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

Albandry Khaled Alotaibi; Kholood Mohammad Alsager; Albandry Khaled Alotaibi; Kholood Mohammad Alsager

doi:10.3934/math.20251340

AIMS Mathematics

2025, Volume 10, Issue 12: 30544-30593. doi: 10.3934/math.20251340

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Research article

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

Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia

Received: 08 September 2025 Revised: 15 December 2025 Accepted: 16 December 2025 Published: 25 December 2025
MSC : MSC2010, 03B52, 03E72

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.
- $ \mathfrak{M} $-polar 3-spherical $ \mathcal{Q} $-fuzzy soft set,
- decision-making,
- pattern recognition,
- cluster analysis,
- correlation coefficients
Citation: Albandry Khaled Alotaibi, Kholood Mohammad Alsager. A multi-criteria approach to decision-making using a hybrid $ \mathfrak{M} $-polar 3-spherical $ \mathcal{Q} $-fuzzy soft sets model[J]. AIMS Mathematics, 2025, 10(12): 30544-30593. doi: 10.3934/math.20251340

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Abstract

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.

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