Statistical hypo-convergence in sequences of fuzzy sets

This study addresses a statistical generalization of the concept of hypo-convergence, which was developed to examine the limit behavior of sequences of fuzzy sets. The study begins by introducing the fundamental structures such as fuzzy sets, level sets, and hypographs. It then presents a detailed characterization of hypo- convergence using hypo-limit infimum and supremum, supported by relevant topo- logical and sequential properties. Subsequently, statistical hypo-limits are defined, and their topological characterizations are provided through several lemmas and theorems. The theoretical results are further analyzed in the context of optimiza- tion theory, particularly regarding the convergence of maximizers and supremum values. In this context, it has been shown that statistical hypo-convergence offers a comp- lementary and explanatory structure for different situations compared to classical hypo-convergence. The findings shed light on potential applications, especially in terms of fuzzy optimization and decision making problems.