Fuzzy random renewal process and renewal reward process
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Fuzzy random variable is a measure function from a probability space to a collection of fuzzy variables. Based on the fuzzy random theory, this paper addresses some properties of fuzzy random renewal processes generated by a sequence of independent and identically distributed (iid) fuzzy random interarrival times. The relationship between the expected value of the fuzzy random renewal variable and the distribution functions of the alpha-pessimistic values and alpha-optimistic values of the interarrival times is discussed. Furthermore, the fuzzy random style of renewal equation is provided. Finally, fuzzy random Blackwell's renewal theorem and Smith's key renewal theorem are also given