Fuzzy random renewal reward process and its applications

This paper studies a renewal reward process with fuzzy random interarrival times and rewards under the ⊤⊤-independence associated with any continuous Archimedean t-norm ⊤⊤. The interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are ⊤⊤-independent fuzzy variables. Under these conditions, some limit theorems in mean chance measure are derived for fuzzy random renewal rewards. In the sequel, a fuzzy random renewal reward theorem is proved for the long-run expected reward per unit time of the renewal reward process. The renewal reward theorem obtained in this paper can degenerate to that of stochastic renewal theory. Finally, some application examples are provided to illustrate the utility of the result.