G.I.S. and Fuzzy Sets for the Land Suitability Analysis

A. Laganà et al. (Eds.): ICCSA 2004, LNCS 3044, pp. 1036–1045, 2004.© Springer-Verlag Berlin Heidelberg 2004

G.I.S. and Fuzzy Sets for the Land Suitability Analysis

Beniamino Murgante and Giuseppe Las Casas

University of Basilicata, Via S.Caterina, 85100 Potenza, [email protected]

Abstract. This paper reports about uncertainty in defining boundaries, whichassume an institutional significance when transposed in planning prescription.Every discipline involved in environmental planning uses different approachesto represent its own vision of reality. Geological sciences or hydraulics evaluaterisks by consistent mathematical models which are relevantly different to nonlinear models emploied in the field of ecology, and at the same timeinformation about significance and value of cultural heritage in a givenenvironment does not easily correspond to a value attribution. These questionsrepresent an interesting field of research, related with the different character ofinformation deriving from different disciplinary approaches, and with the moreappropriate way of combining the same information. Different ways ofmanaging values correspond to different ways of giving information. The resultis a set of discrete representations of the physical space which correspond to aset of different values referring to areas which are considered homogeneousaccording to each disciplinary point of view, but very difficult to combine tocreate landscape units according to the whole of disciplines. The present paperillustrates a reflection on a G.I.S. application in a land suitability study on asub-regional area of Southern Italy. Emerging questions are related to the needto combine contributions of all environmental information which arerepresented at different scales, with different interpretative models, withdifferent precision of identification of landscape unit, etc.

1 Introduction

Urbanisation and the diffusion of haphazard settlements belong to the most importantfeatures of the spatial development in many industrialized countries. Current land useinstruments are not enough to steer the environmental protection for several reasons:scattering of the extra urban settlement system, ongoing soil sealing by construction,considerable abandonment of potentially agricultural soils, increase in hydro-geologichazard, pauperization of environmental and landscape valuable components are oftenconceived as a decrease of life quality in rural areas.In urban planning, the attempt to change this tendency needs to consider many aspectsas demographic dynamics, economic factors, environmental issues, protection ofsoils, morphological features, agronomic evaluations.

During the last three decades, after the fundamental contribution by Mcharg [1],several authors in the world developed evaluation procedures of land capability orsuitability, based on overlay mapping techniques. One of the aims was the integration

G.I.S. and Fuzzy Sets for the Land Suitability Analysis 1037

of all the aspects mentioned above. In fact, the evaluation of land use attitudes is amultidisciplinary question and can be supported by a multicriterial approach.A good example of intersection between fuzzy aspects of multidisciplinaryapproaches in geographical classification and multicriterial evaluation is representedby the identification of boundaries of areas suitable for the realisation of settlements.In that case the amount of features to be considered in defining urbanised areas (e.g.by the definition of a combinatory rule of criteria such as density of settlements, landeconomic value, degree of urbanisation, degree of naturality and so on) has somecharacteristics of a fuzzy multicriterial evaluation problem [2]; on the other hand, theintrinsic fuzzy characteristics of geographical elements to be identified (e.g. by theidentification of thresholds of settlement density, land economic value, degree ofurbanisation, degree of naturality and so on) link to the concept of fuzzy boundary ofa region.

This paper reports about G.I.S. application in the experience of a rural planningcarried out in Italy. The plan proposes a reorganization project for both insediativeand infrastructural systems, to thicken the existing settlements with disadvantage fordevelopment of new residential areas in open territory; it favours actions of buildingcompletion and new transformation, inside the centres, or of intensifying the centresthemselves.To achieve this purpose a mechanism of transfer of development rights has beenadopted in transformation areas from zones in which promoting the export ofvolumetric rights was suitable to guarantee the safeguard of environmental,naturalistic and agricultural characteristics, in agreement with the Administration.This paper aims to compare the classical approach to land suitability through G.I.S.with an approach based on G.I.S. and fuzzy evaluation.

2 G.I.S. and Classification by Sharp Boundaries

In Italy recent developments in regional planning systems give great emphasis to theproduction of maps, which represent both actual and more suitable attitudes in landuse, as a support for developing local planning instruments. This operation can becarried on only by the support of G.I.S. application, and evaluation routines. In thepresent case of study the classical approach to land suitability was adopted, usingsharp boundaries and definite thresholds. According to this method the followinginclusive rules were developed:

1. better accessible areas: after the classification of road network relative to itsfunctional role, 100 m buffers starting from the upper level road networkwere created. In this way areas with a better accessibility, defined areas closeto the road network, were identified;

2. small rural settlements:• 137 small rural settlements were defined through a simple

geometric rule (at least 20 buildings and a distance among them notless than 25 m);

1038 B. Murgante and G. Las Casas

• a proximity area for each rural settlement was defined by means ofthe representation of a 250 m buffer around each of them, accordingto administrative directives;

• areas close to the road network were intersected with the ruralsettlement buffers to determine areas close to both road network andsmall rural settlements;

• the remaining part of centre buffers, outside the small ruralsettlement perimeter and not comprised in road network buffers,were defined as areas close to small rural settlements.

Fig. 1. Flow chart of land suitability procedure

These rules determine the first level of suitability, and are schematized in figure 1.The degree of suitability characterizes a first level of attitude to the urbanisation. Thelast level of suitability for settlements was determined by means of a methodologysimilar to the one used by Mcharg [1] having the remarkable advantage of using theG.I.S. (figures 1, 2, show more clearly this methodology). In all rural territories thefour classes described above were taken in account, by subtracting all factorsconsidered poorly compatible with settlement aims. Forests, areas close to rivers andhigher than 1200 m a.s.l., archaeological sites, landslides, hydro-geological


constraints and high slopes were not considered as suitable areas. The reduction canbe seen clearly in geographic components (see figure 2): a part of the previous fourclasses has been eliminated in all the steps among the levels of suitability. Whenlooking at the buffer of small rural settlements (figure 2, lower right corner) this kindof reduction appears obvious.

Fig. 2. Layout of the four-steps of the progressive selection process

3 The Fuzzy Classification

The planning context creates further constraints in representing spatial informations.The difficulty of identifying certain boundaries in spatial analysis is not considered inthe institutional planning system, especially in the field of land use planning, wherephysical limits of spatial categories correspond unequivocally to the limits of spatialprescriptions. The geographical classification and the estimate of land use attitudesshow operational and evaluative issues which are interesting. The geographicalclassification of land use deals with problems of uncertainty, which typically are thetopic of G.I.S. literature.

The uncertainty of analysis needs to be solved necessarily within the land-use plan,characterised by "institutional certainty" of boundaries and land use rights. A possibleperspective is to transform the dichotomy (0,1) = (precise, imprecise) in a passage to aownership function (by the use of fuzzy logic), which varies for each category ofspatial entities. The identification of boundaries appears often as a “fuzzy” question.In fact, Couclelis [3] refers to ill-boundaries, Leung [4] to core areas with maximumdegree of certainty, and so on. The accuracy in definition of “border” varies along aline. The integration of elements of fuzzy set theory in geographical databaseapplications can give a measure of the variation of accuracy along the border line ofareas identified in land use maps. The question of boundaries is usually treated as aquestion of threshold definition. A hill-shaped ownership function, for instance, canbe used to represent a spatial attribute which varies from a core area to a backgroundarea. The threshold is a horizontal line which defines the passage from an


unacceptable ownership value to an acceptable one. But the hill-shaped ownershipfunctions vary by each entity, as well as the threshold which distinguishes core andbackground areas [5]. Consequently we can find easy thresholds for hill-definedcontiguity of entities when existing a symmetric transition from one attribute toanother, or very difficult conditions, when contiguous attributes vary by very differenthill-shaped ownership functions.The second situation is quite frequent in spatial analysis. The characteristic of a fuzzyinformation depends on several factors. An information can be intrinsically fuzzy ornot. An information can appear fuzzy in some conditions, and can become crisp insome other conditions. In this case the information is not intrinsically fuzzy (fig.3).The causes of fuzziness in information can be roughly considered as follows:

• lack of information: the nature of the information/phenomenon isquantitative, but there are not enough data and the expression of theinformation is anyway qualitative (e.g. the information/phenomenon"employment rate" can be expressed by a percentage, but when data aremissing, it can be expressed by expert's judgement, such as "high level ofemployment" or "low level of employment");

• complexity: due to the multiplicity of factors, the information is so complexthat it is impossible to be completely expressed by any kind of reduction toquantitative data. In this case each subject expresses a judgement accordingto complex implicit mental relationships between various factors (e.g. theaesthetic value of a landscape can be considered as a subjective value, or asthe synthesis of several judgements, expressed by the use of qualitativeterms).

Fig. 3. Fuzzy and crisp information

The intrinsically fuzzy information is expressed by linguistic variables, which are notreferable to quantitative information. A high level of precision can be obtained onlywhen studying simple spatial systems.

As Zadeh [6] postulated, precision and complexity are often based on conflict. Theprinciple of incompatibility affirms that when system complexity increases, thepossibility of describing the behaviour of the same system in a precise way decreases


until the complexity leads to the impossibility of description. In planning questionsthe character of fuzziness is also related to the spatial character of information.

Starting from traditional objects with sharp boundaries defined as Crisp-CrispObject (CC-Object) Cheng et al. [7] classified fuzzy objects according to thefollowing three patterns: Crisp-Fuzzy Object (CF-Object), with well definedboundaries and uncertain content; Fuzzy-Crisp Object (FC-Object), with precisethematic content and undefined spatial edge; Fuzzy-Fuzzy Object (FF-Object), withuncertainty in both contents and boundaries.

Two different ways of representing spatial data in G.I.S. application can be oftenconceptualized differently under field and object views. The first approach allows toassimilate the space to a grid, where each element is considered homogeneous. Thespace is therefore subdivided in finite elements, to be classified according to amultidimensional analysis. Each spatial information represents one dimension of theanalysis. The boundary of an object is defined a priori, corresponding with the borderof the element of the grid; the fuzziness factor can concern the attribution of eachelement to a cluster or to another. The fuzziness is managed by substituting thetraditional way of classification with a fuzzy clustering. In this case a thresholddefines the minimum value of acceptability of the membership function, whichexpresses the belonging to each cluster. The spatial partition is represented by theexpression in figure 4 (left panel) and equation 1:

Fig. 4. Field fuzzyness (left) and Object fuzzyness (right)

. 1 Φ+== AiU niS (1)

. 11 Φ=+== ijU nijAiU n

iS (2)

where Ai represents all finite elements of the grid which belong certainly to a cluster,and Φ represents the group of elements without certain membership to any cluster.On the contrary the second approach is characterised by punctual, linear andpolygonal elements. The density of these elements defines the belonging to a cluster.In this case the fuzziness factor of clustering is related to the threshold value fordensity of each type of punctual elements; the traditional way can be substituted bythe construction of a set of complex fuzzy rules to identify different fuzzy clusters. Infigure 4 (right panel) and equation 2 Ai represents all finite elements, which havecertain spatial definition, and Φij represents the element ij which lies between the


elements Ai and Aj without certain spatial definition. The spatial partition is thereforecomposed by geometric elements which can be identified by a core (certain) and abackground (uncertain) area.

In the case of study we reasoned about the variability of the borderline situation.The boundary of Ai and Aj in fact, can depend on several conditions. Theseconditions can coexist or cannot occur along the borderline of Ai and Aj. This is thereason of the variability of uncertainty of boundary definition along the borderline ofAi and Aj. This means also that Φij represents a combination of conditions which canappear fuzzy along some partitions of the boundary, but can appear crisp along otherpartitions of the same boundary.The function Φ in both models represents the grey zone, i.e. the transition betweentwo core areas. It can be considered as an ownership function which varies form 0 to1. Analyzing the previous land suitability case, we can consider the function Φ as acombination of the inclusive rules (areas close to the road network and areas close tosmall rural settlements), defined by the following membership functions, respectively:

.

250 ,0

250100 ,150

250

100 ,1

100 ,0

10010 ,1

100 ,10

>

≤<−≤

=

>≤<

≤>

=

x

xx

x

Bx

x

xx

A µµ (3)

These functions can have many shapes, according to different requirements. Forinstance the areas close to the road network and the areas close to small ruralsettlements (see figure 5) are represented with two different trapeziums.

Fig. 5. Areas close to road network (left) and Areas close to small rural settlements (right)

It is possible to combine the last two images following the rule of the fundamentaloperation of fuzzy set. In this way we can identify the same classes of suitabilityachieved with sharp boundaries. For instance, areas close to both the road networkand small rural settlements, obtained as the intersection of areas close to small ruralsettlements and areas close to road network, can be achieved as the intersection(fig.6):

( ) ( ) ( )[ ] . , min xBxAxBA µµµµ =∩ (4)


Fig. 6. Areas close to road network and small rural settlements

In the same way it is possible to consider the exclusive rules taking in account allfactors poorly compatible with settlement aims, such as areas in geological hazard, onsteep slopes or in forests. For the sake of clearness the exclusive rules can be groupedin two different classes. The first includes all the features that can be classified withsharp boundaries which identify an abrupt transition; for instance areas close to theriver, upper than 1200 m a.s.l., archaeological sites, landslides and areas in hydro-geological hazard can be considered without a gradual transition.

The second class considers all the features that present a certain degree of fuzzinessas the slopes and the forests; in these two cases it is possible to realize two ownershipfunctions µ, related to the function Φ previously defined.

.

150,1

15010,150

10

10,0

30,1

300,30

0,0

>

≤<−≤

=

>

≤<

=

=

x

xx

x

d

x

xx

x

c µµ (5)

The function µc represents the slope suitable for settlement aims; its value cannotexceed 30 % (see figure 7 left panel).

Fig. 7. Areas in steep slopes (left) and Areas in forest (right)

In general it is possible to define a “forest” if stand density is greater than 150 treesper hectare. The function µd represents the transition among meadow, ecotone andforest (see figure 7 right panel).


4 Final Remarks

The relationship among fuzziness and classical planning theory has been described byLeung [4] through four classes: going from a typical Rational Comprehensive kind ofplan to a Strategic one.The first class is an ideal case where it is possible to build a plan with certainobjectives based on certain analyses. The result is a set of discrete representations ofthe physical space which correspond to a set of different values, referring to areasconsidered homogeneous according to each disciplinary point of view. This situationinvolves the production of a huge number of polygons, which are difficult to combinefor creating landscape units according to the whole of disciplines. The second class isthe case of a plan with crisp boundaries, based on fuzzy analyses. If data areimprecise, human evaluation and experience are employed. A typical example is theneed to give an answer to a specific problem with certain economic resources. Thethird class is very frequent in sector plans (e.g. transport) where the need to achievewidely flexible results and the possibility to obtain several alternatives correspond toa certainty of data. The fourth class is the case of the strategic plan which identifiesthe fundamental issues and purposes driving the update process. This is a typicalcyclic process where all original choices can be modified and the policy is continuallymade and re-made, avoiding errors related to radical changes in policy. In this casewe have the combination of a fuzzy objective based on a fuzzy analysis.

The planner has his own patterns, both classificatory and decisional, often far fromthe data model processing schematized in three steps by Molenaar [8]: acquisitionoriented data model, query oriented data model and output oriented data model.Each discipline involved in environmental planning uses a different approach torepresent its own vision of reality. Geological sciences or hydraulics evaluate risks byconsistent mathematical models which are relevantly different to non linear modelsutilised in the field of ecology, and at the same time information about significanceand value of cultural heritage in a given environment does not easily correspond tovalue attribution. Different ways of managing values correspond to each method ofgiving information.

The growing importance of the relationship between interdisciplinarity andtechnological innovation in environmental analyses connected to plans leads to adangerous consciousness about the possibility of managing great amounts of data, bythe use of Geographic Information Systems.Normally, planners face with incomplete, heterogeneous and multiscale spatialinformation which constitutes a weak support to the construction of prescriptive landuse plan. Normally there is a difference of scale between each kind of analyses (e.g.settlement system and environmental system); if data with a different accuracy arecombined adopting a common scale there is the risk of an error propagation and theresults can be meaningless or potentially dangerous [9].

This situation, widely diffuse among planners, is related to the attitude ofmanaging data and objects in order to build complex spatial analyses, starting frommono-thematic studies or simple spatial data. In this case, planners often forget thatthe original sources of data have different degrees of precision and that geographicobjects have different spatial characters. Synthetically, planners using G.I.S.developed the attitude to cross and overlay, without taking in account some relevant


differences between objects to be mixed. This attitude becomes more significant,when the approach to G.I.S. tends to build continuous spatial representations, closerto the real world [10]. Entities become objects in the planner’s perception. Oftenobjects do not have crisp boundaries or do not have boundaries at all [11], [12]. Inmany cases geographic entities are compressed in a crisp boundary described by asingle attribute; this representation often is very far from the reality. Contextually anew difficulty rises to the fore, regarding the need of traducing G.I.S. supportedcomplex analyses and evaluative routines in planning instruments which have onlycrisp definition of zoning, due to their normative issues in land-use regulation. Infact, as Couclelis [3] highlights, spatial analyses in planning context are characterisedby uncertain nature of entities and uncertain mode of observing real world, even if theuser’s purpose is certain (land-use zoning).

References

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4. Leung Y.: Spatial analysis and planning under imprecision. Elsevier Science Publishers,Amsterdam (1988)

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8. Molenaar M.: An Introduction to the Theory of Spatial Object Modelling for GIS. Taylor& Francis, London, (1998)

9. Zhang J., Goodchild M.F.: Uncertanty in geographic information. Taylor and Francis,London, (2002)

10. Johnston K.M.: Geoprocessing and Geographic Information System Hardware andSoftware: Looking towards the 1990’s. In H.J. Sholten and J.C.H. Stillwell (eds):Geographical Information System for Urban and Regional Planners, Kluwer AcademicPublisher, Dordrecht (1990) 215-227

11. Couclelis H.: People manipulate objects (but cultivate fields): beyond the raster-vectordebate in GIS. In Frank A.U., Campari I., Formentini U. (eds): Theories and Methods ofSpatio-temporal Reasoning in Geographic Space. Computer Science, Springer, Berlin(1992) 45-55

12. Burrough Peter A., Frank Andrew U. (eds): Geographic Objects With IndeterminateBoundaries. Taylor and Francis, London (1996)

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G.I.S. and Fuzzy Sets for the Land Suitability Analysis