On Topological Nearness. Topological Near Sets Approaches to Set Aproximations

      Аннотация: Science is the only way to solve human problems. Mathematics is a cognitive framework, which regulates and codifies the science in all its aspects. To understand the mysterious data and extract knowledge from it, we must be find new ways to deal with it. The problem considered in this book is the approximation of sets of perceptual objects that are qualitatively near each other. Near sets theory grew out of the idea that two or more rough sets can share objects with matching descriptions. The main advantage of rough set and near sets theories in data analysis is that, it does not need any preliminary or additional information about data. Most real life situations need some sort of approximation to fit mathematical models. One of the most powerful notions in system analysis is the concept of topological structures. The purpose of this book is to put a starting point for the applications of abstract tpological theory into near sets analysis by using general relations, near open sets and different neighborhoods. Finally, we introduce nearness relations in a multi-valued systems.

Ключевые слова: Topology, Rough set approximations, Near sets, Near open sets, Multi-Valued system