Fuzzy Optimization and Decision Making

, Volume 12, Issue 1, pp 79–87 | Cite as

Delayed renewal process with uncertain interarrival times

  • Xingfang Zhang
  • Yufu Ning
  • Guangwu Meng


Delayed renewal process is a special type of renewal process in which the first interarrival time is quite different from the others. This paper first proposes an uncertain delayed renewal process whose interarrival times are regarded as uncertain variables. Then it gives an uncertainty distribution of delayed renewal process and an elementary delayed renewal theorem.


Renewal process Uncertain process Uncertainty theory 


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  1. Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2): 263–292MATHCrossRefGoogle Scholar
  2. Liu B. (2007) Uncertainty theory. (2nd ed). Springer, BerlinMATHGoogle Scholar
  3. Liu B. (2008) Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems 2(1): 3–16Google Scholar
  4. Liu B. (2009) Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1): 3–10Google Scholar
  5. B. B., B. B. (2011) Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer, BerlinGoogle Scholar
  6. Liu B. (2012a) Why is there a need for uncertainty theory. Journal of Uncertain Systems 6(1): 3–10Google Scholar
  7. Liu, B. (2012b). Extreme value theorems of uncertain process with application to insurance risk model.Soft Computing (to be published).Google Scholar
  8. Yao, K. (2012). Uncertain calculus with renewal process. Fuzzy Optimization and Decision Making. doi: 10.1007/s10700-012-9132-y.
  9. Yao, K., & Li, X. (2012). Uncertain alternating renewal process and its application. IEEE Transcations on Fuzzy Systems. doi: 10.1109/TFUZZ.2012.2194152.
  10. Yu X. C. (2012) A stock model with jumps for uncertain markets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20(3): 421–432MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of Mathematical SciencesLiaocheng UniversityLiaochengChina
  2. 2.Department of Computer ScienceDezhou UniversityDezhouChina

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