Yager[5] proposed a transformation for opposing(negating) the occurence of an event that is not certain using the idea that one can oppose the occurence of any uncertain event by allocating its probability among the other outcomes in the sample space without preference to any particular outcome \textit{i.e.} the probability of every event in the sample space is redistributed equally among the other outcomes in the sample space. However this redistribution increases the uncertainty associated with the occurence of events. In the present work, we have established bounds on the uncertainty associated with negation of a probability distribution using well known Jensen inequality. The obtained results are validated with the help of various numerical examples. Finally a dissimilarity function between a probability distribution and its negation has been developed.

翻译：Yager[5]提出了一种针对不确定事件发生进行取反（否定）的变换方法，其核心思想是通过将不确定事件的发生概率无偏好地重新分配给样本空间中的其他结果，从而实现对该不确定事件发生的反对。然而，这种重新分配过程会增大事件发生本身所蕴含的不确定性。在本文中，我们利用著名的Jensen不等式建立了与概率分布取反相关的不确定性界限。通过多种数值示例对所获得的结果进行了验证。最后，我们构建了一个用于衡量概率分布与其取反形式之间差异性的函数。