Abelian and Tauberian results for statistical convergence in credibility spaces

This paper establishes Abelian and Tauberian results for statistical convergence in credibility spaces. We prove that every uniformly bounded sequence of fuzzy variables which is statistically convergent in credibility is also statistically Cesàro summable in credibility to the same limit, while the converse fails in general. Our main contribution is a characterization theorem providing necessary and sufficient Tauberian conditions to recover statistical convergence in credibility from statistical Cesàro summability in credibility. These conditions are formulated through the asymptotic behavior of appropriate forward and backward moving averages of the sequence. As further consequences, we obtain two practical criteria based on statistical slow oscillation and a Hardy-type boundedness condition. These results extend classical Abelian-Tauberian theory to fuzzy variables in credibility spaces.