Fuzzy Rule Extraction from GIS Data with a Neural Fuzzy System for Decision Making Ding Zheng, Wolfgang Kainz Division of Geoinformatics, Spatial Information Theory and Applied Computer Science International Institute for Aerospace Survey and Earth Sciences (ITC) P.O. Box 6, 7500 AA Enschede, The Netherlands Tel: +31-53-4874493, +31-53-4874434
E-mail:
[email protected],
[email protected] However, it is still difficult for the network to directly use its internal configuration to interpret the process of acquiring knowledge. Fuzzy classification assumes the boundary between two neighbouring classes as a continuous, overlapping area within which an object has partial membership in each class. This viewpoint not only reflects the reality of many applications in which categories have fuzzy boundaries, but also provides a simple representation of the potentially complex partition of the feature space. For example, a simple fuzzy If-Then rule can be used to describe a classifier: if slope is slight and elevation is not high then arable suitability is good. Fuzzy logic systems, which can reason with imprecise information, are good at explaining their decision but cannot automatically acquire the knowledge they use to make these decisions. Neural networks are good at recognising patterns, but not good at explaining how they reach their decision. These limitations have been a central driving force behind the creation of intelligent hybrid systems where two or more techniques are combined in a manner that overcomes the limitations of individual techniques. The integrated approach makes them suitable for real applications by their noise tolerance and their ability to learn non-linear patterns [6, 11].
ABSTRACT This study focuses on a new methodology to model a complex process of fuzzy rule acquisition from GIS data. The proposed method of neural fuzzy network described in this paper differs from the other methods in construction of the network by a simple representation of specific knowledge. Our goal is to use semantic If-Then rules instead of numerical values in the analytical models when uncertainty is involved in data. Such a method is expected to solve realistic problems in natural resource analysis and management. This paper discusses an adaptive neural network based on a fuzzy inference system that is able to learn fuzzy sets and fuzzy rules from data by the algorithm of steepest gradient descent. The fuzzy rules that are created by this approach can be very well interpreted to support decision-making. The method is tested in a case study of land suitability assessment. The result shows that the neural fuzzy network successfully extracted fuzzy rules with multidimensional spatial features obtained from GIS and simulated the decision process.
Keywords GIS, neural network, fuzzy rule inference, decision-making
There is no doubt that GIS can deal with spatial information by powerful spatial analysis and data processing tools. However, it lacks modern intelligent spatial analysis [10]. This indicates that the learning/tuning knowledge ability of conventional GIS systems is restricted. In this paper we propose and discuss an adaptive neural network based on a fuzzy inference system. This network is applied for extracting a specific knowledge in the form of fuzzy If-Then rules from GIS data for decision-making. Our aim is to use this new method to support linguistic decision-making. The structure of this paper is the following. Section 2 describes an adaptive neural fuzzy system. Section 3 discusses the method of extracting fuzzy rules. Section 4 tests this method in a case study of land suitability assessment. The test results and discussion are shown in section 5, followed by some conclusive remarks.
1. INTRODUCTION In most cases, conventional approaches of spatial pattern classification in GIS not only demand specialists who possess much professional knowledge but also assume data to be errorfree. As the demands often are restricted in reality, the emerging fuzzy set technology has aroused general attention in natural resources assessment and spatial data processing [1, 2, 4]. At the same time, the applications of artificial neural network technology in particular for expert systems also have been very popular within the domain [12, 5, 9, 14]. However, problems still exist in two aspects. One appears in processing incomplete, imprecise, vague or uncertain information in analysis. The second, knowledge acquisition and representation, remains a headache for most knowledge engineers.
2. NEURAL FUZZY SYSTEM
An advantage of neural networks often cited is the ability to automatically acquire knowledge by a learning algorithm. Permission to make digital or hard copies of part or all of this work or personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers, or to distribute to lists, requires prior specific permission and/or a fee. ACM GIS ’99 11/99 Kansas City, MO USA © 1999 ACM 1-58113-235-2/99/0011 … $5.00
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Rule-based symbolic processing could be the best platform to explain human intelligence in learning, object recognition, natural language understanding, and a variety of other activities. A general fuzzy rule system can be described as R1 : if ( x1 is L11 Θ L Θx n is L1n ) then y is B 1 M Rm : if ( x1 is L1m Θ L Θx n is Lmn ) then y is B m
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S = R1 Θ L ΘR m where L denotes linguistic terms; (x1,x2,…xn) are rule variables; Θ represents linguistic conjunctions ‘AND’ or ‘OR’; y is an output
as rule1 and rule 2, respectively. If we consider a full combination of xp1 and xp2, there should be two more rules R3 and R4 in the network. As shown in figure1, layer 1 and layer 2 represent the antecedents of fuzzy rules; layer 3 represents the consequence of the rules. Certainly, along with the increment of either dimension of feature space (number n) or the number of linguistic terms, the number of rules will grow rapidly and consequently the network may become much more complex. Therefore, simplifying the neural network is a necessary process for extracting effective fuzzy rules.
variable; B is a control linguistic term or crisp values; S is an output variable of the system. We give a fuzzy logic formula 1 2 m f ( L i , Li ,..., L i , i ∈ [1, n]) as the antecedent part of a rule. The superscripts stand for rules, subscripts stand for an element in rule antecedents. When Θ represents ‘AND’ f ( Li , Li ,..., Li ) = Li • Li • ... • Li 1
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The purpose of a rule system is to find one or more outputs from one or more input values. We define Y as the domain of the output and the X1,…,Xn as the domains of input variables x1,…,xn, respectively. The inference function of the rule system can be described as (4) X 1 ×L × X n → Y Such an inference process often needs three steps to compute the output Y. In the first step, known as fuzzification, the numerical input x = (x1,…,xn) is converted into a fuzzy set of linguistic terms A′ . In the second step, the fuzzy implication B′ of A′ under the rule system S is computed. In the third step, a crisp value y′ is computed from B′ by some methods of defuzzification.
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2.2 Definition of Layers in NF Network Layer 1 is defined as the fuzzification layer. Each node of this layer stands for a linguistic term. The output of the node is the degree to which the given input (xj) satisfies the linguistic term associated with this node. Usually, these terms are associated with some parameterised membership functions, which are used to obtain the fuzzified values. In this study we employed a bellshaped membership function with two parameters cji and aji. The membership function of the jth input for the ith rule is mji which is defined as
{
m ji ( x j ) = 1 + [( x j − c ji ) a ji ] 2
}
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Layer 2 is defined as implication layer of a fuzzy rule in the neural fuzzy network model. Each node generates an output corresponding to the conjunctive combination of individual matching degrees. The nodes of this layer are called rule nodes. According to the reasoning mechanism of the fuzzy system, the fuzzy conjunction 'AND' can be modelled by a product operation. Thus, the antecedent of fuzzy rule is inferred from the intersection (the fuzzy ‘AND’ operation) of the linguistic labels expressed by a membership grade. Hence, each rule node may compute the firing strength of the associated rule by the product operator. n
R i = ∏ m ji ( x j )
2.1 Expression of Knowledge in a NF Network
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We use a simple example to show how a set of linguistic If-Then rules is constructed in a neural fuzzy network for classification. Assume that k data sets xp = (xp1, …,xpn), p=1, …,k, are given from two classes (C1, C2), where xp is a n-dimensional crisp vector. If there are two linguistic terms (e.g, “very suitable” and “suitable”) used for describing the variation of data, typical fuzzy classification rules for n = 2 are like
Rule2:
R1
Figure 1: Expression of fuzzy rules in a neural network
Spatial decision making in GIS, is a mapping procedure in which the input space of many features is projected into the output space of partitions. This procedure can be described as function (4). The spatial features may be regarded as independent variables in the mapping function f(x). However, the important issue is how to determine the function which describes the relationship between input space and output space. An adaptive neural network was introduced for learning and tuning such a function to carry out fuzzy reasoning as universal approximator for medical diagnosis [13]. In their study, fuzzy rules regarded as knowledge are presented in the structure of the network. The computing units of the hybrid network implement fuzzy operators and a number weights the importance of each fuzzy rule. In order to simplify fuzzy rules to be easily accepted we made some modifications on this network and applied it in this study.
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where, Ri is the ith rule value. Layer 3 is defined as defuzzification layer. A simple linear combination (equation (7)) is used to express the matching degrees of the rules and a sigmoidal function (8) is applied to calculate the degree of belonging to a certain class at this layer. m
Z l = ∑ wli Ri
If xp1 is very suitable (A11) and xp2 is suitable (A22) then xp= (xp1, xp2) belongs to C1
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wli is a rule weight of link strength between the ith node at layer 2 and the lth node at this layer. Zl is the lth matching degree of the desired class. Ol is the system output of the lth-desired class.
where xp1 and xp2 are the features of the spatial pattern p (polygon or grid in GIS), and linguistic terms characterised by appropriate membership functions. Note that the A11 and A21, A12 and A22 are different membership functions although they have the same meaning of the linguistic terms.
For a classification problem, the rule base of a fuzzy classifier uses rules representing an approximation of an (unknown) function f : ℜ m → {0,1}lth class where f ( x) = (c1 , L , c l ) such that ci =1 and ck = 0 (k∈{1,…,l},k≠i ), i.e. x belongs to class ci. In the inference process, the fuzzy rule base actually does not
Figure 1 illustrates a neural network constructed by fuzzy rules, in which the paths of the long and short dashed lines are expressed
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approximate f but the function f ′ : ℜm → {0,1}lth class . We can obtain f (x) by f ( x) = f ′( x) , where f reflects the interpretation of the classification result obtained from the fuzzy classifier. In this study the class with the largest activation value max(Ol ) is chosen based on (8).
Stage one: data collection. According to different requirements of decision-making, available spatial data and attribute data can be extracted by GIS operations. In this study, we convert all GIS data into grid files of binary format so that the data can be easily connected into the neural fuzzy network model. Stage two: extraction of fuzzy rules. We developed a VisualC++ program for this stage. At first we normalise all data into the range [0,1] and employ the C-means clustering model to calculate initial parameters of membership functions. Secondly, using the neural fuzzy network, we extract fuzzy rules. As mentioned in previous sections, if we consider a full combination of fuzzy rules in the network, there should be a huge number of rules. Such a rule base involves many non-useful, non-rational and conflicting rules. Moreover, if the full combination of rules is taken into computation in the neural fuzzy network, it will cost too much time. To extract efficient fuzzy rules from this rule base, the following methods are proposed.
2.3 NF Network Learning We have presented the neural fuzzy network model in previous sections. In order to realise the mapping of the network from the input space to the output space, we have to teach the system how to reach the final goals. This process is called network learning. A set of training data with input and desired output pairs are adopted for a supervised learning problem to find the parameters of membership function at layer 1 and connecting weights of the linear combination at layer 3. At the beginning of the network learning, initial values of the parameters should be given in the system. The difference between the output of the system and the desired output is used to calculate errors of output nodes at layer 3 that are used to adjust the parameters of the system. If the difference is less than a threshold or there is no further change, the learning is complete and the network is ready for solving problems. The error function is defined as: 1 L (9) E = E (a ji , c ji , wli ) = ∑ (Ol − Old ) 2 2 l =1 where Oldis the desired output for the lth output node and E is a function of membership function parameters: aji and cji ( j = 1,2, L , n and i = 1,2, L , m ), and weight of link strength wli (l = 1,2, L , L ) . The steepest descent method can be used to learn these parameters of membership functions and the weights of link strength in a recursive manner in the hybrid network. a ji (t + 1) = a ji (t ) − η a (∂E ∂a ji ) (10) c ji (t + 1) = c ji (t ) − η c (∂E ∂c ji )
(11)
wli (t + 1) = wli (t ) − η w (∂E ∂wli )
(12)
Method 1. For a given input pattern during the process of constructing the network, a rule is created by finding the combination of fuzzy sets, where each yields the highest degree of membership for the respective input feature. If this combination is not identical to the antecedents of an already existing rule then a new rule is created [8]. Method 2. The network checks the initial fuzzy rules. If it detects some conflicting rules, which have the same “if-part” but different “then-part”, the network should calculate the soundness degree for each rule, and then only keep the rule with the greatest soundness degree. One strategy [3] was proposed to assign a soundness degree D(Rule i ) to a rule by the ratio of the number of data pairs i which support the rule N Rule and the total number of patterns
which have the same if part N ifi . i D(Rule i ) = N Rule / N ifi
(13)
By using this frequency-based degree, the strategy actually incorporates statistical information into the fuzzy system, which results in more reliable decision making. Method 3. As described in section 2.2, a linear combination is used at layer 3 in equation (7) in which wli could be interpreted as rule weight. We can express a weighted rule by appending “with w” to it, e.g., if x1 is A1 and x2 is A2 then z belongs to class l with w, where w is a real valued rule weight. The meaning of the “with-operation” that ties a weight to a rule can be explained as a rule weight is applied to complete a rule: the antecedent of a rule is evaluated to determine a degree of fulfilment which is then multiplied by a rule weight. Furthermore, extending the meaning of rule weight, the weighting of rules is sometimes interpreted as a measure of “importance”, “influence” or “reliability” [7], which indicates to what degree the rule supports the class. For instance, if a rule weight is a negative number, it means to what degree the rule does not belong to that class. According to this meaning of rule weight, in the original neural network, each rule has L weights, because we have L nodes (classes) in the output layer. Thus, the rule should be changed into “if (…) then it belongs to (class 1 with w1 and class 2 with w2 , …, class L with wl)”. Such a rule is not very simple and can not be easily applied in reality. Therefore, the original structure of the neural fuzzy network is modified in this study. We define that each rule has only one weight, which links its “then-part” in the output layer of the network. This method provides not only a simple rule form but also a hint for refining the rule base based on the physical
ηa, ηc, and ηw are the learning rates that control the magnitudes for the modification of these parameters at each iteration. The t indexes the number of the adjustments of parameters. The detailed algorithm of the steepest gradient descent was shown in [15]. If a set of training data (xj = [x1, x2,…,xn], Old, l =1, 2, …, L) has been collected, the procedure of tuning the parameters can be described as follows: 1) Initialise all parameters, and set t =1, Eold = 0, and Enew = 0. 2) Calculate the fuzzy grades at layer1 using membership functions of linguistic labels. 3) Calculate the matching degree of an input-output pair for each rule using equation (6) at layer 2. 4) Calculate the matching degree of rules-outputs of system by linear combination equation (7) at layer 3. 5) Calculate the degree of belonging to a certain decision alternative using equation (8). 6) Calculate the error Enew using equation (9). If Enew is smaller than a pre-specified small value or it remains unchanged, stop. Otherwise, Eold = Enew and Enew = 0, go to step 7. 7) Update parameters by equations (10), (11), and (12); go back to step 2.
3. EXTRACTING FUZZY RULES The method of the neural fuzzy network for extracting fuzzy rules from GIS data consists of three stages.
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meaning of rule weight. For the rules, which have different “ifpart” but have the same “then-part” we can delete the rules contributing the weight with a value of approximately zero after the first network learning. Further, in order to simplify the rule form, the rules obtained from the first network learning are trained again in the network with the weight fixed as 1. In this case, the network only modifies the parameters of the membership functions during the learning process. Hence, the final fuzzy rules have no weights and thus approximate natural language better.
“small”, “middle” and “large” based on the value of the data. The real implication of the terms can be understood based on the properties of the data. According to the model of neural fuzzy network, there should be 27 membership functions. We select a bell-shaped function (5) with different parameters. This is because it has two parameters to be easily adjusted. Note that this study does not focus on how to select membership functions. In principle, any membership function can be used in the method. For network learning, we have to give a set of initial parameters of membership functions to the network. Although the selection of initial parameters is not very important, rational parameters can speed up the network learning. In this study, we use the C-means clustering method to determine the initial parameters of the membership functions for three clusters of each data feature. For details about this method see [3]. The centre and two times variances of each cluster are regarded as parameters a and c in equation (5).
Stage three: Visualisation. The final results of a specific application can be obtained by the extracted fuzzy rules. They are converted into GIS format to be visualised by GIS functions.
4. METHODOLOGY TEST The methodology is tested by a spatial classification of land suitability under the assumption that we do not have the knowledge of land assessment. The data is collected from Dayandian Township, Hefei municipality, China. The area is characterised by its fringe location resulting in experiencing pressure for urban-oriented development. To protect prime agricultural land, the Rural Land Administration Bureau of Hefei municipality (RLMB) undertook a general arable land investigation and produced a suitability map of agricultural land based on land physical quality, land use index and land economic index in 1995. This classification is compared with the results obtained by the approach in this study.
4.2 Implementation The neural fuzzy system was programmed in C++ so that the system can easily link GIS data and export results back to GIS. The learning rate of the network is set as 0.01. We selected 61 training sample data given from 4 classes based on field investigation and a map of available arable land evaluation made by local experts. The initial structure of the network is described in table 1. Input Layer 1 Layer 2
According to the suggestions of the local experts, land use, land economic combination and location conditions were selected as dominant factors for land assessment. Land use index, land economic index and soil categories within specific land parcels were extracted using the overlay and polygon selection capabilities of ARC/INFO. Six new data layers were generated in which four kinds of soil attributes: organic matter content, nitrogen (N) content, potassium (K) content and depth to plough pan (DPP) are included. All data were converted to grid format. In total, 500*490 grid cells cover this area and each grid cell has the size of 20 square meters. Location influences come from road, house and irrigated ditch distribution that are practically taken into account in this study. To express these influences of location distribution, a distance grade was adopted which was computed by GIS functions. A shorter distance gets assigned a higher grade and a longer distance will be assigned a lower grade.
Layer 3
9 Feature spaces. Each has three linguistic terms. Number of nodes: 3*9 (sum of all membership functions) Number of nodes: 39 (full combination of features and terms) Number of nodes: 4 (desired classes)
Table 1: Description of initial network structure
5. RESULTS AND DISCUSSION 5.1 Fuzzy Rules A total of 24 fuzzy rules were extracted to construct the neural network by method 1 mentioned in section 3. The number of rules is reduced to 19 by method 2 after the initial network training, which takes 450 learning epochs to reach a stable situation where the learning errors can not be further reduced. In this learning, we found two data points that still can not be recognised when other 59 data points were classified correctly (96.7% correct). We carefully refine these rules into 14 fuzzy rules by method 3 and again train the network without weight parameters at layer 3. After 1849 learning epochs, the same result had been reached. This indicates that the two kinds of network learning all can reach the goal of classification, but the fuzzy rules obtained from the second learning are easier to be understood because they have no weights in the “then-part” of the rules. The difference between the first and the second learning is that the parameters of the membership functions and weight parameters are adjusted in the first learning, but only the former was adjusted in the second learning. Note that the changes of parameters of the membership functions are different within both approaches. The extracted 14 fuzzy rules are described as follows.
4.1 Initial Membership Functions As described in the previous section, 9 data features were selected. Each feature is defined to correspond to three linguistic terms: “very suitable”, “suitable” and “normal”. Note that the number of linguistic terms is completely determined by the user. There is no limitation on the number of linguistic terms in this methodology. From the viewpoint of a neural network, it does not consider the physical meaning of linguistic terms. It is possible that the same data value has different physical meaning of linguistic terms for a different data feature. For example, if the distance is closer to a road the grade of distance should be higher, the order of linguistic terms can be “very suitable”, “suitable” and “normal”. On the other hand, for the characteristics of land economic combination, a higher index stands for better benefit. Therefore, the order of linguistic terms should be “normal”, “suitable” and “very suitable”. The meaning of linguistic terms actually is not important to the network. We only divide the data of the feature space into three clusters in terms of ascending data value. Hence, in this study we define the linguistic terms as
R1: if ( l l s s s m m l s ) then class 1 R2: if ( l l s s s s s l m ) then class 1 R3: if ( l m s s s m m m s) then class 1 R4: if (m m m s s m m l s) then class 2 R5: if (m m s s s m m l s ) then class 2 R6: if (s m m s s m m l s ) then class 2 R7: if ( s s s m m m m l s) then class 3
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R8: if ( s s s m m m m s l) then class 3 R9: if ( s m s s s m m l s ) then class 3 R10: if (s m s s s l l s m) then class 3 R11: if ( s s s s s m m m s ) then class 4 R12: if ( s s s m m m m m s) then class 4 R13: if (s s s s s m m l s) then class 4 R14: if ( s s s s m s s m l ) then class 4
fuzzy rule base autonomously infers the results of classification we define the following: • The rules of the rule base having the same “then-part” are going to be defined in the same fuzzy rule group. For example, R1, R2 and R3 can be defined as group one. • The performance µ (s) of each fuzzy rule group is to be inferred by the Max-Product Method. That means the fuzzy implication of a single rule is modelled by a product operation. The rule connection in a group is interpreted as 'OR' operation and defined by the maximum operator. n n µ (s ) = max ∏ m j1 ( x j ),..., ∏ m jm ( x j ) (14) j =1 j =1 Figure 3 shows the performance of the rule base. From the figure, at first, each rule group always has significant performance on an area by its “then-part”. If it matches with the boundary of classes resulting from the neural fuzzy network, this performance is shown as the most significant in the “then-part” of all rule groups. That means a fuzzy rule group may provide a kind of knowledge to help us to understand the characteristics of land suitability. Secondly, within the boundary of classes, it still can recognise the influences by different evaluating factors based on their vague shapes. Thirdly, the final performance of the fuzzy rule base basically meets the binary classification. Assume that the binary classification is completely correct we can get 92% correct on area after overlaying two maps. Fourthly, it should be mentioned here, besides the area within class boundaries, each rule group also has performance on other areas where the significant degree is less than inside of the class boundary. This can prove that the fuzzy rules extracted from the hybrid network reflect the continuous variation of land suitability. For example, rule group 2 has performance in class 1. Group 4 has performance in group3.
The order of factors in the “if-part” is land economic index (P1), land use index (P2), irrigated distance grade (P3), house distance grade (P4), road distance grade (P5), organic matter content (P6), N content (P7), K content (P8) and DPP (P9). It can be found from the rule base that the land economic index and land use index have controlling impact on the results. Their numerical value is reversibly associated with classes. When their numerical values vary from large to small the class is going to vary from 1 to 4. Subsequently, three distance factors have to keep the “small” linguistic term in class 1. However, they have no evidential influence on other classes. Moreover, the “large” term of distance factors has no influence on rules, because it is not shown in the rule base. The soil properties seem to slightly influence the classes.
5.2 Membership Functions During the learning phase of the neural fuzzy network, for each rule a classification error is determined, and used to modify the membership function that is responsible for the rule activation. The modification results in shifting the fuzzy set, and obtaining a larger or smaller membership degree depending on the current error. Figure 2 illustrates the final changes of membership functions, which indicates two points. One is the degree of shape change resulted by the size of parameters adjusted in network learning. Another is that the three factors of distance (P3, P4, P5) have not any change on their “large” fuzzy set because the “large” term is not selected in the extracted rule base.
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5.3 Performance of Fuzzy Rules The final classes of land suitability in the experimental area can be obtained easily by the trained neural network. However, we should take note of the classification that resulted from the linear combination of fuzzy rules and a conversion of a sigmoidal function at layer 3 of the network. To show how the extracted
Class Boundary NF-Classes (network)
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Figure 3: Performance of extracted fuzzy rules
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There are 4 points selected in table 2 in which they have different classification results within the NF-class and the B-class. Point Distance to house (in meters) Distance to ditch (in meters) Distance to road (in meters) Land economic index Land use index Soil unit NF-class B-class
1 301 900 2230 4.8 3.8 40619 3 4
2 964 1608 2761 4.8 3.8 40619 4 3
3 284 1474 2024 9.5 8.0 40617 2 1
suitability from soil profile observations and topography. Journal of Soil Science, 1992, 43:193-220.
4 98 1300 1063 9.5 8.0 40617 1 2
[3] Chi, Z., Yan, H., Pham, T., Fuzzy Algorithms: With Application to Image Processing and Pattern Recognition, 1996, World Scientific Publishing, Singapore. [4] Davidson D.A., Theocharopoulos S.P., and Bloksma R.J., A land evaluation project in Greece using GIS and based on Boolean and fuzzy set methodologies. International Journal of Geographical Information System, 1994, 8(4): 369-384.
Table 2: Properties of evaluating factors in 4 points From this table, points 1, 2 and points 3, 4 have the same soil properties due to the same soil unit. Obviously, in binary classification, land economic and land use index control the class results because distance factors are not considered. In this study, point 1 and 4 were recognised as class 3 and 1, respectively, because they have good distance conditions. For the same reason, point 2 and 3 were classified as 4 and 2, respectively, because of their poor distance conditions.
[5] Fisher, P.F., Mackaness, W.A., Peacegood, G., and Wilkinson, G.G., Artificial intelligence and expert system in geo-data processing, Progress in physical Geography, 1988, 12: 371-388. [6] Lippman, R.P., An introduction to computing with neural nets. IEEE ASSP Magazine,1987, 4(2): 4-22. [7] Nauck, D., Kruse, R., How the Learning of Rule Weights Affects the Interpretability of Fuzzy Systems. IEEE International Conference on Fuzzy Systems 1998 (FUZZ-IEEE’98), Anchorage, AK, May 4-9, 1998, 1235-1240. [8] Nauck, D., Kruse, R., What are Neuro-Fuzzy Classifiers. In Proceeding Seventh International Fuzzy Systems Association World Congress IFSA’97, 1997, 4: 228-233, Academia Prague.
6. CONCLUSIONS We have shown that a new methodology of neural fuzzy systems can be used as a tool to extract fuzzy rules from GIS data. The proposed network learning algorithm emphasises on keeping and interpreting the semantic characteristic of fuzzy rules instead of pure classification by a general neural network. Extracted fuzzy rules provide a simple representation of complex procedures of decision making and reflect a kind of knowledge, which can be applied in real world applications. In the view of GIS, fuzzy rules undoubtedly have great potential to be considered as an intelligent model for spatial operations such as semantic querying and decision making. The example with the land suitability assessment data shows that not only the trained neural fuzzy network can reach the goal of classification, but also extracted fuzzy rules can perfectly simulate the variation of classes and infer the result of classification as well. Such a method is very useful to help us to be acquainted with land suitability when we do not have the knowledge of land assessment.
[9] Openshaw, S., Modelling spatial interaction using a neural net. In M.M. Fischer and P. Nijkamp (eds), GIS, Spatial Modelling and Policy. Springer-Verlag, Berlin, 1993, 147-164. [10] Openshaw, S., Openshaw, C., Artificial intelligence in geography, 1997, John Wiley & Sons Inc, New York. [11] Ripley, B.D., Pattern Recognition and neural Networks, Cambridge University Press, 1996, Cambridge, UK.
However, the problem with neural fuzzy networks is that they require good training data sets that should be a good representation of the complete data set. Otherwise, if there are not obvious differences between training data, it is difficult to extract an efficient rule base. Moreover, such data could lead to an unpredictable convergence rate of the network learning, which may potentially threaten the successful application. From the viewpoint of fuzzy rules, superfluous rules not only are not good at interpreting knowledge but also increase the complexity of decision making. Therefore, it is necessary to further study methods for reducing the number of rules, and investigate their fuzziness and ambiguity. At the same time, more experiments are needed.
[12] Smith, T.R., Artificial intelligence and its applicability to geographical problem solving, Professional Geographer, 1984, 12:147-158. [13] Sun, C. T., and Jang, J. S., A neuro-fuzzy classifier and its application. In Proceedings of Second IEEE International Conference on Fuzzy System, San Francisco, U.S.A, 1993, 94-98. [14] Wang, F., The use of artificial neural networks in a geographical information system for agricultural landsuitability assessment, Environment and planning, 1994, A, 26: 265-284. [15] Zheng, D., Kainz, W., Modelling of A Neural Fuzzy System for Preservation of Cultivated Land, In Proceedings Association of Geographic Information Laboratories in Europe, 1998, In press.
7. REFERENCES [1] Burrough P.A., Fuzzy mathematical methods for soil survey and land evaluation. Journal of Soil Science, 1989, 40:477-492. [2] Burrough P.A., Macmillan. R. A., van Deursen. W., Fuzzy classification methods for determining land
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