In order to elaborate a theory of communication which could be useful
for designing a great variety of real communication systems it is nece
ssary to consider the superposition of two kinds of uncertainties: pro
babilistic and possibilistic. For example Zadeh's general formula for
the entropy of fuzzy random events takes into account these two basic
uncertainties. In this paper we consider Zadeh's entropy, structurally
related with this quantity a weighted entropy of De Luca and Termini
and also the genetic connection of these entropies with Shannon's entr
opy function. (C) 1997 Elsevier Science B.V.