الفهرس 
Topology and Uncertainty TheoriesOnly 14 pages are availabe for public view
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Abstract
Topology is generally considered to be one of the three linchpins of modern abstract mathematics (along with analysis and algebra). In the early history of topology, results were primarily motivated by investigations of real-world problems. Rough set theory (RST) is one of the newest mathematical tools to deal with the imperfect knowledge. This theory depends on a special topological structure (a quasi discrete topology). In this thesis, the fundamental concepts of RST have been presented. As well as, several extensions of this theory based on family of general relations have been exhibited. The concept of solitary set has been introduced. We have generalized one of these extensions to a family of general relations. And, also we have extended the concept of solitary set to our extension. The concept of K- step relation has been showed. We have generalized the K-step relation to a family of general relations. Our generalizations have been studied and compared. Also, we have introduced an extension of RST depending on topology theory, and the concept of variable precision [by ziarko]. This extension has treated the problem of discrete topology that may appear when you use some topological generalizations of rough set model (RSM) in data analysis.