedence method). Equation 2 is generated from equation 1 and the weights (Wj) given in Table VII: U = 0.27 S + 0.27 M + 0.18 L.U. + 0.12 L + 0.12 N.L.C. + 0.06 D where: U is the capability for urban areas growth S is the Slope M is the Morpho-dynamics L.U. is the Land use L is the Lithology N.L.C. is the Natural land cover D is the Distance to existing urban areas 5. RESULTS FROM THE TWO METHODS Application of the procedures provides two covers in PC-ARC/INFO with urban capability values for each alternative (polygons). A priori, we stablish six capability groups for each model in order to, later on, compare them. The initial cover overlay yields a large number of polygons (7908). However, both procedures provided only 1172 polygons appropriate for urbanizing which did not show any constraints (values -100 or -1 in Tables I-VI). a) Results from precedence method In the precedence method, three iterations were necessary to obtain the values for N3 and N4, providing the final order of cover polygons. From the calculated N3 and N4 values we obtained a total of 105 classes of capability. The 1172 cases were distributed among the 105 classes, where N3 is the number of classes before (precede) a certain class i and N4 is the number of classes after (preceded) class i. The initial and final values for the 105 classes were: class 1 (N3 = 0, N4 = 104); 2 (1, 103); 3 (2, 101); 4 (3, 100); ... ; 104 (100, 1) and 105 (104, 0). Once N3 and N4 values were established, we focused on ordering (high capacity - low capacity) the 105 classes, in which the 1172 polygons are distributed. The method produced good results to select the optimum areas (the best class) (see figure 5). However, it was not possible to order the 105 classes because of the ambiguous position of some classes relative to the other. The six capability groups previously stablished were obtained carrying out a multi-variate classification procedure (a cluster analysis) with the K-means algorithm. Then, a discriminate analysis validated the result; we obtained a value of 0.0169 for 1 Wilk's Lambda, which showed that the variables used (N3 and N4) in group forming may be considered efficient in group differentiation. Finally, we assigned the code of group to the model's cover polygons, and obtained figure 3. b) Results from the WLS method The capability for urban growth, as calculated from the WLS method ranges between 0.81 to 4.50. Later on, we grouped data per percentiles, in a percentage rank of 16.67 % (percentiles, 100/6 = 16.67 %). Then, we took a hypothesis test to validate the groups obtained. The null hypothesis (H0) means that every pair of groups is not significantly different, while research hypothesis (H1) means the opposite, that is each pair of groups is significantly different. The level of significance is 0.01, the confidence level is 99 %, with infinite degrees in the Gauss distribution. According to Gauss table, the critical area is: (Zc) = |2.33|. Since Zc was exceeded by each pair of groups, the search hypothesis (H1) is then verified for every pair of groups. We can assume, at a confidence level of 99 %, that there is a significant difference in each pair of groups. We can say that the groups are homogeneous inherently and significantly different among them. We obtain seven groups of capability for urban growth: the six groups calculated above plus a seventh group for nonurbanizing areas (Figure 2). From the initial cover overlay, we obtained another cover with the optimum urban capability areas, that is, the polygons with the highest value (ri = 4.50) in the method's application (Figure 4). c) Comparison of results The maps (Figures 2 and 3) allow comparison between the two methods, showing an important surface of non-urbanizing areas, which are common in both maps. Non-urbanizing areas occupy the largest zone (59.73 %) while the urbanizing areas cover just 16.80 % of the basin. The previously urbanized areas and lakes occupy 11.6% and 11.8% respectively. The cross tabulation matrix (table VIII) was prepared from figures 2 y 3. Both methods show good agreement, as tested with the Ji2 value (Ji2 = for freedom degrees at level of significance, a value higher than that read in the Ji2 table). Regarding the capability for urban growth, the main diagonal of table VIII indicates very good agreement between both methods for the groups classified as unapropiate for urban growth (VERY LOW and EXTREMELY LOW CAPABILITY, table VIII) and good agreement for the groups classified as very appropriate (EXCELLENT and HIGH CAPABILITY, table VIII). The fact that the accord is not good for intermediate groups (AVERAGE and LOW CAPABILITY, table VIII) is not very important because these places are not of much interest for territorial planning. The main difference between the two methods is that the WLS procedure assigns lower capability values than the precedence method does. This is partially due to the use of weighted factors (wj) in the WLS method which cannot be employed in the precedence method. 1 In any case a place classified as EXCELLENT or HIGH CAPABILITY with the WLS procedure is considered as VERY LOW or EXTREMELY LOW capability in the other method. Furthermore, the two maps (figures 4 and 5) representing areas with maximum urban capability value, obtained from both methods, show a quasi-perfect correlation. The polygons appearing in the WLS map coincide with those resulting from the precedence proocedure (ri = 4.50 in the WLS method and N3 = 0, N4 = 104 in the precedence method). From the above discussion, it can be concluded that the WLS and precedence methods produce comparable results. Table VIII. Cross tabulation of the models' covers (values in % of total column. PRECEDENCE MODEL). (Note: urbanizing areas groups were taken into consideration only). Precedence Model Total 6 4 5 2 3 Groups 1 EXCE HIGH AVER LOW VERY EXTR % en LOW EMEL WLS AGE LLEN method Y T LOW CAPA BILIT Weighted Y Linear Sum Model 51.7 0 0 0 0 0 25.2 1 EXCELL ENT 55.0 0 0 0 0 36.5 HIGH 45.7 0 0 0 0 7.0 aVERA 2.5 22.2 GE 33.2 0.7 0 9.2 LOW 0.1 22.4 19.1 83.0 2.4 15.1 VERY 0 0.5 80.5 65.6 LOW 97.6 7.0 0 0 0.3 1.2 16.3 6 EXTRE MELY LOW TOTAL 100.00 100.00 100.00 100.00 100.00 100.00 100.00 % total 48.4 25.8 5.7 6.5 7.1 5.85 100.00 6. CONCLUSIONS 1 - The integration of MCE and GIS techniques provides a powerful tool for decision-making procedures in regional planning since it allows a coherent and efficient use of thematic spatial data. - The WLS method can be employed with factors measured in an ordinal scale, providing similar results to those obtained from the PRECEDENCE method. - An aspect to point out from both methods, is the high correspondence between the selected optimum areas which is relevant when the models are used to select only the best areas according to their urban capability. - The model's easy implementation is an important question in cartographic models making. In this sense, the weighted linear sum procedure is the best, since the current software makes its implementation much more versatile, fast and operative. FOOTNOTES 1 Department of Geography, Universidad de Alcalá de Henares (Spain). Supported partially by Comisión Interministerial de Ciencia y Tecnología (Project no. AMB 941017). 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