“7th AGILE Conference on Geographic Information Science” 29 April-1May 2004, Heraklion, Greece Parallel Session 4.1- “Geographic Knowledge Discovery” 333
Fuzzy Modelling in GIS Environment to Support Sustainable Land Use Planning
Vladimir Badenko1, Dmitry Kurtener2
1St. Petersburg State Technical University, Polytechnical 29, 195251, St. Petersburg, Russia: [email protected]
2Agrophysical Research Institute, Grazhdansky prospect 14, 195220 St. Petersburg, Russia: [email protected]
ABSTRACT The combination of GIS with fuzzy set theory and deterministic models is known as GIS Fuzzy
Modelling (GISFM). GISFM was adopted for support sustainable land use planning. In particular GISFM is applied for solution of the problem of investment allocation into worse part of the land drainage systems located in the Saint-Petersburg suburbs. The missing data about loads on water bodies by agriculture waste products from land drainage system is calculated and mapped automatically by the use of the ecological model and software developed. Complex evaluations of land drainage plots are carried out by fuzzy model with the use of four criteria (technological, economical, ecological and social) for two special tasks: 1) ecological criterion is more important and 2) economical criterion is more significant. The results show the opportunity of plots ranging by criterion of fund efficiency. All results are provided by measure of mistrust, which was created by GISFM.
1 INTRODUCTION Geographical Information Systems (GIS) are important tools for spatial planning (Brail, 2001).
Spatial planning involves decision-making techniques that are associated with techniques such as Multi Decision Criteria Analysis (MCDA) and Multi Criteria Evaluation (MCE). Combining GIS with MCDA methods creates a powerful tool for spatial planning (Jankowski, 1995; Malczewiski, 1999). MCE is perhaps the most fundamental of decision support operations in GIS. Another category of decision-making techniques utilised in spatial planning is based on the application of fuzzy set theory (Bogardi, 1996; Burrough, 1992; Mays, 1997; Smith, 1992; Wang, 1990; Xiang, 1992). Fuzzy set theory was introduced by Zadeh (Zadeh, 1965) although the underlying concepts predate this. Overviews have been provided by Zimmermann (1985), Jager (1995) and Pedrycz (1998). Nowadays, fuzzy set theory is a hot topic and is used in many different fields and technical arenas to address a variety of questions and problems, both mundane and abstract (Ross, 1995). Combining GIS with the application of fuzzy set theory presents a relatively new approach to location choice and land suitability assessment.
The combination of GIS with fuzzy set theory and deterministic models is known as GIS Fuzzy Modelling (GISFM). During the last few years, several applications of this approach for spatial planning have been attempted. In particular, GISFM was used for the assessment of burned forest areas with the aim of planning land restoration (Kurtener, 2000), for land suitability assessment in the process of agricultural experimentation (Kurtener, 2000a), for the land use management (Kurtener, 2000b), for assessment of agricultural lands to plan site-specific residue management (Kurtener, 2000b), for risk management of agricultural drought mitigation (Kurtener, 2003) and for the multi-dimensional evaluation of areas on the land market (Yakishev, 2000). Common problems of using of fuzzy algorithms to support spatial planning had been discussed in (Kurtener, 2002).
Many elements of sustainable land use management planning have uncertainties on the one hand and geo-located characteristics on the other hand. Uncertainty is inherent in processes of the planning, which involve data and model uncertainty. It originates from the features of objects (variability, instability, etc) and also from the way of obtaining data (measurement accuracy, processing error, quality of data source,
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etc). GISFM is a useful approach for dealing with uncertainty and imprecision. Here common GISFM approach is illustrated on the base of development of to fuzzy algorithms: one algorithm - for creation of complex criterion on the base of partial criteria, and another algorithm - for evaluation of data quality.
Quality of GIS database plays an important role in GIS database formation (especially attribute data collection). GIS database is based on various sources of information, which are characterized by different quality. In the process of data integration the known facts obtained with different level of accuracy join together. As the result the accuracy of geographic data is decreased. For assessment of quality of GIS database geographical database the method based on GISFM has been developed (Kurtener, 2001). The measure of mistrust has been calculated and mapped automatically by the developed software.
GISFM approach was adopted for solution of the problem of investments allocation into worse parts of the land drainage system that requires transformations. In particular GISFM was applied for complex evaluation of land drainage systems located in the suburbs of Saint-Petersburg agricultural area. The missing data about loads on water bodies (rivers in region) by agriculture waste products from land drainage system is calculated and mapped automatically by the use of the ecological model and software developed by authors. Complex evaluations of land drainage plots are carried out by fuzzy model with the use of four criteria (technological, economical, ecological and social) for two special tasks: 1) ecological criterion is more important and 2) economical criterion is more significant. The results show the opportunity of plots ranging by criterion of fund efficiency. All results were provided by measure of trust, which was created by GISFM.
2. APPROACHES AND METHODS The term fuzzy model is used as an umbrella term to describe an end product of fuzzy modelling. In
the same way that various applications of fuzzy set theory can be developed, combinations of fuzzy applications with crisp models could be the end products of fuzzy modelling. GISFM interfaces GIS with fuzzy models. The terms interface and interfacing may be used to indicate the simultaneous use of GIS and modelling tools, since they do not imply a specific level of interaction between them and the terms linking, combining, and integrating indicate the degree of interfacing (Hartkamp, 1999). In this context, the term linking is defined as merely the exchange of input and output data between a GIS and a fuzzy model. The term integrating implies incorporating one system into the other. The term combining can be defined as a special case when one part of the fuzzy model is linked with GIS and second part of the fuzzy model is integrated into GIS.
The four main steps used to realise a GISFM approach are as follows (Kurtener, 2002): Structuring phase: perception of problem, identification of input and output data, obtaining of missed data using crisp models, definition of alternatives and criteria; Fuzzy modelling phase: building of fuzzy sets and membership functions, selection of fuzzy algorithm for integration in GIS environment; Programming phase: selection of suitable existed software or designing of a new one; Evaluation phase: creation of thematic maps, perception of results obtained.
The distinguishing feature of the GISFM approach is the fact that indicators or criteria are defined using membership functions (Badenko, 2001). The structuring phase includes the identification of criteria as membership functions. A membership function is selected for each indicator or criterion. The choice of a membership function is somewhat arbitrary and should mirror the subjective expert opinion. Thus, each indicator (or criterion) is defined by a specific fuzzy sub-model. The GISFM approach is an adequate way to integrate an expert’s subjective perception as a statement of the meaning of a criterion. The approach can handle simultaneously quantitative and qualitative variables (Kurtener, 2002).
GISFM software is built up in accordance with a special kind of interfacing. In the case of the integration of a fuzzy model into a GIS environment, the same programming language should be used both in the GIS software and for programming of the fuzzy model. For example, if it is assumed that
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GISFM approach will be carried out on the basis of MapInfo® software, then MapBasic® should be used as the language for programming of the fuzzy model. The example of the approach reported in this chapter uses MapBasic®.
In the design of transformation of land drainage systems it is necessary to solve the problems of allocation of investment between parts of the system that need renovations. In other words, each land drainage system can contain some elements that need to be improved, and funds for their transformation and rehabilitation are limited in most cases. Thus, it is necessary to solve the following problem: how to allocate the available investment between these parts. Figure 1 has shown a structure of GISFM adopted for complex evaluation of land drainage systems.
GIS Environment
GIS database
Fuzzy model for complex assessments of current state of land drainage
systems
Fuzzy model for
assessments of data quality
Model described loads on water
bodies by some contamination from land drainage system
Figure 1: Structure of GIS FKM adopted for complex evaluation of land drainage systems.
It is obvious that the solution of the problem should include consideration of the following items: Evaluation of possibility of efficient use of funds for transformation of land drainage system. Evaluation of possible ecological effects, if the transformations will not be carried out. Evaluation of social reaction on this activity.
Consideration of the items is associated with uncertainty analysis. Significance of GISFM is difficult to overestimate when we try to interpret information about the current state of land drainage systems, particularly when this is made automatically in the GIS environment. Combination of fuzzy modelling and GIS technology with process-oriented (or object-oriented) models and expert systems creates a new opportunity for decision making. Methodological basis of complex evaluation of land drainage plots is the section of fuzzy set theory devoted to multi-criteria evaluation and choice of alternatives (Kurtener, 2000b). Coefficients of relative significance of criteria are determined by the pairwise comparison method, which was developed by Saaty (Malczewski, 1999).
In the process of planning to renovate a drainage system, it is necessary to assess the current state of each land drainage plot and evaluations of land drainage systems for allocation of investment. In connection with this, the problem can be defined as requiring the following:
To collect data sets. To estimate a measure of mistrust for GIS database To obtain missing data about loads on water bodies (rivers in region) by some
contamination from land drainage system.
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To carry out complex evaluation of land drainage systems for special cases when ecological criterion is more important.
To make similar analysis for other cases in which economical criterion is more important.
All these steps have been illustrated for a drainage system near Saint-Peterburg, Russia.
The missing data about loads on water bodies (rivers in region) by some contamination (products of agriculture) from land drainage system is calculated and mapped automatically by the use of the above-mentioned model and software developed by authors. This model is based on the regional recommendations (Guideline, 1989) These guideline have the relevant legal status that ensures a legal basis for usage by local administration of the results of the model application. The model is intended for calculation of the amount and concentration of pollutants transported into water objects from agricultural plots through drainage systems. The model contains sub-models for nitrogen (NH4, NO3, NO2) and phosphorus (P). A whole load (L) from agriculture plots with drainage systems per year for any contamination are follow:
L=F(p, l, s, d, sq), (1)
where p - precipitation per year (with probability 10, 50 and 95 percents); l - type of land use (arable land or not); s - soil texture; d - type of drainage system (which determines a proportion between a drainage and surface runoff); sq - area of agriculture plot.
3. RESULTS AND DISCUSSION Application of GISFM was utilised for complex evaluation of land drainage systems located in the
suburbs of Saint-Petersburg agricultural area. GIS database was created with the use of the county plat maps, data of land surveys, cadastre documents, etc. After creation of GIS database for drainage system a measure of mistrust for all attributes has been set on the base of expert opinion, using appropriate fussy model. The integrated measure of mistrust has been defined by the fuzzy operation named Fuzzy Algebraic Product (Bonham-Carter, 1994). As example the measure of mistrust for the soil texture, thickness of topsoil layer and integrated measure of mistrust has been mapped (figure 2).
The missing data about loads on water bodies (rivers in region) by some contamination (products of agriculture) from land drainage system is calculated and mapped automatically by the use of the above-mentioned model and software developed by authors. Figure 3 shows the results. Input data for the model have the measure of mistrust (figure 2) and we can calculate the measure of mistrust for model results for each drainage plot, which are follow: for plot #1 – 0.11, for plot #2 – 0.14, for plot #3 – 0.16, for plot #4 – 0.21. The plot's numbers has shown on figure 2.
Land drainage plots are introduced as alternatives and the five criteria for evaluation of the plots are defined as follows (all criteria are estimated by membership function for fuzzy set "the best land drainage plots for investment"):
Economic criterion (EC): defines the economic efficiency of the use of fund for renovation. Thus, EC =1 if the economic efficiency is high; EC = 0 if it is not.
Technological criterion (TC): defines the labour-intensiveness of the renovation. TC =1 if labour-intensiveness is normal; TC = 0 if labour-intensiveness is greater.
Ecological criterion (ECC): defines the ecological effect of renovation. ECC =1 if the ecological situation has improved greatly; ECC = 0 if it has not improved very much.
Social criterion (SC): defines as the human reaction. SC =1 if the human reaction is very strong; and SC = 0 if it is not.
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Index of multiple evaluation (ME): defines the composite effect of the economic, technological, ecological and social factors. ME =1 if land drainage plot is the best for investment; ME = 0 if it is the worst.
A B
C
Figure 2: GIS database with measure of mistrust.
A – soil granulemetric composition (soil texture). B – thickness of top soil layer.
C – integrated measure of mistrust.
Experts evaluate particular values for all criteria. In this case study, the economic and technological criteria are described by a stepwise linear function (Kurtener, 2002). A social criterion is evaluated using linguistic values. The approach is based on the observation that experts usually use linguistic constructs for the evaluation of ecological and social situations. A five-point membership scale ranging from Absence to Very High values has been assigned (table 1). The expert's job is to evaluate each land drainage plot and then choose the most suitable linguistic value to describe the evaluation of the ecological or social effects of the renovation. Ecological criterion is evaluated using linguistic constructs (table 1) and results of modelling (figure 2).
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A
B
C
D
E
F
Figure 3: Loads on water bodies (rivers in region) by some contamination from land drainage system. A, B - load of NH4; C, D - load of P; E - total load of P; F - total load of NH4.
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Table 1: Linguistic construction with five-point for membership function scale
Linguistic values Quantitative equivalent
Absence 0 Low 0.25
Medium 0.5 High 0.75
Very high 1
A
B
C
D
Figure 4: Criteria for land drainage plots. A -technological criteria; B - economical criteria; C - social criteria; D - ecological criteria.
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Calculation of complex evaluation of land drainage plots (ME criteria) is carried out on the base of Saaty pairwise comparison method (Malczewski, 1999). In the case this method involves pairwise comparisons of 4 criteria (TC, EC, SC and ECC) to create a ratio matrix. It takes as an input the pairwise comparisons and procedures the relative weights as output. Specifically, the weights are determined by normalising the eigenvector associated with the maximum eigenvalue of the ratio matrix. Complex evaluation of land drainage plots is carried out for two special cases: 1) ecological criterion is more important and 2) economical criterion is more important. On the base of Saaty's standard scale of evaluation of relative importance of criteria (technological, economical, ecological and social) for special case when ecological criterion is more significant (task #1) is presented in table 2. Evaluation of relative importance of criteria for special case when economical criterion more significant (task #2) is presented in table 3. A calculated weights also is presented in tables. The weights are used for calculation of ME for these two tasks (figure 5).
Table 2: Pairwise comparisons of evaluation criteria and its weights (task #1) Criterion ECC EC TC SC
ECC 1 5 6 7 0,619 EC 1/5 1 4 6 0,235 TC 1/6 1/4 1 4 0,101 SC 1/7 1/6 1/4 1 0,045
Table 3: Pairwise comparisons of evaluation criteria and its weights (task #2) Criterion EC ECC SC TC Weights
EC 1 4 6 7 0,617 ECC 1/4 1 3 6 0,224 SC 1/6 1/3 1 2 0,097 TC 1/7 1/4 1/2 1 0,062
A
B
Figure 5: Results of complex evaluation (assessment) of land drainage plots – ME criterion. A - task #1,
B - task #2.
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The use of method of multi-criteria assessment for definition the index of multiple evaluation allows to create integrated description of current state of the drainage areas. The study was carried out for two special cases: task #1 where the ecological factor is more important (Figure 5a), and task #2 where the economic factor is more significant (Figure 5b). It is easy to see that in the first case the land drainage plots are ranked as follows: plot # 3, plot # 1, plot # 2, and plot # 4. In the second task we can see another sequence: plot # 1, plot # 4, plot # 3, plot # 2. We can calculate the measure of mistrust for each drainage plot in both tasks, which are follow: task #1 - for plot #1 – 0.17, for plot #2 – 0.18, for plot #3 – 0.21, for plot #4 – 0.22; task #2 - for plot #1 – 0.12, for plot #2 – 0.16, for plot #3 – 0.19, for plot #4 – 0.21. The plot's numbers has shown on figure.
CONCLUSIONS GIS Fuzzy Modelling (GISFM) is a new approach based on interfacing fuzzy and crisp modelling
with GIS. It is an appropriate methodology to support location choice and land suitability assessment, as demonstrated by example of practical implementation to the problem of investment allocation into worse part of the land drainage systems located in the Saint-Petersburg suburbs. The result has demonstrated the advantages of GISFM. In particular, fuzzy models are modelling constructs featuring two main properties6 firstly, they can operate at the level of linguistic terms (fuzzy sets); and secondly, they represent and process uncertainty. Thus by use of fuzzy models, it possible to describe both subjective (knowledge-driven) and deterministic (data-driven) information. Also GISFM is an effective tool for evaluation of the quality of attribute database. In particular, it has been show as all results are provided by measure of mistrust, which was created by GISFM.
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