中文摘要：

Frank算子簇满足相容性定理，基于FrankT／S范数构造柔性概率逻辑算子，是在逻辑框架内解决概率逻辑不确定性推理问题的一种有效探索．论文针对传统概率逻辑算子在相关性方面存在的缺陷，用广义相关系数h建立起与相关性的联系，并基于Frank T／S范数构造了一套运算关系可以随h连续变化的柔性概率逻辑算子．理论证明，该算子既可满足概率测度的基本公理，又具有连续单调可变性．

英文摘要：

Frank operator cluster satisfy compatible theorem, the flexible probability logic operator based on Frank T/S norms,is a effective study which solve the problem of probability logic uncertain reasoning in the framework of logics. Aimed at solving the problem of limitation on the correlativity of the traditional probability logic operator, the paper uses the generalized correlation coefficient h to establish a connection with correlativity, and constructs a set of flexible probability logic operator based on Frank T/S norms, whose operation relation can changes continuously with h. The theory prove that the operator not only can satisfy basic axiom of probability measure,but also show the continuous monotone variability.