Contracting and Involutive Negations of Probability Distributions
  A dozen papers have considered the concept of negation of probability
distributions (pd) introduced by Yager. Usually, such negations are generated
point-by-point by functions defined on a set of probability values and called
here negators. Recently it was shown that Yager negator plays a crucial role in
the definition of pd-independent linear negators: any linear negator is a
function of Yager negator. Here, we prove that the sequence of multiple
negations of pd generated by a linear negator converges to the uniform
distribution with maximal entropy. We show that any pd-independent negator is
non-involutive, and any non-trivial linear negator is strictly contracting.
Finally, we introduce an involutive negator in the class of pd-dependent
negators that generates an involutive negation of probability distributions.
