Probabilistic Entropies for Interval Valued Fuzzy Sets

Shannon entropy, like many other information measures, has been used to evaluate the information associated with probabilistic events. These measures have been extended to non-probabilistic distributions, such as the information measures proposed in the fuzzy set theory and its extensions. Numerous entropies have been proposed  for interval-valued fuzzy sets (IVFS) or Atanassov’s intuitionistic fuzzy sets. However, in this fuzzy  ramework, all these entropies no longer take probabilistic information into account. In this paper, we propose a framework setting out the conditions to be met by a probabilistic entropy for IVFS.