An innovative approach to decision-making through cubical fuzzy Einstein Hybrid aggregation operators

The Cubical Fuzzy Set, as an extension of the classical fuzzy set, provides a novel framework for addressing the imprecision and uncertainty inherent in real-life decision-making cenarios through four unrestricted functions. This paper introduces enhanced algebraic operators for Cubical Fuzzy Numbers, namely the Einstein sum, product and scalar multiplication, which are formulated based on the Einstein t-norms and t-conorms. Using these operations, the concepts of Einstein Averaging and Einstein Geometric Aggregation Operators are developed. By employing the newly proposed Einstein aggregation operators, a multi-attribute decision-making technique is established under the cubical fuzzy environment. Furthermore, the concept of Einstein aggregation operators is extended to other fuzzy environments, including Intuitionistic, Pythagorean, q-Rung Orthopair, Picture, and Spherical Fuzzy Sets. To verify the effectiveness of the proposed approach, comparative analyses are conducted with existing methods, demonstrating the improved accuracy and flexibility of the proposed operators. Finally, a practical case study on iPhone selection is presented to illustrate the real-world applicability of the proposed model, confirming that the Cubical Fuzzy Set framework provides a more reliable and informed basis for decision-making under uncertainty.