Contracting and Involutive Negations of Probability Distributions
This work addresses theoretical issues in probability and information theory, but it appears incremental as it builds on existing concepts of negators.
The paper tackles the problem of defining and analyzing negations of probability distributions, proving that multiple negations by a linear negator converge to the uniform distribution with maximal entropy, and introducing an involutive negator for 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.