ON THE CONTINUITY OF FUZZY ENTROPIES

The entropy as a measure of diversity has been used by ecologists to c haracterize a community by its stability process. After the introducti on of the concept of a fuzzy subset by Zadeh (1965), many definitions of entropies were given emphasizing the subjectivity in evaluations. A pioneering work which relates the classical meaning of entropy (Shann on index) with the modern fuzzy theory was due to De Luca and Termini (1972); Knopfmacher (1975) formulated a generalization of the axiomati cs given by De Luca and Termini; Batle and Trillas (1979) obtained a r esult which is essentially analogous to Knopfmacher's by considering a finite fuzzy measure space and the Sugeno's integrals; and Trillas an d Riera (1978) introduced the concept of fuzzy algebraic entropies. An alyses the continuity properties for these fuzzy entropies and establi shes conditions which guarantee the convergence E(f(n)) --> E(f), wher e (f(n)) is a sequence of fuzzy sets and E is an entropy.