# Contracting and Involutive Negations of Probability Distributions

arXiv: https://arxiv.org/abs/2103.16176 · HTML: https://mlsanity.com/paper/2103.16176/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 22 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 1 of 1)

- [Generating Negations of Probability Distributions](https://mlsanity.com/paper/2103.14986/) (2021)

## Built on by (most cited first, 1 of 1)

- [An Information Theoretic Treatment of Yager's Probability Distribution Negation](https://mlsanity.com/paper/2608.00594/) (2026)

## Abstract (arXiv)

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.