On fuzzy renewal processes for fuzzy random variables and extended theorems

In this paper, we construct fuzzy renewal processes involving fuzzy random variables. We first extend the renewal processes to the fuzzy renewal processes where interarrival times, rewards, and stopping times are all fuzzy random variables. According to these fuzzy renewal processes, we then extend some theorems of renewal processes to those in fuzzy renewal processes. These are elementary renewal theorem, asymptotic expected average reward, and Wald’s equation. In each part, we also give examples for applications. C © 2010 Wiley Periodicals, Inc.