Fuzzy Random Renewal Process Related Theory

In this paper, Fuzzy random variable is a measure function from a probability space(Ω,Γ,P) to a collection of fuzzy variables. Based on the fuzzy random theory, we introduce the concept of fuzzy random renewal processes(FRRP) which were generated by a sequence of independent and identically distributed(idd) fuzzy random interarrival times .address some properties of renewal processes generated by (idd) fuzzy random interarrival times. The relationship between the expected value of the fuzzy random renewal variable and the distributed functions of interarrival times. The fuzzy random renewal equation is provided. Furthermore , fuzzy random elementary renewal theorem, fuzzy random Blackwell's renewal theorem, fuzzy random key renewal theorem, fuzzy random alternating renewal theorem are given. Finally fuzzy random reward renewal theorem and fuzzy random delayed renewal theorem,fuzzy random Erlang renewal process also established.