Coherence measures on finite fuzzy sets
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on measures and aggregation: formal aspects and applications to clustering and decision
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
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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, with which coherence measures are 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.