Fuzzy Sets and Fuzzy Logic with Applications

Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. However, there are many complicated problems in economics, engineering, environment, social science, medical science, etc., that involve data which are not always all crisp. We cannot successfully use classical methods because of various types of uncertainties present in these problems. There are theories, viz., Theory of Probability, Theory of Fuzzy Sets, Theory of Intuitionistic Fuzzy Sets, Theory of Vague Sets, Theory of Interval Mathematics, Theory of Rough Sets and Soft Set which can be considered as mathematical tools for dealing with uncertainties and real life problems inherently involve uncertainties, imprecision and vagueness. Fuzzy Logic is a form of soft computing method which accommodates the imprecision of the real world whereas traditional hard computing, soft computing exploits the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness.In this book all have been deliberated thoroughly with various illustrations and everybody must feel comfortable to understand fuzziness and uncertainties independently.