The law of large numbers and renewal process for T-related weighted fuzzy numbers on Rp

  • Authors:

  • Dug Hun Hong

  • Affiliations:

  • Department of Mathematics, Myongji University, Yongin, Kyunggido 449-728, South Korea

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2013

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Abstract

This paper considers the law of large numbers for T-related weighted fuzzy variables whose underlying spaces are R^p. We provide new sufficient conditions that do not depend on the shape of fuzzy numbers and the additive generator of a t-norm T for the law of large numbers for T-related weighted fuzzy variables. The results provide a far-reaching generalization of previous findings on the law of large numbers for T-related fuzzy numbers. In addition, we prove T-related fuzzy renewal theorems in which the inter-arrival time is characterized as weighted fuzzy numbers under t-norm-based fuzzy operations on R^p by using the law of large numbers for weighted fuzzy variables on R^p. We also investigate the law of large numbers and the renewal process for T-related fuzzy numbers on R^p with respect to the credibility measure, the chance measure, and the expected value.