Title: Extension of Yager's negation of probability distribution based on uncertainty measures Show Chinese title

Title: 基于不确定性度量的Yager概率分布否定的扩展

Abstract: Existing research on negations primarily focuses on entropy and extropy. Recently, new functions such as varentropy and varextropy have been developed, which can be considered as extensions of entropy and extropy. However, the impact of negation on these extended measures, particularly varentropy and varextropy, has not been extensively explored. To address this gap, this paper investigates the effect of negation on Shannon entropy, varentropy, and varextropy. We explore how the negation of a probability distribution influences these measures, showing that the negated distribution consistently leads to higher values of Shannon entropy, varentropy, and varextropy compared to the original distribution. Additionally, we prove that the negation of a probability distribution maximizes these measures during the process. The paper provides theoretical proofs and a detailed analysis of the behaviour of these measures, contributing to a better understanding of the interplay between probability distributions, negation, and information-theoretic quantities. Show Chinese abstract

Abstract: 现有关于否定的研究主要集中在熵和外延上。最近，开发了诸如方差熵和方差外延等新函数，可以将其视为熵和外延的扩展。然而，否定对这些扩展度量（特别是方差熵和方差外延）的影响尚未得到广泛探讨。为了解决这一差距，本文研究了否定对香农熵、方差熵和方差外延的影响。我们探讨了概率分布的否定如何影响这些度量，表明与原始分布相比，否定分布始终会导致更高的香农熵、方差熵和方差外延值。此外，我们证明了概率分布的否定在过程中最大化了这些度量。本文提供了理论证明并对这些度量的行为进行了详细分析，有助于更好地理解概率分布、否定和信息论量之间的相互作用。