A GENERAL-THEORY OF UNCERTAINTY BASED ON T-CONORMS

We first extend a t-conorm C to C(f) for certain f:R(n) --> R, sup \f\ < + infinity. C and f arc used to define a generalized fuzzy measure on a class of subsets of R(n). The generalized fuzzy measure is employed to develop a general theory of uncertain variables including: (1) uncertainty distributions (u.d.'s) of functions of uncertain variables; (2) expected value and variance: (3) marginal and joint u.d.'s; and (4) conditional u.d.'s. Numerous examples are presented showing the theory contains both discrete and continuous possibility theory and probability theory.