Fuzzy orthogonal random measure

AbstractThe fundamental theory of fuzzy orthogonal random measure, the value of which is the element of a Hilbert space, as classical orthogonal random measure, is established perfectly, such as the extension theorem, the corresponding integral, and the inner product of two fuzzy orthogonal random measures. Using Ito's definition of orthogonal random measure makes the mathematical structure of the whole theory very clear. The proof of the extension theorem is not just the same as that of the classical one. Using the fuzzy orthogonal random measure and integral to express a random process will be more convenient than using the classical ones and that makes possible the use of new ways to solve the problem of corresponding random process. The inner product is very similar to the classical theory