Fuzzy Regression Clustering and Generalized Measures of Fuzzy Information

Abstract

The objective of the thesis entitled, Fuzzy Regression, Clustering and Generalized Measures of Fuzzy Informationquot, is to study fuzzy regression, fuzzy clustering with application, to characterize new measures of fuzzy information and to study their various generalizations. Fuzzy set theory has capability to describe the uncertain situations which contain ambiguity and vagueness. Fuzziness is sometimes found in some decisions, in our thoughts and in the way of processing the information. newlineAs probabilistic entropyquot measures uncertain degree of the randomness in a probability distribution, Fuzzy entropy measures fuzziness of a set which arises from the intrinsic ambiguity or vagueness carried by the fuzzy set. The entropy of a fuzzy event is different from the classical Shannon entropy, as no probabilistic concept is needed in order to define it. We should note that fuzzy entropy deals with vague and ambiguous uncertainties, while Shannon entropy deals with probabilistic uncertainties. There are number of measures of fuzzy entropy corresponding to the various probabilistic entropy measures have been proposed and studied in literature. newline newline