On fuzzy-qualitative descriptions and entropy (Q289016)

In this paper, a genereralization of qualitative labels and qualitative descriptions over a well-ordered set using fuzzy sets is proposed. The intended application is in assessments of a group of experts evaluating features or objects by means of linguistic descriptions. A fuzzy-qualitative label is such a fuzzy set whose core is a (crisp) qualitative label. Fuzzy-qualitative labels are provided with a lattice structure. A fuzzy-qualitative description of a set \(\Lambda\) by the set of fuzzy-qualitative labels \(\mathcal{L}\) is then defined as an \(\mathcal{L}\)-fuzzy set on \(\Lambda\). Finally, the entropy of a fuzzy-qualitative description \(Q\) using a measure of specificity Sp and a normalized additive measure \(\bar{\mu}\) is defined as the Lebesgue integral of the measurable map \(\mathrm{Sp} \circ Q\) with respect to \(\bar{\mu}\).