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The Enhancement of ArcGIS with Fuzzy Set Theory
Tahsin A. Yanar and Zuhal Aky¨urek
Introduction
Geographic Information Systems (GIS) are computer-based systems that store and
process (e.g. manipulation, analysis, modeling, display, etc.) spatially
referenced data at different points in time [1]. Geographic data, stored and
processed Since pervasive imprecision of the real world is unavoidably reduced to artificially precise spatial entities when the conventional crisp logic is used for modeling, an alternative approach fuzzy set theory, which provides a formal framework to represent and reason with uncertain information, can be used to model the real world. In this study, a commercial GIS software namely ArcGIS, which is a major GIS desktop system, is enhanced with fuzzy set theory. Component Object Model (COM) environment is used for developing fuzzy inference system for ArcMap, where COM is a protocol that connects one software component, or module, with another and defining the manner by which objects interact through an exposed interface. The implementation of the fuzzy inference system tool for a commercial GIS product, ArcMap is divided into two parts: 1) Fuzzy Inference Engine implementation, 2) Fuzzy Inference System Module implementation. The general architecture design and workflow of the fuzzy inference system for cell-based information modeling is shown in Fig. 1.
The interface is a collection of logically related operations that define some behavior [5]. However, commercial GIS application and Fuzzy Inference System act as two separate applications. Fuzzy Inference System is designed as an ActiveX module. Within the Fuzzy Inference System Module, precompiled libraries Fuzzy Inference Engine and ESRI ArcObjects Library are used. Since Component Object Model (COM) environment is used, applications can interact with objects only through their public interfaces. ESRI applications are COM clients; their architecture supports the use of software components that adhere to the COM specification [6]. Hence, components can be built with different languages including Visual Basic and Visual C++, and these components can then be added to the applications easily. Visual Basic and Visual C++ are used to create COM components to enhance the functionality of cell-based information modeling in the form of extensions. An extension is a component or a set of components that implements an interface that is expected by the application and registers itself with the application so that it may be loaded at the appropriate time. End-users can control what pieces of functionality are installed on a machine or loaded at run time. ArcGIS provides developers the key benefit of standard mechanisms for plugging extensions and other components into the system [6]. The developed system can be viewed as a scheme for capturing experts’ knowledge on a specific problem. Through the use of linguistic variables, experts’ experiences in the problem domain, even though they naturally involve imprecision, are converted to fuzzy rules. Therefore, the proposed system allows users to handle imprecision in the decision-making process by knowing only the fuzzy logic background. Easy to use graphical user interfaces (GUIs) enable users to define fuzzy rules without necessarily knowing all the underlying concepts of the fuzzy set theory [7]. Applications One of the main tasks in GIS is making decisions using information from different layers. The decision-making is affected by many factors and sometimes needs many criteria. In numerous situations involving a large set of feasible alternatives and multiple, conflicting and incommensurate criteria, it is difficult to state and measure these factors and criteria [8]. Indeed most of the information about the real world contains uncertainties. In conventional decision-making process, a common type of operation is threshold model. For each of the criterion the study area is classified into two subregions describing whether a property value of a specific location is in the defined limit values or not. Then, maps produced for each criterion are overlaid using logical connectives (i.e., Boolean overlay). Each criterion can be weighted based on their importance to decision-maker.
Such models can cause problems since they are inherently rigid. On the other hand, the developed system can be used to make decisions capturing uncertain information using fuzzy set methodologies. In the sequel a set of criteria is used to select suitable sites for industrial development. Associated input raster maps are: “slope map” is depicted in Fig. 2, “proximity to roads” is depicted in Fig. 3, and map showing “proximity to town” is depicted in Fig. 4. To find Boolean answer to site selection problem, first for each criterion (i.e., slope, distance to road and distance to town) a map containing 0s and 1s is produced. Pixel values that are less than the threshold values are assigned one in the output map and zero otherwise.
Second, theseusing linguistic terms instead of precise numerical values. As it is seen, rule is very similar to the criteria posed by the experts in the domain. Membership functions for linguistic terms are depicted in Fig. 6. Membership functions can be chosen by the user arbitrarily based on user’s experience, hence the membership functions for two user could be quite different depending upon their experiences and perspectives. Before starting to design membership functions, associated input raster maps are added to a map in the ArcMap (Fig. 7).
The developed system can be used not only to make decisions but also to
classify the study area into classes, which are defined as linguistic
terms (i.e., classes do not have sharply defined
intervals). For the developed system, classification
is similar to making decisions using rules. Using fuzzy logic methodologies
in the classification avoid the high loss of information, which occurs
when data are processed using conventional classification methods [9].
Since 13 fuzzy logic
approach allows a user-defined tolerance to the class limits in the
form of transition zones, intermediate conditions can be better described
and gradual changes or transitions in the property
values can be better expressed. Therefore, more
continuous approach to classification leads to more realistic
assessment of continuous landscape. Discussion The classical set theory used in conventional GIS software imposes artificial precision on inherently imprecise information about the real world and fails to model the way of human thinking about the real world. Fuzzy logic offers a way to represent and handle uncertainty present in the continuous real world. Extending GIS with fuzzy set theory assist the GIS user to make decisions using experts’ experiences in the decision-making process. Experts’ experiences and human knowledge described in natural languages can be captured by fuzzy if-then rules. Therefore, decision-makers can express their constraints through the use of natural language interfaces. A GIS with fuzzy set theory enable decision-makers to express imprecise concepts that are used with geographic data. The capacity of taking linguistic information from decision-makers permits the decision-maker to more easily develop the criteria and softens the constraints and goals in order to find suitable sites. In addition, decision-maker has no longer need to produce maps for each criterion. Moreover, all locations in the input space are mapped to a degree of suitability using property values of locations and rules defined by the decision-maker. Therefore, values of locations in the fuzzy output map derived from fuzzy inference process can be available in orderly manner. Note that Boolean result contains only a set of 1 and 0 values. Another advantage of fuzzy inference is that fuzzy result of a decision-making process provides a set of locations whose attribute values partially satisfy the constraints posed by the user. The proposed system provides not only a powerful tool to the GIS user to make decisions in vague concepts but also the system has easy to use graphical user interfaces which enable even a newcomer to fuzzy set theory to define rules without necessarily knowing all the underlying concepts of the fuzzy set theory, is not dedicated to a specific GIS problem, covers the most commonly used membership functions, provides different inference methods and aggregation methods, has different operators for set operations (i.e., conjunction and disjunction operators), 14 offers different defuzzification methods, and is rich with the number of possible designs. This richness of the system allows GIS users to approximate various complex ill-defined problems in decision-making processes and classification. References [1] S. Aronoff, Geographic Information Systems:A Management Perspective, WDL Publications, Ottawa, 1989. [2] F. Wang, G. B. Hall, Fuzzy representation of geographical boundaries in gis, Int. Journal of GIS 10 (5) (1996) 573–590. [3] P. A. Burrough, Principles of Geographic Information Systems for Land Resource Assessment, Claredon Press, Oxford, 1986. [4] G. B. M. Heuvelink, P. A. Burrough, Developments in statistical approaches to spatial uncertainty and its propagation, Int. Journal of GIS 16 (2) (2002) 111–113. [5] M. Kirtland, Designing Component-Based Applications, Microsoft Press, 1999.
[6] ESRI, ArcObjects 8.1 Developer Help, Environmental Systems Research [7] T. A. Yanar, The enhancement of the cell-based gis analyses with fuzzy processing capabilities, Msc. thesis, Middle East Technical University (2003). [8] J. Malczewski, A gis-based approach to multiple criteria group decision-making, Int. Journal of GIS 10 (8) (1996) 955–971. [9] V. J. Kollias, D. P. Kalivas, The enhancement of a commercial geographical information system (arc/info) with fuzzy processing capabilities for the evaluation of land resources, Computers and Electronics in Agriculture 20 (1998) 79–95. |
