Measures of fuzziness and entropy of fuzzy information

Vagueness of knowledge results from the imprecision and uncertainty of knowledge. In fuzzy theory, much attention has being paid to the measure of fuzziness of a fuzzy subset, while entropy, as a measure of uncertainty, plays a significant role in the field of information theory. This paper discusses, when there is or not a probability distribution on the non-empty definite universe U, the measure of fuzziness and entropy of a fuzzy subset and the conditional fuzzy entropy of a fuzzy subset, when existing additional probability information and fuzzy information.