Recently, Zhao et al. (in Fuzzy Optimization and Decision Making 2007 6, 279–295) presented a fuzzy random elementary renewal theorem and fuzzy random renewal reward theorem in the fuzzy random process. In this paper, we study the convergence of fuzzy random renewal variable and of the total rewards earned by time t with respect to the extended Hausdorff metrics d ∞ and d 1. Using this convergence information and applying the uniform convergence theorem, we provide some new versions of the fuzzy random elementary renewal theorem and the fuzzy random renewal reward theorem.
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Hong, D.H. Uniform convergence of fuzzy random renewal process. Fuzzy Optim Decis Making 9, 275–288 (2010). https://doi.org/10.1007/s10700-010-9085-y
- Fuzzy renewal process
- Fuzzy renewal reward process
- Fuzzy random variable
- Fuzzy variable