Renewal reward process for $$T$$ T -related fuzzy random variables on $$(\mathbb {R}^{p}, \mathbb {R}^{q})$$ ( R p , R q )

Abstract

In this paper, following our previous studies, we investigate the renewal rewards process with respect to the necessity, credibility, chance measure and the expected value in which the random inter-arrival times and random rewards are characterized as weighted fuzzy numbers under $$t$$ t -norm-based fuzzy operations on $$\mathbb {R}^{p}$$ R p and $$\mathbb {R}^{q}\,\,p,\,q \ge 1,$$ R q p , q ? 1 , respectively. Many versions of $$T$$ T -related fuzzy renewal rewards theorems are proved by using the law of large numbers for weighted fuzzy variables on $$\mathbb {R}^{p}$$ R p . An application example is provided to illustrate the utility of the results.