Some Inequalities on Credibility Measure

Based on the axioms of credibility measure, some inequalities for the sum of fuzzy variables are presented and the rth inequality for credibility measure is obtained. An inequality on credibility measure for the functional of fuzzy variables is also proved and a lower bound moment estimate of Cr(| ¿ |¿ t) is obtained as corollary. By using the credibility inversion theorem, an upper bound estimate of fuzzy variables which take countable integers values is proved at the same time.