On the statistical core of sequences of fuzzy numbers

This thesis explores the convergence properties of bounded sequences of fuzzy numbers defined in the space E^1, focusing on the roles of level sets and the core concept. Classical limit definitions are not directly applicable to fuzzy structures, leading to the development of alternative lower and upper limit formulations using level sets. These definitions are compared, and examples are provided to illustrate their differences. The concept of the core of a fuzzy number sequence is studied in detail. Its relationship with the set of limit points is analyzed, and it is shown that the core provides meaningful insights, especially in the case of non-convergent sequences. Furthermore, the notion of statistical convergence is adapted to fuzzy number sequences through level sets. Statistical liminf and limsup are redefined and contrasted with classical counterparts. The statistical core, is also introduced, offering a way to understand the asymptotic behavior of sequences even when classical convergence fails.