Delta Cube Root as a General Concept of the Cube Root of a Fuzzy Number

Since Zadeh introduced fuzzy sets, various operations for fuzzy numbers, including power and roots, have been proposed. Both square and cube roots are essential in fields that use numbers, including fuzzy numbers. Byun et al. (in Soft Computing, vol. 26, pp. 4163-4169, 2022) introduced the delta root for the square root of a fuzzy number. This study extends this concept by proposing a delta-cube root, offering a functional approach that maintains the integrity of alpha-level sets and aligns them with Zadeh's extension principle. Additionally, we introduce the delta n-th root, which generalizes both the delta and delta cube roots, thus broadening the scope of operations on fuzzy numbers.