The probability theories for IVFSs and IVIFSs

Since the concept of IFS-probability was proposed, the probability theory for IF-events has been constructed. In this paper the concepts of IVFS-probability and IVIFS-probability are proposed for the first time. And the representation theorem for IVFS-probability is given. Furthermore, the relationships between IFS-probability, IVFS-probability and IVIFS-probability are discussed.