الفهرس 
Chapter-1- Pretopological Spaces and Fuzzy Pretopological SpacesOnly 14 pages are availabe for public view
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Abstract
Due to the tremendous use of computers, the need for dealing with digital information continues to grow. This has led to the need for constructing a structure for saving information in a way that eases data retrieval and processing. An information system is a table form that contains all the data needed for a user to reach a decision. In this work, a mathematical representation of the information system is to be presented. The proposed representation takes advantage of the properties of a pretopological space which is deduced from the information system under study. To this end, the proposed methodology is twofold; the first is to construct a crisp pretopological space represent the information system, while the second depends on constructing a weighted pretopological space using the concepts of fuzzy pretopological space to represent the information system. For that purpose, we propose to construct the crisp pretopological space to represent the information system in two ways; the first one is by computing the similarity between the objects of the information system. While, the second way depends on computing the distance between the objects of the information system. On the other hand, we use the correlation coefficient between the objects of the information system in order to construct a fuzzy pretopological space to represent the information system under consideration. Whereas the dimension of the deduced space is high, our aim is to produce an automated methodology for reducing the dimension by choosing core attributes. In this thesis, our proposed method, we use the concepts inherited from the pretopological spaces to construct a pretopology for the information system in hand, hence using its properties to reduce the number of its attributes. The properties and some basic operations relevant to the new type were investigated.
Therefore, the thesis will be divided into three parts; in the first part, we devoted to propose a strategy for attributes’ reduction based on a similarity relation and pretopological concepts and this part will be covered in chapter two. The second part of this thesis introduces a methodology for attributes’ reduction by measuring the accuracy degree of decision sets in an information system and this part will be covered in chapter three. The third part of this thesis introduces a weighted pre-topology that represents the information system under consideration and this part will be covered in chapter four.