Fuzziness Measure in the Pliant System: The Vagueness Measure

Abstract

The basic idea of fuzzy sets is the introduction of the membership function, which replaces the classical characteristic function. It is an interesting question to learn how close the membership function is to the characteristic function, when we use a certain class of membership functions. This measure is called the fuzziness measure.
Below we shall present an operator-dependent fuzziness measure called the vagueness measure. We will show that this measure satisfies the usual classical assumptions for the fuzziness measure. In addition, we will show that there is a connection between this measure and the entropy function.