الفهرس 
Topological StructuresOnly 14 pages are availabe for public view
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Abstract
The aim of this thesis is to illustrate how to use topological notions to construct the connections between rough sets and mathematical morphology. Mathematical morphology is an active, growing area of image processing and analysis. It is based on set theory and topology.The mathematical morphology was introduced mainly to deal with shapesin images. In this thesis, we provide new operators and concepts of the mathematical morphology through the concepts of set theory and topological spaces. The structural element plays an important and influential role in mathematical morphology, so, we studythe effect of using the global/local structure element on the properties of sets when applying the proposed morphological operators.Based on the deduced global/local structure elements,the neighborhood concept and system of neighborhood structure elements is to be constructed.Also, several operators are introduced using these structure elements, such as:neighborhood-dilation and neighborhood-erosion. Moreover, the properties of the proposed mathematical morphological operators are deduced and proven. Furthermore, an empirical information system is used to experiment with the proposed operators and compared with the concepts derived from rough set theory. Finally, two novel accuracy measurements are introduced using the concept of the proposed neighborhood morphological operators, namely,the morphological accuracy and weighted morphological accuracy.
To extend our work, we apply the proposed operators for some information systems. One of the vital dealings with these data stored in information systems is to be classified into a set of categories or clusters. Cluster analysis is the formal study of algorithms and methods for grouping or classifying data. We propose a novel clustering algorithm namely, the morphological accuracy clustering algorithm (MAC-algorithm).The proposed algorithm uses a morphological accuracy measure to define the centroid of the cluster. The empirical results show that our proposed algorithm reaches steady clustering in fewer iterations than dose the k-mean algorithm. Moreover, the clusters deduced using the k-mean algorithm are sensitive to the choice of the initial centroid’s maid by the user.
Attribute reduction, which involving high-dimensional descriptions of input features (attributes) is an important preprocessing step for data mining and has become a hot research topic in machine learning. It is therefore not surprising that much research has been done on dimension reduction.We propose a novel attributes’ reduction technique for information systems. The proposed technique namely, morphological accuracy reduction (for short, MAR) computes morphological accuracy using morphological operators (neighborhood-erosion, neighborhood-dilation). Compared with reduction using nanotopology, the experimental results show that the proposed MAR method is an efficient algorithm for reducingattributes and calculating core attributes. The main advantage of the new method is that it helps to reduce the amount of data without losing useful information, saves time and reaches the best core in fewer steps.
Key words:mathematical morphology, topological space, rough set theory, information system, reductions attribute, nano-topology, supra-topology, data clustering, neighborhood dilation, neighborhood erosion, morphological accuracy, k-mean cluster, k-medoid cluster, morphological accuracy reduction.