### Abstract

Using extension principle associated with a class of continuous Archimedean triangular norms, this paper studies a fuzzy random renewal process in which the interarrival times are assumed to be independent and identically distributed fuzzy random variables. Some limit theorems in chance measure and in expected value for the sum of fuzzy random variables are proved on the basis of the continuous Archimedean triangular norm based arithmetics. Furthermore, we discuss the fuzzy random renewal process based on the obtained limit theorems, and derive a fuzzy random elementary renewal theorem for the long-run expected renewal rate. The renewal theorem obtained in this paper can degenerate to the corresponding classical result in stochastic renewal process. Finally, two case studies of queueing systems are provided to illustrate the application of the fuzzy random elementary renewal theorem.

Original language | English |
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Pages (from-to) | 1232-1248 |

Number of pages | 17 |

Journal | Computers and Mathematics with Applications |

Volume | 57 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2009 Apr |

### Keywords

- Archimedean triangular norm
- Elementary renewal theorem
- Extension principle
- Fuzzy random variables
- Interarrival times
- Queueing system
- Renewal process

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Modelling and Simulation
- Computational Mathematics

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## Cite this

*Computers and Mathematics with Applications*,

*57*(7), 1232-1248. https://doi.org/10.1016/j.camwa.2009.01.030