The law of large numbers and renewal process for T -related weighted fuzzy numbers on Rp R p
This paper considers the law of large numbers for T -related weighted fuzzy variables whose underlying spaces are Rp 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 Rp R p by using the law of large numbers for weighted fuzzy variables on Rp R p . We also investigate the law of large numbers and the renewal process for T -related fuzzy numbers on Rp R p with respect to the credibility measure, the chance measure, and the expected value.
law of large numbers fuzzy numbers chance measure continuous archimedean t-norm fuzzy renewal process possibility measure