Uncertainty-Based Analysis of Negation of Probability Distributions

Accepted April 2026

Abstract

We analyse Yager’s negation operator for discrete probability distributions using Shannon entropy, varentropy and varextropy. For non-uniform distributions with n ≥ 3, negation increases entropy and varextropy but decreases varentropy. The uniform distribution is invariant and extremises these measures. Repeated negation converges to the uniform distribution for n ≥ 3, whereas the binary case is involutive. These results unify complementary information transformation with both first- and second-order uncertainty quantification.