Entropy conserving probability transforms and the entailment principle

Our main result here is the development of a general procedure for transforming some initial probability distribution into a new probability distribution in a way that the resulting distribution has entropy at least as great as the original distribution. A significant aspect of our approach is that it makes use of the Zadeh's entailment principle which is itself a general procedure for going from an initial possibility distribution to a new possibility distribution so that the resulting possibility has an uncertainty at least as great of the original.