COMPARISON OF MULTI-CRITERIA EVALUATION METHODS INTEGRATED IN GEOGRAPHICAL INFORMATION SYSTEMS TO ALLOCATE URBAN AREAS

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).
REFERENCES
ALEGRE, P. (1983): Una aplicacio del programa MAP a Catalunya Barcelona,
Departamento de Geografía, Universidad Autónoma, 156 pags.
Bosque, J. Et Alia. (1991) Factores en la Dinámica de Ocupación del Suelo, in
Proceedings III Conferencia Latinoaméricana sobre Sistemas de Información
Geográfica, oct. 1991, Viña del Mar.
CAN, A. (1993). "Residential quality assessment. Alternative approaches using GIS". en
M.M. Fischer y P. Nijkamp (Eds.): Geographic Information Systems, Spatial Modelling
and Policy Evaluation. Berlin, Springer-Verlag, pp. 199-212
Carver, S. (1991) Integrating Multi-Criteria Evaluation with Geographical Information
Systems, International Journal of Geographical Information Systems, vol. 5, n. 3, 321339.
CEOTMA (1991) Guía para la Elaboración de Estudios del Medio Físico: Contenido y
Metodología, Centro de Estudios de Ordenación del Territorio y Medio Ambiente, 3º
Ed., Ministerio de Obras Públicas y Urbanismo, 1º Ed. 1981, Madrid.
Chuvieco, E. (1993) "Integration of Linear Programming and GIS for Land-Use
Modelling", International Journal of Geographical Information Systems, vol. 7, n. 1, 7183.
1
EASTMAN, J.R. y otros (1993): GIS and Decision Making. Explorations in Geographic
Information Systems Technology. Vol. 4 Ginebra, UNITAR European Office, 112 p. (3
discos)
EASTMAN, J.R. (1993):IDRISI. Version 4.1. Update manual Worcester, Ma., Clark
University, 209 p.
EASTMAN, J.R., JIN, W., KYEN, P.A.K. y TOLEDANO, J. (1995): "Raster
Procedures for Multi-Criteria/Multi-Objective Decisions". Photogrammetric
Engineering & Remote Sensing, vol. 61, nº 5, pp. 539-547
EGEOGRAN (1988): "Bases Físicas para una Ordenación Territorial de la Vertiente Sur
de Sierra Nevada (Alpujarra, Granada)", Cuadernos Geográficos de la Universidad de
Granada, n. 11.
Fischer, M. Y Nijkamp, P. (1993) "Desing and Use of Geographic Information Systems
and Spatial Models", in M. Fischer y P. Nijkamp Eds. Geographic Information Systems,
Spatial Modelling, and Policy Evaluation, Springer-Verlag. Berlín.
Gray de Cedrán, N. (1991) Capacidad Portante del Medio Urbano, in Proceedings III
Conferencia Latinoamericana sobre Sistemas de Información Geográfica, oct. 1991,
Viña del Mar.
Guevara, J. M. (1.983) Geografía de las Regiones Capital y Central, Ariel Seix-Barral
Venezolana, Caracas.
HOPKINS, L.D. (1977): "Methods for Generating Land Suitability Maps: A
Comparative Evaluation" Journal of American Institute of Planners, vol. 43, nº 4, pp.
386-400
JANSSEN, R. y RIETVELD, P. (1990): "Multicriteria analysis and Geographical
Information Systems: an application to agricultural land use in the Netherlands" en H.J.
Scholten y J.C.H. Stillwell (eds.): Geographical Information Systems for Urban and
Regional Planning, Kluwer Academic Pub. p. 129-139
JOERIN, F. y MUSY, A. (1995): "Localisation d'un site par l'utilisation combinee de
SIG et de methodes multicriteres" en 41e Journées du Groupe de travail européen "Aide
multicritere à la décision". Lausanne, Ecole Polytechnique federale.
Lasanta, M. Et Alia. (1989) Evolución Superficial del Espacio Cultivado en Cameros
Viejo (Sistema Ibérico) y su Relación con Algunos Factores Geoecológicos. Estudios
Geográficos, n. 197.
Mc Harg I. L. (1969) Design with Nature. The Natural History Press, New York.
1
Openshaw, S. (1991) A Spatial Analysis Research Agenda. in I. Maser y M.
Blackemore Eds. Handling Geographical Information, Methodology and Potential
Applications, Longman, N.Y.
PEREIRA, J.M.C. y DUCKSTEIN, L. (1993): "A multiple criteria decision-making
approach to GIS-based land suitability evaluation". Int. J. Geographical Information
Systems, vol. 7, nº 5, pp. 407-424.
RAMOS FERNÁNDEZ, A. (Ed.) (1979): Planificación física y Ecología. Modelos y
métodos. Madrid, EMESA.
Ruiz Pérez, M. Et Alia. (1990) Diseño de un Sistema de Información Geográfica Raster
para la Planificación Territorial, in Actas del IV Coloquio de Geografía Cuantitativa,
Asociación de Geógrafos Españoles, Palma de Mallorca.
Turkstra, J. (1991) An Application of GIS to Townplanning case Study, Manizales,
Colombia, in Proceedings EGIS91, Second European Conference on Geographical
Information Systems, vol. 2, Bruselas.
Voogd, H. (1983) Multicriteria Evaluation for Urban and Regional Planning, Pion,
Londres.
1