Abstract
<abstract> <p>Motivated by the concept of type-2 fuzzy sets, we introduce a novel framework known as trapezoidal type-2 Pythagorean fuzzy sets (TRT-2-PFSs), an extension of triangular fuzzy sets. Basic operations like addition and scalar multiplication of two TRT-2-Pythagorean fuzzy numbers (TRT-2-PFNs) are defined. We also explore comparative analysis and distance measurements between two TRT-2-PFNs. A methodology for evaluating unknown weight vectors and criteria weights is proposed. Building upon TRT-2-PFSs, an extension of the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method is developed to address intricate decision-making challenges. Ultimately, the newly introduced TRT-2-PFS-based TODIM technique is employed to tackle multi-criteria decision-making (MCDM) problems.</p> </abstract>
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