On generalized fuzzy information measures and fuzzy clustering techniques

Abstract

The new measures of fuzzy information and to study their various properties, to study the fuzzy clustering techniques with application to dynamic pattern recognition techniques. Fuzzy set theory has capability to describe the uncertain situations, containing ambiguity and vagueness. Fuzziness is found in our decision, in our thinking, in the way we process information and particularly in our language. Probabilistic entropy measures uncertain degree of the randomness in a probability distribution, while the 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. In literature, a number of measures of fuzzy entropy corresponding to the various probabilistic entropy measures have been proposed and studied. The new measures of fuzzy information and to study their various properties, to study the fuzzy clustering techniques with application to dynamic pattern recognition techniques. Fuzzy set theory has capability to describe the uncertain situations, containing ambiguity and vagueness. Fuzziness is found in our decision, in our thinking, in the way we process information and particularly in our language. Probabilistic entropy measures uncertain degree of the randomness in a probability distribution, while the 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. In literature, a number of measures of fuzzy entropy corresponding to the various probabilistic entropy measures have been proposed and studied.