The law of large numbers and renewal process for T-related weighted fuzzy numbers on [formula omitted

Abstract

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