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Random fuzzy delayed renewal processes

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Abstract

In renewal processes, fuzziness and randomness often coexist intrinsically. Based on the random fuzzy theory, a delayed renewal process with random fuzzy interarrival times is proposed in this paper. Relations between the renewal number and interarrival times in such a process are investigated. Useful theorems such as the elementary renewal theorem, the Blackwell renewal theorem and the Smith key renewal theorem in a conventional delayed renewal process are extended to their counterparts for random fuzzy delayed renewal processes.

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Acknowledgments

This work was partly supported by UK EPSRC grant EP/D057086 and partly by National Natural Science Foundation of China Grant No. 70571056, 70471049, the Program for New Century Excellent Talents in University. The authors are grateful to the project team members for helpful discussions, but will take full responsibility for the views expressed in this paper. The authors are also grateful to the anonymous referees for their constructive comments that are helpful in directing the revision of this work.

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Authors and Affiliations

  1. School of Science, Tianjin University of Commerce, 300134, Tianjin, China

    Shunqin Li

  2. Department of Computer Science, Aberystwyth University, Wales, SY23 3DB, UK

    Qiang Shen & Ruiqing Zhao

  3. Institute of Systems Engineering, Tianjin University, 300072, Tianjin, China

    Wansheng Tang

Authors
  1. Shunqin Li
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  2. Qiang Shen
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  3. Wansheng Tang
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  4. Ruiqing Zhao
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Correspondence to Qiang Shen.

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Li, S., Shen, Q., Tang, W. et al. Random fuzzy delayed renewal processes. Soft Comput 13, 681–690 (2009). https://doi.org/10.1007/s00500-008-0372-2

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