Interplay between Negation of a Probability Distribution and Jensen Inequality

Abstract: 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.