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 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 as the original.