The Negation of a Probability Distribution: A Generalized Approach

The probability distribution function has been extensively used in several application areas to represent uncertain information. The negation of a probability distribution, proposed by Yager, provides a new approach to characterize uncertain information more effectively. It is also noted that the negation of a probability distribution can be generated a whole set of possible probability distributions. In the present communication, we propose a new generalized method to obtain the negation of a probability distribution. The paper discusses several important properties associated with the proposed negation of the probability distribution. It is interesting to note that the defined generalized negation of a probability distribution converges to the uniform distribution and reduces to Yager's negation as a limiting case. By considering different values of the parameter, a whole set of negations associated with a probability distribution can be generated, which follow different paths to approach convergence. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed approach.