On Level-Wise Ideal Convergence of Sequences of Fuzzy Numbers

This paper is devoted to the investigation of ideal-type level-wise convergence for sequences of fuzzy numbers. By using α-level sets, we define level-wise I-convergence, uniformly level-wise I-convergence, and almost everywhere level-wise I-convergence. A characterization of level-wise I-convergence is obtained via the endpoint functions of the α-cuts, and uniqueness of the limit is established. It is shown that uniformly level-wise I-convergence implies level-wise I-convergence, whereas the converse fails in general. Furthermore, we prove that level-wise I-convergence yields almost everywhere level-wise I-convergence, whereas the converse implication does not hold in general. Several examples are included to illustrate the strictness of these implications.