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AIMS Mathematics

2023, Volume 8, Issue 12: 30462-30486. doi: 10.3934/math.20231556
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Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy

  • 1.
    Department of Mathematics, College of science, Northern Border University, Arar, Saudi Arabia
  • 2.
    Department of Mathematics & Statistics, Hazara University, Mansehra 21300, KPK, Pakistan
  • Received: 24 August 2023 Revised: 17 October 2023 Accepted: 29 October 2023 Published: 09 November 2023

  • MSC : 03B52, 03E72, 08A72

  • 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.

    Citation: Nasser Aedh Alreshidi, Muhammad Rahim, Fazli Amin, Abdulaziz Alenazi. Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy[J]. AIMS Mathematics, 2023, 8(12): 30462-30486. doi: 10.3934/math.20231556

    Related Papers:

  • 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.


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