Abstract.

A fuzzy variable is a function from a credibility space to the set of real numbers. The convergence of fuzzy variables is a crucial element in credibility theory. Building on this concept of convergence, we define the concept of almost-sure ideal convergence, ideal convergence in credibility, ideal Cauchy sequences in credibility, and ideal convergence in mean for fuzzy variables, and put forward a notion of ideal completeness for credibility space. Furthermore, the relationships between these modes of convergence are discussed. Specifically, we demonstrate that ideal convergence in credibility implies ideal Cauchy sequences in credibility.

Keywords:

fuzzy variable, credibility measure, credibility theory, ideal convergence, ideal Cauchy sequence