On the definition of coherence measure for fuzzy sets

Studying comparison methods for fuzzy sets is an essential task for the good understanding of the underlying theory in this field. Most of these tools deal with fuzzy sets from the view of similarity, order relationships and so forth. In this paper however, based on a former comparison measures introduced by the authors, the so called Coherence Measures, the extension and analysis of these tools to a measurable Lebesgue set X is carried out. Furthermore we present how coherence measures could be linked to the Fishburn-Yager's ambiguity measures.. Besides, two methods for constructing coherence measures, one from ambiguity measures and another from metrics on Pf(X), the set of fuzzy sets on X, are shown and exemplified by a variety of measures and metrics. Finally some illustrative examples testing the coherence measures introduced are provided.