Uncertain Delayed Renewal Reward Process and Its Applications

Uncertain process is a sequence of uncertain variables indexed by time. This paper aims to introduce a kind of uncertain process named uncertain delayed renewal reward process whose interarrival times and rewards (or costs) are regarded as uncertain variables with the first interarrival ( i.e., renewal) time and reward different from the others, respectively. The main results include the uncertainty distribution of delayed renewal reward process and two uncertain delayed renewal reward theorems on the limit value of reward rate. Finally, the application of the uncertain delayed renewal reward theorem are discussed and four examples are given.