Generalization of negation of a probability distribution

Negation is absolutely essential in all conversations that allows for denial, contradiction and other countering aspects of human linguistic systems. Intuitively, the negative sentences are less informative and less specific than the affirmative ones. In other words, it has more uncertainty embedded in it. If an event is uncertain, negating it will require some sort of probabilistic formulation. Yager (IEEE Trans Fuzzy Syst 25:1899–1902, 2015) gave a probabilistic definition of negation of a probability distribution based on unbiased distribution of probabilities. In the present work, a generalization of negation based on the concept of biased distribution is proposed. Some numerical examples have been discussed for determining the validity and efficacy of the proposed generalization. Finally an application in medical diagnosis has been considered.