Some classes of fuzziness measures from local divergences

The aim of this paper is to study divergence measures, a very important concept in Questionnaire Theory, in the framework of fuzzy set theory, and also to show some relationships between divergence measures and fuzziness measures. Thus, we propose a way of measuring the fuzziness of a fuzzy set by means of a function of the divergence between this fuzzy set and its complementary, that is, the fuzziness of any fuzzy set à is a function of the difference between à and Ã^c. We can also measure the fuzziness of a fuzzy set by comparing, by means of a divergence measure, the fuzzy set with its closest crisp set or with the equilibrium. Therefore, using divergence measures, we construct a wide clas of fuzziness measures.