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A robust multi-criteria supplier selection framework based on linguistic cubic interval-valued intuitionistic fuzzy
Shakil Ahmad1, Zeeshan Ali2, Yahya Shah1
1Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, Pakistan.
Scientific Reports
|May 19, 2026
Summary
This study introduces linguistic cubic interval-valued intuitionistic fuzzy sets (LCuIVIFSs) to address complex decision-making problems with ambiguity and uncertainty. The new model offers reliable and flexible outcomes for real-world applications.
Area of Science:
- Decision Sciences
- Fuzzy Set Theory
- Computational Intelligence
Background:
- Real-world decision-making (DM) faces challenges from ambiguity, expert hesitation, and incomplete information, limiting traditional fuzzy set (FS) and intuitionistic fuzzy set (IFS) models.
- Existing frameworks struggle to integrate diverse uncertainties like linguistic assessments and interval-valued data effectively.
Purpose of the Study:
- To propose an innovative and expressive model, linguistic cubic interval-valued intuitionistic fuzzy sets (LCuIVIFSs), for handling complex DM problems.
- To develop novel aggregation operators (AOs) and a multi-criteria decision-making (MCDM) technique within the LCuIVIFSs framework.
- To demonstrate the model's applicability and superiority in real-world scenarios, such as supplier selection in smart manufacturing.
Main Methods:
- Definition and systematic introduction of basic operations (union, intersection, complement) for LCuIVIFSs.
- Development and investigation of various aggregation operators (arithmetic, geometric, weighted) for combining uncertain information.
- Application of a novel MCDM technique using the proposed AOs to a practical case study.
Main Results:
- The LCuIVIFSs model effectively integrates interval-valued intuitionistic fuzzy uncertainty, linguistic information, and cubic structures.
- Proposed aggregation operators provide robust methods for combining complex and uncertain data.
- The MCDM technique yields reliable, flexible, and robust decision outcomes, outperforming existing FS-based models.
Conclusions:
- LCuIVIFSs offer a powerful and flexible framework for addressing complex decision-making problems characterized by linguistic and cubic uncertainty.
- The developed MCDM technique provides a valuable decision-support tool for practical applications in uncertain environments.
- This research enhances the capabilities of fuzzy set theory in handling real-world decision complexities.
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