Network Modeling and methods for describing and measuring networks and proving properties of networks are well-developed There are a variety of network models in GISystems, which are primarily differentiated by the topological relationships they maintain Network models can act as the basis for location through the process of linear referencing Network analyses such as routing and flow modeling have to some extent been implemented, although there are substantial opportunities for additional theoretical advances and diversified application REFERENCES Ahuja, R K., Magnanti, T L., & Orlin, J B (1993) Network Flows: Theory, Algorithms, and Applications Upper Saddle River, NJ: PrenticeHall, Inc Cooke, D F (1998) Topology and TIGER: The Census Bureau’s Contribution In T W Foresman (Ed.), The History of Geographic Information Systems Upper Saddle River, NJ: Prentice Hall Curtin, K M., Noronha, V., Goodchild, M F., & Grise, S (2001) ArcGIS Transportation Data Model Redlands, CA: Environmental Systems Research Institute Curtin, K M., Qiu, F., Hayslett-McCall, K., & Bray, T (2005) Integrating GIS and Maximal Covering Models to Determine Optimal Police Patrol Areas In F Wang (Ed.), Geographic Information Systems and Crime Analysis Hershey: Idea Group Dueker, K J., & Butler, J A (2000) A geographic information system framework for transportation data sharing Transportation Research Part CEmerging Technologies, 8(1-6), 13-36 Evans, J R., & Minieka, E (1992) Optimization Algorithms for Networks and Graphs (2nd ed.) New York: Marcel Dekker 120 Federal Highway Administration (2001) Implementation of GIS Based Highway Safety Analysis: Bridging the Gap (No FHWA-RD-01-039) McLean, VA: U.S Department of Transportation Federal Transit Administration (2003) Best Practices for Using Geographic Data in Transit: A Location Referencing Guidebook (No FTA-NJ26-7044-2003.1) Washington, DC: U.S Department of Transportation Fletcher, D., Expinoza, J., Mackoy, R D., Gordon, S., Spear, B., & Vonderohe, A (1998) The Case for a Unified Linear Reference System URISA Journal, 10(1) Fohl, P., Curtin, K M., Goodchild, M F., & Church, R L (1996) A Non-Planar, Lane-Based Navigable Data Model for ITS Paper presented at the International Symposium on Spatial Data Handling, Delft, The Netherlands Harary, F (1982) Graph Theory Reading: Addison Wesley Kansky, K (1963) Structure of transportation networks: relationships between network geogrpahy and regional characteristics (No 84) Chicago, IL: University of Chicago Koncz, N A., & Adams, T M (2002) A data model for multi-dimensional transportation applications International Journal of Geographical Information Science, 16(6), 551-569 Noronha, V., & Church, R L (2002) Linear Referencing and Other Forms of Location Expression for Transportation (No Task Order 3021) Santa Barbara: Vehicle Intelligence & Transportation Analysis Laboratory, University of California Nyerges, T L (1990) Locational Referencing and Highway Segmentation in a Geographic Information System ITE Journal, March, 27-31 Rodrigue, J., Comtois, C., & Slack, B (2006) The Geography of Transport Systems London: Routledge Network Modeling Scarponcini, P (2001) Linear reference system for life-cycle integration Journal of Computing in Civil Engineering, 15(1), 81-88 Sutton, J C., & Wyman, M M (2000) Dynamic location: an iconic model to synchronize temporal and spatial transportation data Transportation Research Part C-Emerging Technologies, 8(16), 37-52 Vonderohe, A., Chou, C., Sun, F., & Adams, T (1997) A generic data model for linear referencing systems (No Research Results Digest Number 218) Washington D.C.: National Cooperative Highway Research Program, Transportation Research Board Wilson, R J (1996) Introduction to Graph Theory Essex: Longman KEYWORDS Capacity: The largest amount of flow permitted on an edge or through a vertex Graph Theory: The mathematical discipline related to the properties of networks Linear Referencing: The process of associating events with a network datum Network: A connected set of edges and vertices Network Design Problems: A set of combinatorially complex network analysis problems where routes across (or flows through) the network must be determined Network Indices: Comparisons of network measures designed to describe the level of connectivity, level of efficiency, level of development, or shape of a network Topology: The study of those properties of networks that are not altered by elastic deformations These properties include adjacency, incidence, connectivity, and containment 121 122 Chapter XVI Artificial Neural Networks Xiaojun Yang Florida State University, USA Abstr act Artificial neural networks are increasingly being used to model complex, nonlinear phenomena The purpose of this chapter is to review the fundamentals of artificial neural networks and their major applications in geoinformatics It begins with a discussion on the basic structure of artificial neural networks with the focus on the multilayer perceptron networks given their robustness and popularity This is followed by a review on the major applications of artificial neural networks in geoinformatics, including pattern recognition and image classification, hydrological modeling, and urban growth prediction Finally, several areas are identified for further research in order to improve the success of artificial neural networks for problem solving in geoinformatics INTRODUCT ION An artificial neural network (commonly just neural network) is an interconnected assemblage of artificial neurons that uses a mathematical or computational model of theorized mind and brain activity, attempting to parallel and simulate the powerful capabilities for knowledge acquisi- tion, recall, synthesis, and problem solving It originated from the concept of artificial neuron introduced by McCulloch and Pitts in 1943 Over the past six decades, artificial neural networks have evolved from the preliminary development of artificial neuron, through the rediscovery and popularization of the back-propagation training algorithm, to the implementation of artificial neu- Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited Artificial Neural Networks ral networks using dedicated hardware Theoretically, artificial neural networks are highly robust in data distribution, and can handle incomplete, noisy and ambiguous data They are well suited for modeling complex, nonlinear phenomena ranging from financial management, hydrological modeling to natural hazard prediction The purpose of the article is to introduce the basic structure of artificial neural networks, review their major applications in geoinformatics, and discuss future and emerging trends B ACKGROUND The basic structure of an artificial neural network involves a network of many interconnected neurons These neurons are very simple processing elements that individually handle pieces of a big problem A neuron computes an output using an activation function that considers the weighted sum of all its inputs These activation functions can have many different types but the logistic sigmoid function is quite common: f(x) 1 e x where f(x) is the output of a neuron and x represents the weighted sum of inputs to a neuron As suggested from Equation 1, the principles of computation at the neuron level are quite simple, and the power of neural computation relies upon the use of distributed, adaptive and nonlinear computing The distributed computing environment is realized through the massive interconnected neurons that share the load of the overall processing task The adaptive property is embedded with the network by adjusting the weights that interconnect the neurons during the training phase The use of an activation function in each neuron introduces the nonlinear behavior to the network There are many different types of neural networks, but most can fall into one of the five major paradigms listed in Table Each paradigm has advantages and disadvantages depending upon specific applications A detailed discussion about these paradigms can be found elsewhere (e.g., Bishop, 1995; Rojas, 1996; Haykin, 1999; and Principe et al., 2000) This article will concentrate upon multilayer perceptron networks due to their technological robustness and popularity (Bishop, 1995) Figure illustrates a simple multilayer perceptron neural network with a 4×5×4×1 structure This is a typical feed-forward network that allows the connections between neurons to flow in one direction Information flow starts from the neurons in the input layer, and then moves along weighted links to neurons in the hidden layers for processing The weights are normally determined through training Each neuron contains a nonlinear activation function that combines information from all neurons in the preceding layers.The output layer is a complex function of inputs and internal network transformations The topology of a neural network is critical for neural computing to solve problems with reasonable training time and performance For any neural computing, training time is always the biggest bottleneck and thus, every effort is needed to make training effective and affordable Training time is a function of the complexity of the network topology which is ultimately determined by the combination of hidden layers and neurons A trade-off is needed to balance the processing purpose of the hidden layers and the training time needed A network without a hidden layer is only able to solve a linear problem To tackle a nonlinear problem, a reasonable number of hidden layers is needed A network with one hidden layer has the power to approximate any function provided that the number of neurons and the training time are not constrained (Hornik, 1993) But in practice, many functions are difficult to approximate with one hidden layer and thus, Flood and Kartam (1994) suggested using two hidden layers as a starting point 123 Artificial Neural Networks Table Classification of artificial neural networks (Source: Haykin, 1999) No Type Example Brief description Feed-forward neural network Multi-layer perceptron It consists of multiple layers of processing units that are usually interconnected in a feed-forward way Radial basis functions As powerful interpolation techniques, they are used to replace the sigmoidal hidden layer transfer function in multi-layer perceptrons Kohonen self-organizing networks They use a form of unsupervised learning method to map points in an input space to coordinate in an output space Simple recurrent networks Contrary to feed-forward networks, recurrent neural networks use bi-directional data flow and propagate data from later processing stages to earlier stages Recurrent network Hopfield network Stochastic neural networks Boltzmann machine They introduce random variations, often viewed as a form of statistical sampling, into the networks Modular neural networks Committee of machine They use several small networks that cooperate or compete to solve problems Other types Dynamic neural networks They not only deal with nonlinear multivariate behavior, but also include learning of time-dependent behavior Cascading neural networks They begin their training without any hidden neurons When the output error reaches a predefined error threshold, the networks add a new hidden neuron Neuro-fuzzy networks They are a fuzzy inference system in the body which introduces the processes such as fuzzification, inference, aggregation and defuzzification into a neural network Figure A simple multilayer perceptron(MLP) neutral network with a X X X structure 124 Artificial Neural Networks The number of neurons for the input and output layers can be defined according to the research problem identified in an actual application The critical aspect is related to the choice of the number of neurons in hidden layers and hence the number of connection weights If there are too few neurons in hidden layers, the network may be unable to approximate very complex functions because of insufficient degrees of freedom On the other hand, if there are too many neurons, the network tends to have a large number of degrees of freedom which may lead to overtraining and hence poor performance in generalization (Rojas, 1996) Thus, it is crucial to find the ‘optimum’ number of neurons in hidden layers that adequately capture the relationship in the training data This optimization can be achieved by using trial and error or several systematic approaches such as pruning and constructive algorithms (Reed, 1993) Training is a learning process by which the connection weights are adjusted until the network is optimal This involves the use of training samples, an error measure and a learning algorithm Training samples are presented to the network with input and output data over many iterations They should not only be large in size but also be representative of the entire data set to ensure sufficient generalization ability There are several different error measures such as the mean squared error (MSE), the mean squared relative error (MSRE), the coefficient of efficiency (CE), and the coefficient of determination (r2) (Dawson and Wilby, 2001) The MSE has been most commonly used The overall goal of training is to optimize errors through either a local or global learning algorithm Local methods adjust weights of the network by using its localized input signals and localized first- or second- derivative of the error function They are computationally effective for changing the weights in a feed-forward network but are susceptible to local minima in the error surface Global methods are able to escape local minima in the error surface and thus can find optimal weight configurations (Maier and Dandy, 2000) By far the most popular algorithm for optimizing feed-forward neural networks is error back-propagation (Rumelhart et al., 1986) This is a first-order local method It is based on the method of steepest descent, in which the descent direction is equal to the negative of the gradient of the error The drawback of this method is that its search for the optimal weight can become caught in local minima, thus resulting in suboptimal solutions This vulnerability could increase when the step size taken in weight space becomes too small Increasing the step size can help escape local error minima, but when the step size becomes too large, training can fall into oscillatory traps (Rojas, 1996) If that happens, the algorithm will diverge and the error will increase rather than decrease Apparently, it is difficult to find a step size that can balance high learning speed and minimization of the risk of divergence Recently, several algorithms have been introduced to help adapt step sizes during training (e.g., Maier and Dandy, 2000) In practice, however, a trial-and-error approach has often been used to optimize step size Another sensitive issue in back-propagation training is the choice of initial weights In the absence of any a priori knowledge, random values should be used for initial weights The stop criteria for learning are very important Training can be stopped when the total number of iterations specified or a targeted value of error is reached, or when the training is at the point of diminishing returns It should be noted that using low error level is not always safe to stop the training because of possible overtraining or overfitting When this happens, the network memorizes the training patterns, thus losing the ability to generalize A highly recommended method for stopping the training is through cross validation (e.g., Amari et al., 1997) In doing so, an independent data set is required for test purposes, and close monitoring of the error in the training set and the test set is needed Once the error in the test set increases, the training should 125 Artificial Neural Networks be stopped since the point of best generalization has been reached APP LIC AT IONS Artificial neural networks are applicable when a relationship between the independent variables and dependent variables exists They have been applied for such generic tasks as regression analysis, time series prediction and modeling, pattern recognition and image classification, and data processing The applications of artificial neural networks in geoinformatics have concentrated on a few major areas such as pattern recognition and image classification (Bruzzone et al., 1999), hydrological modeling (Maier and Dandy, 2000) and urban growth prediction (Yang, 2009) The following paragraphs will provide a brief review on these areas Pattern recognition and image classification are among the most common applications of artificial neural networks in remote sensing, and the documented cases overwhelmingly relied upon the use of multi-layer perceptron networks The major advantages of artificial neural networks over conventional parametric statistical approaches to image classification, such as the Euclidean, maximum likelihood (ML), and Mahalanobis distance classifiers, are that they are distribution-free with less severe statistical assumptions needed and that they are suitable for data integration from various sources (Foody, 1995) Artificial neural networks are found to be accurate in the classification of remotely sensed data, although improvements in accuracies have generally been small or modest (Campbell, 2002) Artificial neural networks are being used increasingly to predict and forecast water resource variables such as algae concentration, nitrogen concentration, runoff, total volume, discharge, or flow (Maier and Dandy, 2000; Dawson and Wilby, 2001) Most of the documented cases used a multi-layer perceptron that was trained by using 126 the back-propagation algorithm Based on the results obtained so far, there is little doubt that artificial neural networks have the potential to be a useful tool for the prediction and forecasting of water resource variables The application of artificial neural networks for urban predictive modeling is a new but rapidly expanding area of research (Yang, 2009) Neural networks have been used to compute development probability by integrating a set of predictive variables as the core of a land transformation model (e.g., Pijanowski et al., 2002) or a cellular automata-based model (e.g., Yeh and Li, 2003) All the applications documented so far involved the use of the multilayer perceptron network, a gridbased modeling framework, and a Geographic Information Systems (GIS) that was loosely or tightly integrated with the network for input data preparation, modeling validation and analysis CONC LUS ION AND FUTURE TRENDS Based on many documented applications within recent years, the prospect of artificial neural networks in geoinformatics seems to be quite promising On the other hand, the capability of neural networks tends to be oversold as an allinclusive ‘black box’ that is capable to formulate an optimal solution to any problem regardless of network architecture, system conceptualization, or data quality Thus, this field has been characterized by inconsistent research design and poor modeling practice Several researchers recently emphasized the need to adopt a systematic approach for effective neural network model development that considers problem conceptualization, data preprocessing, network architecture design, training methods, and model validation in a sequential mode (e.g., Mailer and Dandy, 2000; Dawson and Wilby, 2001; Yang, 2009) There are a few areas where further research is needed Firstly, there are many arbitrary decisions Artificial Neural Networks involved in the construction of a neural network model, and therefore, there is a need to develop guidance that helps identify the circumstances under which particular approaches should be adopted and how to optimize the parameters that control them For this purpose, more empirical, inter-model comparisons and rigorous assessment of neural network performance with different inputs, architectures, and internal parameters are needed Secondly, data preprocessing is an area where little guidance can be found There are many theoretical assumptions that have not been confirmed by empirical trials It is not clear how different preprocessing methods could affect the model outcome Future investigation is needed to explore the impact of data quality and different methods in data division, data standardization, or data reduction Thirdly, continuing research is needed to develop effective strategies and probing tools for mining the knowledge contained in the connection weights of trained neural network models for prediction purposes This can help uncover the ‘black-box’ construction of the neural network, thus facilitating the understanding of the physical meanings of spatial factors and their contribution to geoinformatics This should help improve the success of neural network applications for problem solving in geoinformatics REFERENCES Amari, S., Murata, N., Muller, K R., Finke, M., & Yang, H H (1997) Asymptotic statistical theory of overtraining and cross-validation IEEE Transactions On Neural Networks, 8(5), 985-996 Bishop, C ( 1995) Neural Networks for Pattern Recognition (p 504) Oxford: University Press Bruzzone, L., Prieto, D F., & Serpico, S B (1999) A neural-statistical approach to multitemporal and multisource remote-sensing image classification IEEE Transactions on Geoscience and Remote Sensing, 37(3), 1350-1359 Campbell, J B (2002) Introduction to Remote Sensing (3rd ) (p 620) New York: The Guiford Press Dawson, C W., & Wilby, R L (2001) Hydrological modelling using artificial neural networks Progress in Physical Geography, 25(1), 80-108 Flood, I., & Kartam, N (1994) Neural networks in civil engineering.2 systems and application Journal of Computing in Civil Engineering, 8(2), 149-162 Foody, G M (1995) Land cover classification using an artificial neural network with ancillary information International Journal of Geographical Information Systems, 9, 527- 542 Haykin, S (1999) Neural Networks: A Comprehensive Foundation (p 842) Prentice Hall Hornik, K (1993) Some new results on neuralnetwork approximation Neural Networks, 6(8), 1069-1072 Kwok, T Y., & Yeung, D Y (1997) Constructive algorithms for structure learning in feed-forward neural networks for regression problems IEEE Transactions On Neural Networks, 8(3), 630645 Maier, H R., & Dandy, G C (2000) Neural networks for the prediction and forecasting of water resources variables: A review of modeling issues and applications Environmental Modelling & Software, 15, 101-124 Pijanowski, B C., Brown, D., Shellito, B., & Manik, G (2002) Using neural networks and GIS to forecast land use changes: A land transformation model Computers, Environment and Urban Systems, 26, 553–575 Principe, J C., Euliano, N R., & Lefebvre, W C (2000) Neural and Adaptive Systems: Fundamentals Through Simulations (p 565) New York: John Wiley & Sons 127 Artificial Neural Networks Reed, R (1993) Pruning algorithms - a survey IEEE Transactions On Neural Networks, 4(5), 740-747 Rojas, R (1996) Neural Networks: A Systematic Introduction (p 502) Springer-Verlag, Berlin Rumelhart, D E., Hinton, G E., & Williams, R J (1986) Learning internal representations by error propagation In Parallel Distributed Processing D E Rumelhart, & J L McClelland Cambridge: MIT Press Yang, X (2009) Artificial neural networks for urban modeling In Manual of Geographic Information Systems, M Madden American Society for Photogrammetry and Remote Sensing (in press) Yeh, A G O., & Li, X (2003) Simulation of development alternatives using neural networks, cellular automata, and GIS for urban planning Photogrammetric Engineering and Remote Sensing, 69(9), 1043-1052 key TER MS Architecture: The structure of a neural network including the number and connectivity of neurons A network generally consists of an input layer, one or more hidden layers, and an output layer 128 Back-Propagation: The training algorithm for the feed-forward, multi-layer perceptron networks which works by propagating errors back through a network and adjusting weights in the direction opposite to the largest local gradient Error Space: The n-dimensional surface in which weights in a networks are adjusted by the back-propagation algorithm to minimize model error Feed-Forward: A network in which all the connections between neurons flow in one direction from an input layer, through hidden layers, to an output layer Multiplayer Perceptron: The most popular network which consists of multiple layers of interconnected processing units in a feed-forward way Neuron: The basic building block of a neural network A neuron sums the weighed inputs, processes them using an activation function, and produces an output response Pruning Algorithm: A training algorithm that optimizes the number of hidden layer neurons by removing or disabling unnecessary weights or neurons from a large network that is initially constructed to capture the input-output relationship Training/Learning: The processing by which the connection weights are adjusted until the network is optimal 129 Chapter XVII Spatial Interpolation Xiaojun Yang Florida State University, USA Abstr act Spatial interpolation is a core component of data processing and analysis in geoinformatics The purpose of this chapter is to discuss the concept and techniques of spatial interpolation It begins with an overview of the concept and brief history of spatial interpolation Then, the chapter reviews some commonly used interpolations that are specifically designed for working with point data, including inverse distance weighting, kriging, triangulation, Thiessen polygons, radial basis functions, minimum curvature, and trend surface This is followed by a discussion on some criteria that are proposed to help select an appropriate interpolator; these criteria include global accuracy, local accuracy, visual pleasantness and faithfulness, sensitivity, and computational intensity Finally, future research needs and new, emerging applications are presented INTRODUCT ION Spatial interpolation is a core component of data processing and analysis in geographic information systems It is also an important subject in spatial statistics and geostatistics By definition, spatial interpolation is the procedure of predicating the value of properties from known sites to un-sampled, missing, or obscured locations The rationale behind interpolation is the very common observation that values at points close together in space are more likely to be similar than points further apart This observation has been formulated as the First Law of Geography (Tobler, 1970) Data sources for spatial interpolation are normally scattered sample points such as soil profiles, water wells, meteorological stations or counts of species, people or market outlets Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited Rough Sets and Granular Computing in Geospatial Information Petry, 2004) Rough set formalism offers improved semantics for handling imprecision due to finite spatial or semantic resolution (Worboys, 1998) Ahlqvist et al (2000) offers a rough set-based classification and accuracy assessment method for spatial data An empirical spatial knowledge discovery technique has been offered for rough rule induction from spatial data (Aldridge, 2000) Beaubouef et al (2004) used rough set for uncertainty management in spatial databases Sikder et al (2003) extended the integration approach of rough set and evidence theory to model the effects of spatial neighborhood evidence in the supervised classification The integration of rough set and evidence theory offers inference mechanism to reason over spatial neighborhood evidences which can be used to manage uncertainty in location-based services (Sikder & Gangapadhayay, 2007) C onc lus ion Information granules of spatial information come with underlying rules describing syntax and semantics The research agenda of granular computing includes conceptual and algorithmic aspects of information granules such as their granularity, usefulness, communication and interoperability between various platforms of granular computing The promise of practical applications includes the computing aspect of adaptive spatio-temporal granular formation, characterization, robust synthesis, and uncertainty management In particular, among the issues that need to be explored in spatial reasoning, knowledge discovery and data mining are methods for synthesis of complex information granule in distributed environment, discovery of decomposition of rules, fusion mechanism, uncertainty handling and adaptive spatio-temporal reasoning R eferences Ahlqvist, O., Keukelaar, J., & Oukbir, K (2000) Rough classification and accuracy assessment International Journal of Geographical Information Science, 14(5), 475–496 Aldridge, C H (2000) A Theoretical Foundation for Geographic Knowledge Discovery in Databases Paper presented at the First International Conference on Geographic Information Science, Georgia, USA Beaubouef, T., Ladner, R., & Petry, F (2004) Rough set spatial data modeling for data mining International Journal of Intelligent Systems, 19(7), 567 - 584 Bittner, T., & Stell, J G (1998) A boundarysensitive approach to qualitative location Annals of Mathematics and Artificial Intelligence, 24, 93-114 Burrough, P., & Frank, A (1996) Geographic Objects with Indeterminate Boundaries London: Taylor and Francis Cohn, A G., & Gotts, N M (1996) The ‘eggyolk’ representation of regions with indeterminate boundaries In P A Burrough & A U Frank (Eds.), Geographic Objects with Indeterminate Boundaries, 2, 171–187 London: Taylor & Francis Lehmann, F., & Cohn, A G (1995) The eggyolk reliability hierarchy: Semantic data integration using sorts with prototypes Paper presented at the The third international conference on Information and knowledge management Liu, Q., & Jiang, S L (2002) Reasoning about information granules based on rough logic Paper presented at the International Conference on Rough Sets and Current Trends in Computing Openshaw, S (1984) The modifiable areal unit problem Norwich,United Kingdom: Geo Books 157 Rough Sets and Granular Computing in Geospatial Information Pawlak, Z (1991) Rough sets: Theoretical aspects of reasoning about data (Vol 9) Kluwer, Dordrecht presented at the Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing Pedrycz, W (2001) Granular computing: An emerging paradigm Heidelberg; New York: Physica-Verlag Yao, Y Y (2001) Information granulation and rough set approximation International Journal of Intelligent Systems, 16(1), 87-104 Pedrycz, W., & Vukovich, G (1999) Granular computing in the development of fuzzy controllers International Jouranl of Intelligent Systems, 14(4), 419-447 Zadeh, L A (1996, September) The Key Roles of Information Granulation and Fuzzy logic in Human Reasoning Paper presented at the IEEE International Conference on Fuzzy Systems Sikder, I., & Gangapadhayay, A (2007) Managing Uncertainty in Location Services Using Rough Set and Evidence Theory Expert Systems with Applications, 32, 386-396 Zhang, L., & Zhang, B (2004) The quotient space theory of problem solving Fundamenta Informatcae, 59(2-3), 287-298 Sikder, I., Gangapadhayay, A., & Yoon, V (2003) Visualization of Uncertainty in Spatial Classification, Proceedings of Ninth International Conference on Distributed Multimedia Systems, 383-386 Sikder, I U., Sarkar, S M., & Mal, T K (2006) Knowledge-Based Risk Assessment Under Uncertainty for Species Invasion Risk Analysis, 26(1), 239-252 Skowron, A., Stepaniuk, J., & Tsumoto, S (2000) Information Granules for Spatial Reasoning Paper presented at the PAKDD Stell, J G., & Worboys, M F (1998) Stratified map spaces Paper presented at the Proceedings of the 8th International Symposium on Spatial Data Handling Wang, S L., Wang, X Z., & Shi, W Z (2001) Development of a Data Mining Method for Land Control Geo-spatial Information Sciences, 4(1), 68-76 Worboys, M F (1998) Imprecision in finite resolution spatial data GeoInformatica, 2, 257-280 Yao, J T., & Yao, Y Y (2002) Induction of classification rules by granular computing Paper 158 Zhang, Y Q., Fraser, M D., Gagliano, R A., & Kandel, A (2000) Granular neural networks for numerical-linguistic data fusion and knowledge discovery IEEE Transactions on Neural Networks, 11(3), 658-667 K ey T er ms Egg-Yolk Model: A model of indeterminate regions where indeterminate regions are represented in terms of their minimal and maximal extents Equivalence Relation: A binary relation which is reflexive, symmetric and transitive Granular Computing: Theories, tools and techniques that make use of granules, i.e., groups, classes, or clusters of a universe, in the process of problem solving Indiscernibility: A relationship among a finite collection of elements where objects are indiscernible with respect to a particular observation if any pair of elements in the collection cannot be distinguished from each other by the observation Rough Sets and Granular Computing in Geospatial Information Modifiable Areal Unit Problem (MAUP): The “modifiable” nature of area units used in spatial analysis can influence the analysis and modeling results Qualitative Spatial Reasoning: An inference mechanism that is concerned with the cognitive, computational, and formal aspects of making logical inferences by representing continuous properties of real world space by discrete systems of symbols Reduct: The minimal set of attributes that preserve the original classification defined by a set of attributes Region-Connection Calculus (RCC): A logical framework for incorporating spatial reasoning into AI systems by axiomatization of space in which regions are considered primitives 159 Section IV Ontologies 161 Chapter XXI Geospatial and Temporal Semantic Analytics Matthew Perry University of Georgia, USA Amit Sheth University of Georgia, USA Ismailcem Budak Arpinar University of Georgia, USA Farshad Hakimpour University of Georgia, USA Abstr act The amount of digital data available to researchers and knowledge workers has grown tremendously in recent years This is especially true in the geography domain As the amount of data grows, problems of data relevance and information overload become more severe The use of semantics has been proposed to combat these problems (Berners-Lee et al., 2001; Egenhofer, 2002) Semantics refer to the meaning of data rather than its syntax or structure Systems which can understand and process data at a semantic level can achieve a higher level of automation, integration, and interoperability Applications generally use semantic technology for three basic purposes: (1) semantic integration, (2) semantic search and contextual browsing, and (3) semantic analytics and knowledge discovery (Sheth & Ramakrishnan, 2003) Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited Geospatial and Temporal Semantic Analytics INTRODUCT ION This chapter focuses on semantic analytics and knowledge discovery in the geographic information science domain Semantic analytics applications provide capabilities for analyzing relationships and patterns in semantic metadata So far, research in this area has concentrated on thematic relationships between entities (e.g., the fact that two glycopeptides participated in the same biological process) However, for many domains and applications, spatial and temporal relationships cannot be overlooked Next generation geoinformatics applications that can successfully combine knowledge of real-world entities and relationships with knowledge of their interactions in space and time will have huge potential in areas such as national security and emergency response The remainder of this chapter reviews background concepts from the Semantic Web community and describes state-of-the-art work in semantic analytics and discovery in the purely thematic dimension It then discusses our ongoing work in realizing semantic analytics and discovery in all three dimensions of information: thematic, spatial, and temporal B ACKGROUND In preparation for our discussion of geospatial and temporal semantic analytics, we first review basic concepts of ontologies, for the Semantic Web and thematic analytics Ontology Ontologies are central to realizing semantic applications as they provide a concrete way to specify the semantics of an application domain Ontology is classically defined as “a specification of a conceptualization” (Gruber, 1993) We can think of an ontology as consisting of two parts: a schema 162 and instance data The schema models a domain by defining class types (e.g., University, City) and relationship types (e.g., located_in) The schema is populated with instances of classes and relationships (e.g., The University of Georgia located_in Athens) to create facts representing knowledge of the domain A number of ontologies describing thematic aspects of data have been developed at the Large Scale Distributed Information Systems (LSDIS) lab Some recent examples include GlycO and ProPreO in the Bioinformatics domain (Sahoo et al., 2006) and more general-purpose ontologies such as the Semantic Web Evaluation Ontology (SWETO) (Aleman-Meza et al., 2004) There has been significant work regarding the use of geospatial ontologies in geographic information science Ontologies in geographic information systems (GIS) are seen as a vehicle to facilitate interoperability and to limit data integration problems both from different systems and between people and systems (Agarwal, 2005) Fonseca et al (2002) present an architecture for an ontology-driven GIS in which ontologies describe the semantics of geographic data and act as a system integrator independent of the data model used (e.g., object vs field) Kuhn (2001) claims that, for maximum usefulness, geo-ontologies should be designed with a focus on human activities in geographic space and thus present a method for constructing domain ontologies based on the text analysis of domain documents (e.g., German traffic code text for the car navigation domain) Kuhn and Raubal (2003) also introduce the concept of semantic reference systems, of which ontologies are a component, as a means to describe the same geographic information from varying perspectives This includes notions of semantic transformation and projection of ontologies These operations could potentially be used to present geographic information from different scales and granularities Frank (2003) goes a step beyond purely spatial ontologies and argues for the inclusion of the temporal dimension by de- Geospatial and Temporal Semantic Analytics scribing a multi-tier ontology with space-time as the fundamental dimension of physical reality From a Web context, Kolas et al (2005) outline specific types of geospatial ontologies needed for integration of GIS data and services: base geospatial ontology, feature data source ontology, geospatial service ontology, and geospatial filter ontology The base geospatial ontology provides core geospatial knowledge vocabulary while the remaining ontologies are focused on geospatial web services T he S emantic W eb The Semantic Web has received much attention recently Its vision promises an extension of the current web in which all data are accompanied with machine-understandable metadata allowing capabilities for a much higher degree of automation and more intelligent applications (Berners-Lee et al., 2001) To make this idea more concrete, consider the statement “The University of Georgia is located in Athens, GA.” To a human with knowledge of colleges and universities and the geography of the southeastern United States, the meaning of this statement is clear In addition, upon seeing this statement, other related information comes to mind such as professors who work at the University In a Semantic Geospatial Web context (Egenhofer, 2002), this related information would be GIS data and services, such as road network data and facility locations for the Athens area which could be combined with wayfinding services The goal of the Semantic Web is to make the semantics of such data on the Web equally clear to computer programs and also to exploit available background knowledge of related information On the Semantic Web this statement would be accompanied with semantic metadata identifying an instance of the concept “University” with the name “The University of Georgia” Similarly, the instance of City and State, “Athens, GA,” would unambiguously describe the university’s geographic location Note the distinction between semantic metadata describing high-level concepts and relationships and syntactic and structural metadata describing low level properties like file size and format To create this semantic metadata, we must identify and mark occurrences of known entities and relationships in data sources This tagging process is known as metadata extraction and semantic annotation These annotations are especially important for multimedia data, as non-textual data have a very opaque relationship with computers Some examples of annotation of textual and multimedia data are presented in Dill et al (2003), Hammond et al (2002) and Jin et al (2005), respectively To provide ontological metadata in a machine processable form, a standard way to encode it is needed The W3C has adopted Resource Description Framework (RDF)1 as the standard for representing semantic metadata Metadata in RDF is encoded as statements about resources A resource is anything that is identifiable by a Uniform Resource Identifier (URI) Resources can be documents available on the web or entities which are not web-based, such as people or organizations RDF also defines literals which are not real-world entities but values (e.g., Strings, Integers) used to define attributes for resources Relationships in RDF, known as Properties, are binary relationships between a resource and another resource or between a resource and a literal which take on the roles of Subject and Object, respectively The Subject, Predicate and Object compose an RDF statement This model can be represented as a directed graph with typed edges and nodes (see Figure 1) In this graph model, a directed edge labeled with the Property name connects the Subject to the Object RDF Schema (RDFS)2 provides a standard vocabulary for schema-level constructs such as Class, SubClassOf, Domain, and Range In addition, the Web Ontology Language (OWL)3 further extends RDFS by defining additional vocabulary for describing classes and properties (e.g., cardinality, disjointness) Figure illustrates the graph data model of RDF for an 163 Geospatial and Temporal Semantic Analytics example ontology schema and instance data Semantic Analytics Semantic analytics is an emerging form of intelligent information analysis which involves investigation of relationships between entities in populated ontologies and semantic metadata; the latter could be extracted from multiple heterogeneous data sources It can be seen as a combination of querying and knowledge discovery, but it is fundamentally different from statistical data mining because it involves named relationships with well-defined semantics Semantic Web data models such as RDF/RDFS provide an excellent platform for semantic analytics because relationships are first class objects in these data models making it very natural to query and analyze data based on these relationships Our ongoing work in a project titled Semantic Discovery (SemDis)4 addresses key issues in semantic analytics The SemDis project investigates: (1) operators for analyzing complex relationships in ontologies/ metadata, (2) relevance models for ranking com- plex relationships, (3) algorithms for discovering complex relationships, and (4) development of large, populated ontologies Query operators developed for semantic analytics in the SemDis project revolve around the fundamental question of “how is entity A related to entity B?” Anyanwu and Sheth (2003) introduce the concept of semantic associations to help answer such questions A semantic association is described as a complex relationship between two resources in an RDF graph In fact, a semantic association can be defined in terms of connectivity or similarity Two fundamental types of semantic associations are ρ-path (capturing connectivity) and ρ-iso (capturing similarity) Figure illustrates these two types of semantic associations Many useful semantic associations involve some intermediate entities Relationships that span several entities are very important in domains such as national security because they may enable analysts to see the connections between seemingly disparate people, places and events The result set of a semantic association query can involve an extremely large number of paths Figure RDF Metadata Schema-level classes are shown in gray Instance data are shown in white Ovals denote resources, and rectangles denote literals 164 Geospatial and Temporal Semantic Analytics Figure Example semantic associations James Larson (resource &r1) is ρ-path associated with The University of Georgia (resource &r4) because the two resources are connected by a path in the RDF graph, and resource &r5 is ρ-iso associated with resource &r2 because the two resources are involved in instances of two identical schema-level paths: they are both papers authored by university employees leading to information overload To address this problem, we have researched relevance models for ranking semantic associations (Aleman-Meza et al., 2005; Anyanwu et al., 2005) We have also considered subgraph discovery as a complementary solution to discovery and enumeration of semantic associations (Ramakrishnan et al., 2005) In this work, we are interested in finding dense subgraphs containing the “best” set of associations between two resources The concept of semantic associations has been successfully applied in areas such as conflict of interest detection (Aleman-Meza et al., 2006) and searching patent databases (Mukherjea & Bamba, 2004) GEOSP AT IAL AND TE MPOR AL SE MANT IC AN ALYT ICS The basic goal of geospatial and temporal semantic analytics is an extension of thematic analytics which supports search and analysis of spatial and temporal relationships between entities In the following, we present an ontology-based model integrating all three dimensions of data: thematic, spatial and temporal Also, we discuss semantic associations as a means to analyze relationships among the three dimensions Modeling S pace, T ime, and T heme Our current approach to modeling theme, space, and time consists of an upper-level ontology defining a general collection of thematic and spatial entity classes and associated relationships connecting these entity classes We intend for application-specific domain ontologies in the thematic dimension to be integrated into the upper-level ontology through subclassing of appropriate upper-level classes and relationships We make three distinctions of class types in the thematic dimension: Dynamic Entities, Named Places, and Events Dynamic Entities represent those entities with non-stationary (e.g., people, automobiles) or undefined spatial properties (e.g., abstract entities) Named Places are those entities with static spatial properties and clear spatial extents (e.g., a manufacturing plant, an apartment building, and a city) Events are special types of entities which represent oc- 165 Geospatial and Temporal Semantic Analytics currences in space and time (e.g., a car accident or a business meeting) To explain the rationale behind the division of thematic entity classes we must first discuss the geospatial aspects of the model Both qualitative relationships (topology, cardinal direction, etc.) and quantitative relationships like distance should be modeled to support geospatial analytics These are common requirements for geospatial ontologies, so we can utilize existing work on geospatial ontologies from the Semantic Geospatial Web community for this purpose For the remainder of the discussion we will consider a portion of the simple geo-ontology from Jones et al (2004), but it should be noted that our multidimensional model could use any geo-ontology capturing similar basic concepts This ontology models a number of important concepts Two of the main ones are Geographical Place and Footprint Geographical Place represents a geographic feature (man-made or natural) and is analogous to Named Place described previously Footprint models a spatial element; it is a georeferenced point, line, or polygon To give geospatial properties to thematic entities, we adopt the notion of a spatial setting from Worboys & Hornsby (2004) We can define a spatial setting as an instance of the class Footprint To link the thematic ontology with the geo-ontology, we define relationships to connect Event to Footprint and to connect Named Place to Footprint (located_at and has_ footprint, respectively) The remaining aspect of this model is temporal information Gutierrez et al (2005) present a framework to incorporate temporal reasoning into RDF Their framework defines a temporal label for an RDF statement The label denotes the times that the statement or fact holds We can use this framework to give temporal properties to all facts in the ontology This provides temporal settings for relationships in thematic ontologies and provides spatio-temporal settings for relationships connecting thematic ontologies to geo-ontologies Figure illustrates this model 166 S patiotemporal T hematic C ontexts: Inter-D imension C onnections A context intuitively specifies a template for connecting entities in different dimensions; it defines the relevant classes, entities and relations for making the connection You may notice that Dynamic Entities have no direct relationship with Footprints in this model However, Dynamic Entities participate in various thematic relationships with Named Places and Events, so it is through these connecting thematic relationships that Dynamic Entities can obtain different geospatial and temporal properties The thematic relationship connecting the Dynamic Entity provides a context for the connection and allows us to analyze the geospatial and temporal properties of Dynamic Entities with respect to different thematic contexts For example, a person’s spatiotemporal properties with respect to employment relationships (where he works and when he works there) will differ from his spatiotemporal properties with respect to residence (where he lives and when he lives there) Note that this allows us to semantically query geospatial information because we are selecting regions of space using explicit semantic relationships between entities We can build the notion of context around semantic associations and time intervals A thematic context is a schema-level ρ-path association representing the type of an instance-level ρ-path association The type of the association is determined by the class types and property types of the entities and relationships on the path For example, the association Bob - works_ for The University of Georgia - located_in - Athens would have the type (Person, works_ for, University, located_in, City) A temporal context is represented by a time interval An association matches a temporal context if all statements (i.e., Resource Description Framework (RDF) triples) making up the association are valid at some time t within the given time interval A spatiotemporal Geospatial and Temporal Semantic Analytics Figure Ontology-based model of space, time, and theme Events and Named Places are directly linked with footprints which record their geographic location Temporal intervals on relationships denote when the relationship holds Triangles represent arbitrary subclasses of Event, Dynamic Entity, and Named Place thematic (STT) context is a temporal context in combination with a thematic context containing the class Footprint Consider the example of analyzing historical entities and events of WWII as an illustration of the use of STT contexts Suppose we want to know which Military Units came within close spatiotemporal proximity of the 3rd Armored Division during November 1944 The following STT context, which connects Military Unit to Footprint, can be used for this analysis: (Military Unit, participates_in, Battle, located_at, Footprint) with a time interval covering November 1944 Starting from the 3rd Armored Division, we can traverse instances of this context to retrieve the associated geospatial regions Next, spatial relationships, such as intersects, are used to find close spatial regions (Footprints) from which instances of the battle participation context can be traversed to find those Military Units in close spatiotemporal proximity R elated Approaches There is no shortage of spatiotemporal data models for temporal GIS Pelekis et al (2004) identify 10 distinct spatiotemporal data models Of these, the three domain model (Yuan, 1994, 1996) is most relevant to our approach This model represents semantics, space and time separately To represent spatiotemporal information in this model semantic objects are linked via temporal objects to spatial objects This provides temporal information about the semantic (thematic) properties of a given spatial region This is analogous to temporal located_at and has_ footprint relation- 167 Geospatial and Temporal Semantic Analytics ships in our model In the three-domain model there is a one-to-one mapping from semantic and temporal objects to spatial objects and from spatial and temporal objects to semantic objects This is the key difference with our envisioned approach because we incorporate non-spatial entities into the semantic domain and provide the notion of a thematic context to link these entities to the spatial domain in a variety of ways (many-to-many) Our Semantic Web style approach has the potential to incorporate a larger amount of non-spatial information by utilizing indirect connections to the spatial domain, and it allows the direct application of existing thematic analytics techniques CONC LUS ION AND FUTURE D IRECT IONS In this article, we discussed the emerging field of semantic analytics and our thoughts on extending semantic analytics from the purely thematic dimension to all three dimensions of theme, space, and time We presented background work from the Semantic Web community and described how these new technologies can provide a means for semantic analysis of geospatial and temporal information Semantic analytics has applications in general areas like document search and analysis and in more focused domains like Bioinformatics In the future, we see semantic analytics that span the thematic, geospatial, and temporal aspects of information gaining more popularity Diverse applications of such a capability include emergency and natural disaster response, homeland and national security, and education and training REFERENCES Agarwal, P (2005) Ontological considerations in GIScience International Journal of Geographical Information Science, 19(5), 501-536 168 Aleman-Meza, B., Halaschek-Wiener, C., Arpinar, I B., 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Search Results on the Semantic Web Paper presented at the Fourteenth International World Wide Web Conference, Chiba Japan Berners-Lee, T., Hendler, J., & Lassila, O (2001) The Semantic Web - A new form of Web content that is meaningful to computers will unleash a revolution of new possibilities Scientific American, 284(5), 34-+ Dill, S., Eiron, N., Gibson, D., Gruhl, D., Guha, R V., Jhingran, A., et al (2003) SemTag and Seeker: Bootstrapping the Semantic Web Via Automated Semantic Annotation Paper presented at the Twelfth International World Wide Web Conference, Budapest, Hungary Egenhofer, M J (2002) Toward the Semantic Geospatial and Temporal Semantic Analytics Geospatial Web Paper presented at the Tentch ACM International Symposium on Advances in Geographic Information Systems, McLean, VA Fonseca, F T., Egenhofer, M J., Agouris, P., & Camara, G (2002) Using Ontologies for Integrated Geographic Information Systems Transactions in GIS, 6(3), 231-257 Frank, A (2003, September 23, 2003) A Linguistically Justified Proposal for a Spatio-Temporal Ontology Paper presented at the Workshop on Fundamental Issues in Spatial and Geographic Ontology, Ittingen, Switzerland Gruber, T R (1993) A Translation Approach to Portable Ontology Specifications Knowledge Acquisition, 5(2), 199-220 Gutierrez, C., Hurtado, C., & Vaisman, A (2005) Temporal RDF Paper presented at the European Conference on the Semantic Web, Heraklion, Crete, Greece Hammond, B., Sheth, A., & Kochut, K (2002) Semantic Enhancement Engine: A Modular Document Enhancement Platform for Semantic Applications over Heterogeneous Content In V Kashyap & L Shklar (Eds.), Real World Semantic Web Applications (pp 29-49): Ios Press Inc Jin, Y., Khan, L., Wang, L., & Awad, M (2005) Image annotations by combining multiple evidence & wordNet Paper presented at the Thirteenth Annual ACM International Conference on Multimedia, Hilton, Singapore Jones, C B., Abdelmonty, A I., Finch, D., Fu, G., & Vaid, S (2004) The SPIRIT Spatial Search Engine: Architecture, Ontologies, and Spatial Indexing Paper presented at the Third International Conference on Geographic Information Science, Adelphi, MD, USA Kolas, D., Hebeler, J., & Dean, M (2005) Geospatial Semantic Web: Architecture of Ontologies Paper presented at the First International Conference on GeoSpatial Semantics, Mexico City, Mexico Kuhn, W (2001) Ontologies in support of activities in geographical space International Journal of Geographical Information Science, 15(7), 613 - 631 Kuhn, W., & Raubal, M (2003) Implementing Semantic Reference Systems Paper presented at the 6th AGILE Conference on Geographic Information Science, Lyon, France Mukherjea, S., & Bamba, B (2004) BioPatentMiner: An Information Retrieval System for BioMedical Patents Paper presented at the Thirtieth International Conference on Very Large Data Bases, Toronto, Canada Pelekis, N., Theodoulidis, B., Kopanakis, I., & Theodoridis, Y (2004) Literature Review of Spatio-Temporal Database Models The Knowledge Engineering Review, 19(3), 235-274 Ramakrishnan, C., Milnor, W H., Perry, M., & Sheth, A P (2005) Discovering Informative Connection Subgraphs in Multi-relational Graphs SIGKDD Explorations, 7(2), 56-63 Sahoo, S S., Thomas, C., Sheth, A., York, W S., & Tartir, S (2006) Knowledge Modeling and its Application in Life Sciences: A Tale of two Ontologies Paper presented at the Fifteenth International World Wide Web Conference, Edinburgh Scotland Sheth, A P., & Ramakrishnan, C (2003) Semantic (Web) Technology In Action: Ontology Driven Information Systems for Search, Integration and Analysis IEEE Data Engineering Bulletin, 26(4), 40-47 Worboys, M., & Hornsby, K (2004) From Objects to Events: GEM, the Geospatial Event Model Paper presented at the Third International Conference on Geographic Information Science, Adelphi, MD, USA Yuan, M (1994) Wildfire Conceptual Modeling 169 Geospatial and Temporal Semantic Analytics for Building GIS Space-Time Models Paper presented at the GIS/LIS, Pheonix, AZ tion about content based on a shared metadata model (e.g., ontology) Yuan, M (1996) Modeling Semantical, Temporal and Spatial Information in Geographic Information Systems In M Craglia & H Couclelis (Eds.), Geographic Information Research: Bridging the Atlantic (pp 334-347): Taylor & Francis Semantic Web: A framework that allows data on the web to be shared and reused across application, enterprise and community boundaries The framework is realized through metadata annotations serialized using standard representations like RDF KEY TER MS Ontology: A specification of a conceptualization consisting of a hierarchy of class types and non-hierarchical relationships between classes Resource Description Framework (RDF): A Framework for describing resources on the web RDF makes statements about resources consisting of a Subject, Predicate, and Object which translates to a directed, labeled graph Semantic Analytics: Analyzing, searching, and presenting information using explicit semantic relationships between known entities Semantic Annotation: Identifying and marking occurrences of ontological entities and relationships in raw data (e.g., documents, images, and digital geographic data) Semantic Association: A complex relationship between two resources in an RDF graph Semantic Associations can be a path connecting the resources or two similar paths in which the resources are involved Semantic Geospatial Web: The application of Semantic Web concepts and technologies for the sharing and reuse of geographic data and services on the web Semantic Metadata: Metadata that describe contextually relevant or domain specific informa- 170 Spatiotemporal Thematic Context (STT Context): A specification of the type of ρ-path semantic association used to connect thematic entities to geospatial footprints It is specified using a schema-level semantic association in combination with a time interval Uniform Resource Identifier (URI): Strings that uniquely identify resources on the web E ndnotes http://www.w3.org/RDF/ http://www.w3.org/TR/rdf-schema/ http://www.w3.org/TR/owl-features/ http://lsdis.cs.uga.edu/projects/semdis/ 171 Chapter XXII Geospatial Image Metadata Catalog Services Yuqi Bai George Mason University, USA Liping Di George Mason University, USA Aijun Chen George Mason University, USA Yang Liu George Mason University, USA Yaxing Wei George Mason University, USA Abstr act Three public geospatial image catalog services, FGDC Clearinghouse, NASA ECHO and GMU CSISS CSW, were reviewed, considering the following aspects: metadata generation, metadata ingestion, catalog service conceptual schema, query protocols and system distribution This review results show how it is becoming possible to query metadata holdings through public, standard Web-based query interfaces It also show that the catalog service providers still must define a catalog service schema that meets their particular needs Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited ... a lary D epartm en t [11 , ] K [11 ,4 ] To ys [5 , ] K [4 , ] S h o e s [5 , ] K [0 , ] K [0 , ] H a rd w a re [4 , ] K [4 , ] C lo th in g [0 ,4 ] U [5 , N o w ] [0 ,4 ] U [5 , [0 ,4 ] U [5 ,... fuzzy controllers International Jouranl of Intelligent Systems, 14( 4), 41 9 -44 7 Zadeh, L A (1996, September) The Key Roles of Information Granulation and Fuzzy logic in Human Reasoning Paper presented... Egenhofer, C Freksa, and H Miller (Eds.), Proceeding of GIScience 20 04, Lecture Notes in Computer Science, 32 34, Springer, Berlin, (pp 327- 343 ) Yuan, M (1999) Use of a three-domain representation