A New Class of Fuzzy Subsethood Measures
Fuzzy Subsethood measures; Implication operator; Fuzzy entropy; Penalty functions
This work aims at introducing a new class of fuzzy subsethood measures between fuzzy sets. This new approach was inspired in the mostly known axiomatizations with the leverage of constructing fuzzy subsethood measures by aggregating implication operators. These operators satisfy some properties which have been deeply investigated in the literature, in such a way that for instance, the measure proposed by Goguen becomes a particular case of our measure. We also introduce different construction methods using automorphisms and prove that, with these measures, we can not only build fuzzy entropies, but also generate distances, penalty functions and similarity measures between fuzzy sets.