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.