A multi-criteria approach to decision-making using a hybrid $\mathfrak{M}$-polar 3-spherical $\mathcal{Q}$-fuzzy soft sets model

In this paper, we proposed a hybrid $\mathfrak{M}$-polar 3-spherical $\mathcal{Q}$-fuzzy soft set model by integrating $\mathfrak{M}$-polar, 3-spherical, and $\mathcal{Q}$-fuzzy soft sets. The model handles three-dimensional, $\mathfrak{M}$-polar parametrized data. Fundamental operations such as union, intersection, complement, maximum, minimum, direct sum, direct product, and a weighted geometric aggregation operator were defined within the proposed $\mathfrak{M}$-polar 3-spherical $\mathcal{Q}$-fuzzy soft set framework. The new model enhanced flexibility and effectiveness in managing vagueness and uncertainty in complex decision-making problems. An application to artificial intelligence (AI) model selection and multi-criteria decision-making (MCDM) demonstrated the advantages of the proposed framework.