Topological Applications on Fuzzy Relations

Topology and fuzzy set theory underlay the development of many application fields that help decision maker, the arithmetic over prime numbers leads to generation of perfect codes for secure transmission of data on the Internet; and infinite dimensional representations of groups enable the design of large, economically efficient networks of high connectivity in telecommunications. Topology is defined as it uses elastic instead of strict Acaldine direction. As we can defined it as the unquantitive geometry. This book consists of four chapters, first chapter presented main information and definitions to fuzzy, rough, intuitionistic sets and the relations with these sets, second chapter we suggested a method to find fuzzy sets and another intuitionistic fuzzy sets based on our information and the results of these researches related to this method. Characterizations and properties for the suggested notices are introduced. The third chapter we introduce the concept of fuzzy relation which is applied to construct fuzzy topology and crisp topology on the universe of data in databases.