Negation of a probability distribution: An information theoretic analysis

Yager (2014) proposed a transformation for negating the happening of an uncertain event which opposes the occurrence of any uncertain event by redistributing its probability equally among the other outcomes. Yager's negation applied repeatedly on any probability distribution converges to the uniform distribution (all events having identical probability of occurrence). In most cases, uniform distribution is the maximum entropy probability distribution (MEPD) as it has maximum uncertainty inherent in it. However, if some information is available regarding the occurrence of events associated with a random experiment, then MEPD may or may not be a uniform distribution. In this work, we have first explored some new properties of Yager's negation and then investigated Yager's negation when we have some additional information about the probability distribution other than the natural constraints. The MEPD in the presence of this additional information is determined using the negation of probabilities. It is shown that the existence of MEPD (and as a result the maximum entropy) largely depends on the parameters of the additional constraints. Some numerical examples have been considered for comparing the MEPD with and without additional constraints.