Some Inequalities In The Uncertainty Theory

Changes in the development of objective things is often a necessity and haphazard, clarity and fuzzy, accurate and approximate relations. Uncertainty reflects the links and the development of objective things in disorderly, accidental, ambiguous, similar to the property. In many cases, treatment of complex systems is often difficult to avoid the randomness, fuzziness, roughness, random fuzzy and other multiple uncertainties,and often two or even multiple properties simultaneously in a system。Professor Liu establish the uncertainty theory and the chance theory from axiomatic method is an important tool to deal with these multiple uncertainties. And the inequality, such as the H?lder's, Minkowski, Jensen's, Markov, Chebyshev inequality and so on, in dealing with uncertain property occupies Plays an important role.In this paper, we study inequality and Applications in the uncertainty Theory.In the first part of our paper, we first establish the chance theory fron probability theory and credibility theory, definition the chance space, chance measure, chance operator value ,moments in the chance theory. Given some inequality of a hybrid variables in in the chance theory. Then definition the chance variance, covariance, independence in the chance theory and proof some inequality of two hybrid variables in in the chance theory. Finally, definition the chance convergence theory and given inequality application of the chance theory on the chance convergence theory.In the second part of our paper, we first establish the uncertainty theory from axiomatic method, definition the uncertain space, uncertain measure, uncertain operator value ,moments in the uncertainty theory. Given some inequality of a uncertain variables in in the uncertainty theory. Then definition the uncertain variance, covariance, independence in the uncertainty theory and proof some inequality of two uncertain variables in in the uncertainty theory. Finally, definition the uncertain convergence theory and given inequality application of the uncertain theory on the uncertain convergence theory.