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RENEWAL AND RENEWAL REWARD THEORIES FOR T-INDEPENDENT FUZZY RANDOM VARIABLES
RENEWAL AND RENEWAL REWARD THEORIES FOR T-INDEPENDENT FUZZY RANDOM VARIABLES
KIM JAE DUCK , HONG DUG HUN
Journal of applied mathematics & informatics. 2015. Sep, 33(5_6): 607-625
DOI : http://dx.doi.org/10.14317/jami.2015.607
  • Received : April 29, 2015
  • Published : September 30, 2015
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KIM JAE DUCK
HONG DUG HUN
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KIM JAE DUCK
HONG DUG HUN
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Abstract
Recently, Wang et al. [Computers and Mathematics with Ap-plications 57 (2009) 1232-1248.] and Wang and Watada [Information Sci-ences 179 (2009) 4057-4069.] studied the renewal process and renewal reward process with fuzzy random inter-arrival times and rewards under the T-independence associated with any continuous Archimedean t-norm. But, their main results do not cover the classical theory of the random elementary renewal theorem and random renewal reward theorem when fuzzy random variables degenerate to random variables, and some given assumptions relate to the membership function of the fuzzy variable and the Archimedean t-norm of the results are restrictive. This paper improves the results of Wang and Watada and Wang et al. from a mathematical per-spective. We release some assumptions of the results of Wang and Watada and Wang et al. and completely generalize the classical stochastic renewal theorem and renewal rewards theorem.
Keywords
N(S)Fuzzy sets ;  (I)Stochastic processes ;  Fuzzy renewal process ;  Renewal reward theories ;  Possibility measure
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Citing 'RENEWAL AND RENEWAL REWARD THEORIES FOR T-INDEPENDENT FUZZY RANDOM VARIABLES '
@article{ E1MCA9_2015_v33n5_6_607} ,title={RENEWAL AND RENEWAL REWARD THEORIES FOR T-INDEPENDENT FUZZY RANDOM VARIABLES} ,volume={5_6} , url={http://dx.doi.org/10.14317/jami}, DOI={10.14317/jami} , number= {5_6} , journal={Journal of applied mathematics & informatics} , publisher={Korean Society of Computational and Applied Mathematics} , author={JAE DUCK, KIM and DUG HUN, HONG} , year={2015} , month={Sep}