Several new classes of measures of fuzziness

The authors introduce two new general classes of measures of fuzziness, called the additive and multiplicative classes. Usually three axioms are required for fuzziness measures. The classes not only satisfy these three basic axioms, but also two other desirable axioms. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Constructing a measure of fuzziness under each of these classes is simple, as the required functional form does not have restrictions. It is demonstrated that several existing measures of fuzziness are special cases of these new classes