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Note on Fuzzy Random Renewal Process and Renewal Rewards Process

Hong, Dug-Hun    (Department of Mathematics, Myongji University  );
  • 초록

    Recently, Zhao et al. [Fuzzy Optimization and Decision Making (2007) 6, 279-295] characterized the interarrival times as fuzzy random variables and presented a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process in the fuzzy random renewal process. They also depicted both the interarrival times and rewards are depicted as fuzzy random variables and provided fuzzy random renewal reward theorem on the limit value of the long run expected reward per unit time in the fuzzy random renewal reward process. In this note, we simplify the proofs of two main results of the paper.


  • 주제어

    Renewal process .   Renewal reward process .   Fuzzy random variable .   Fuzzy variable .   Stochastic renewal process.  

  • 참고문헌 (11)

    1. E. Popova &H. Wu, "Renewal reward processes with fuzzy rewards and their applications to T -age replacement policies," European Journal of Operational Research, vol.117, pp.606?617, 1999 
    2. S. Ross, Stochastic processes. New York: John Wiley & Sons, 1996 
    3. L. A. Zadeh, "Fuzzy Sets as a basis for a theory of possibility," Fuzzy Sets and Systems vol.1, pp.3?28 1978 
    4. R. Zhao & B. Liu, "Renewal process with fuzzy interarrival times and rewards," International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, vol.11, pp.573?586, 2003 
    5. R. Zhao & W. Tang, Some properties of fuzzy random processes, IEEE Transactions on Fuzzy Systems, vol.14, pp.173?179, 2006 
    6. R. Zhao, W. Tang & C.Wang, Fuzzy random renewal process and renewal reward process, Fuzzy Optimization and Decision Making, vol.6, pp.279?295, 2007 
    7. Liu, B. Theory and practice of uncertain programming. Heidelberg: Physica-Verlag, 2002 
    8. B. Liu, & Y. Liu, "Expected value of fuzzy variable and fuzzy expected value models." IEEE Transactions on Fuzzy Systems, vol.10, pp.445?450, 2002 
    9. C. Hwang, "A theorem of renewal process for fuzzy random variables and its application," Fuzzy Sets and Systems, vol.116, pp.237?244, 2000 
    10. J. Gao & B. Liu, 'New primitive chance measures of fuzzy random event,' International Journal of Fuzzy systems, vol.3 , pp. 527?531, 2001 
    11. Y. Liu, &B. Liu, "Fuzzy random variables: a scalar expected value operator," Fuzzy Optimization and Decision Making, vol.2 , pp.143?160, 2003 

 저자의 다른 논문

  • Hong, Dug-Hun (29)

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    2. 2004 "Exact Solutions of Fuzzy Goal Programming Problems using $\alpha-cut$ Representations" Journal of the Korean Data & Information Science Society = 한국데이터정보과학회지 15 (2): 457~465    
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    4. 2005 "A NOTE ON SET-VALUED FUZZY INTEGRALS" Journal of applied mathematics & computing 19 (1): 453~456    
    5. 2005 "Entropy and information energy arithmetic operations for fuzzy numbers" 퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems 15 (6): 754~758    
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