Novel Mittag-Leffler-Based Aggregation Operators for Complex Fuzzy Sets, with an Illustrative Application to Generative AI Diagnostic-System Evaluation

Aggregation operators are central to multi-criteria decision-making under complex fuzzy information, where the additional phase dimension of complex fuzzy sets captures periodic or cyclical uncertainty beyond the reach of classical fuzzy sets. Existing Archimedean families used in the complex-fuzzy aggregation-operator literature, namely the algebraic, Einstein, Hamacher, and Aczél–Alsina families, are all generated from integer-order kernels; complete monotonicity of a generator’s pseudo-inverse, the condition known to be necessary and sufficient for a bivariate Archimedean construction to extend consistently to an arbitrary number of arguments, has not, to our knowledge, been established or invoked as a design criterion within that literature. To address this gap, this paper introduces a new family of Complex Fuzzy Mittag-Leffler (CFML) operators generated by a two-parameter additive generator that is built from the one-parameter Mittag-Leffler function Eα and a positive exponent λ. The completely monotone character of this generator guarantees the above consistency across dimensions for every aggregation exponent no smaller than one, and the fractional order α supplies a tunable additional degree of freedom that reweights how criteria are compensated during aggregation. The associated operational laws and the corresponding weighted averaging and weighted geometric operators are defined and proved to be idempotent, bounded, and monotone. Notably, the classical Aczél–Alsina and algebraic product operators emerge as exact limiting cases as the fractional order tends to one. A complete multi-criteria decision-making algorithm is proposed and illustrated, for demonstration purposes only, through a hypothetical case study evaluating generative artificial-intelligence diagnostic systems, with a sensitivity analysis showing that varying the fractional order and the aggregation exponent can alter alternative rankings relative to the classical limiting operators, illustrating the added flexibility that the fractional order provides.