SPATIAL OBJECT MODELING IN FUZZY TOPOLOGICAL SPACES WITH APPLICATIONS TO LAND COVER CHANGESAnahid Bassiri, Mail id: Anahid_bassiri1984@yahoo.com Ali A. Alesheikh, Mail id: alesheikh@kntu.ac.ir Mohammad R. Malek Mail id: malek@ncc.neda.net.ir Dept. of Geodesy and Geomatics Eng., K.N.Toosi University of Technology, Mirdamad Cross, Valiasr St., Tehran, IRAN, Abstract Fuzzy spatial objects have become more and more important in GIS applications. When spatial phenomena are generalized by the crisp form, a lot of quantitative information is lost. Land cover as a fuzzy spatial object should be modeled in a fuzzy framework. In addition, the relationships between fuzzy spatial objects are much more complicated than that are defined between crisp spatial objects. The purpose of this paper is to construct topological relationships, as one of the most important characteristics of spatial object, based on fuzzy logic with the application of land cover. An area in Tehran which has lots of land cover types was considered. Introduction Many natural phenomena have fuzzy characteristics. Fuzziness in such phenomena should be considered in all the aspects of a GIS to have a better understanding of the real world. Fuzzy spatial objects are those with indeterminate boundaries, hence the objects have some degree of membership belonging to a category. In order to define and model fuzzy spatial objects such as land covers, it is necessary to investigate their fuzzy topology. There are various methods to construct the spatial fuzzy topology, namely: point based methods such as: n-intersection matrix that can be based on fuzzy set theory; and intuition fuzzy set theory. Another class of Fuzzy representation is logic base that can be named as point less logic such as RCC which is based on connection as a relation. (Muller Philippe) Landuse and landcover; most of which is obtained from the classification results of satellite images or air-photos; may be good examples of a fuzzy spatial objects. In general, after classification, each pixel in the image is assigned to a particular land cover type; therefore, a pixel belongs to one and only one type. (Tang,2004) In reality, all pixels contain a number of different contributing land use types. In general landcover is continuously distributed in nature, and there is seldom a clear boundary between different natural phenomena. In this study landcover as a spatial fuzzy object is modeled. Results are scientifically assessed in the paper and showed the superiority of the model over conventional ones. Land resources pose one of the biggest problem all around the world. Because of the growth in population and the economy, the contradiction between land resources and humans is becoming more and more severe. On the one hand, more arable land is necessary to feed more people. On the other hand, the growth of the economy accelerates urbanization, which always results in a decrease in cultivated lands. In Iran as a developing country Land Use and Land Cover (LULC), is taken into the great consideration by the government because the government may introduce the correct land policies to achieve the dynamic balance of cultivated lands. (Tang,2004) Among the most important characteristics of qualitative properties of spatial data and perhaps the most fundamental aspect of a space are topology and topological relationships. Topological relations between spatial objects like meet and overlap are such relationships that are invariant with respect to specific transformations due to homeomorphism (Malek,2001). There are various methods to construct the topology, namely: point based methods such as n-intersection matrix that could be based on fuzzy set theory; intuition fuzzy set theory; and rough set theory. The rest are logic base and constructed based on relationships, which can be named point less such as Region Connection Calculus which is based on connection as a relation or some other which are based on influenceability. (Malek,2001) As a case study a part of Iran which has different parcels and also different land cover types is selected. Fundamental concepts for uncertainty modeling of spatial relationships are analyzed from the view point of fuzzy logic. It is demonstrated that how fuzzy logic can provide a model for fuzzy region; i.e., regions with indeterminate boundaries. Fuzziness Almost all the information that we possess about the real world is uncertain, incomplete and imprecise. Uncertainty or fuzziness may include the following aspects (Worboys 1998):
Zadeh generalized a fuzzy set from classical set theory by allowing intermediate situations between the whole and nothing. For a fuzzy set, a membership function is defined to describe the degree of membership of an element to a class. The membership value ranges from 0 to 1, where 0 shows that the element does not belong to a class, 1 means “belong”, and other values indicate the degree of membership to a class. Fuzzy set theory is the extension of classical set theory by allowing the membership of elements to range from 0 to 1. Let X be the universe of a classical set of objects. Membership in a classical subset A of X is often viewed as a characteristic function µ(x) (x is a generic element of X) from X to {0,1} (Dubois and Prade 1980). {0,1} is called a valuation set. If the valuation set is allowed to be the real interval [0,1], A is called a fuzzy set. µ(x) is the membership value (or degree of membership) of x in A.  Fuzzy topology Fuzzy topology is constructed based on fuzzy sets. It is an extension of general (crisp) topology and has several definitions. The notion introduced here is based on the definition proposed by Chang (1968).   Figure1: The concept of Interior, Exterior, and Boundary of a set The boundary of a subset may also have its interior and its boundary of the boundary. On the other hand, the interior and the closure of a subset also have their boundaries. For example The boundary of the boundary of a fuzzy set A is the union of the boundary of the closure and the boundary of the interior of a fuzzy set. Based on this information one can define a maximum of 5 areas for each object: interior, boundary of the boundary, interior of the boundary, boundary of the interior, exterior. Consequently, one can develop the traditional 9-intersection matrix into 25-intersection ones. Generating Fuzzy Land Cover Objects and their topological relationships The importance of land cover needs no more explanation, since it plays a fundamental role in a lot of fields. We address the method for forming fuzzy land covers from Spot images. First of all, these images were classified. Because we needed the membership values so some special programs were developed to achieve our purpose. Consequently, we can assign the pixels into the land cover classes and have their memberships. It seems to have a set whose elements are the pair of pixels and their memberships. So the basis of our study is the fuzzy set. We can define the interior and the boundary of the boundary and boundary of the interior and the exterior. So it is possible to show the relationships between the region into the 25-intersection matrix. It is possible to compare the result with the newer result which is obtained from update images in order to finding the changes and query the spatial fuzzy object. The comparison of land cover maps is the basis for many dynamic analysis of land use and land covers. The traditional method usually compares the differences based on a crisp pixel-by-pixel method. But in this way our judgment is much more precise.  Figure 2: space image (Spot ) Conclusion: During the flowering period and on the basis of degree hours accumulation, this model can forecast the risk of infection of Ervina in host tree.The minimum four-day Celsius degree hour accumulation that appeared to be necessary for infection to occur during a blossom wetting was set at approximately 270 ºC (500 F). The degree hours can be calculated with bellow equation: References:
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