Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy
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 defin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231556?viewType=HTML |
| _version_ | 1797450894786166784 |
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| author | Nasser Aedh Alreshidi Muhammad Rahim Fazli Amin Abdulaziz Alenazi |
| author_facet | Nasser Aedh Alreshidi Muhammad Rahim Fazli Amin Abdulaziz Alenazi |
| author_sort | Nasser Aedh Alreshidi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T14:47:05Z |
| format | Article |
| id | doaj.art-14bb351867fe4bf6a82c4ef2af81832c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-09T14:47:05Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-14bb351867fe4bf6a82c4ef2af81832c2023-11-27T01:22:42ZengAIMS PressAIMS Mathematics2473-69882023-11-01812304623048610.3934/math.20231556Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancyNasser Aedh Alreshidi0Muhammad Rahim 1Fazli Amin2Abdulaziz Alenazi31. Department of Mathematics, College of science, Northern Border University, Arar, Saudi Arabia2. Department of Mathematics & Statistics, Hazara University, Mansehra 21300, KPK, Pakistan2. Department of Mathematics & Statistics, Hazara University, Mansehra 21300, KPK, Pakistan1. Department of Mathematics, College of science, Northern Border University, Arar, Saudi ArabiaMotivated 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.https://www.aimspress.com/article/doi/10.3934/math.20231556?viewType=HTMLpythagorean fuzzy setsensible decision-makingtodimtype-2 fuzzy setmcdm |
| spellingShingle | 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 AIMS Mathematics pythagorean fuzzy set sensible decision-making todim type-2 fuzzy set mcdm |
| title | Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy |
| title_full | Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy |
| title_fullStr | Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy |
| title_full_unstemmed | Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy |
| title_short | Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy |
| title_sort | trapezoidal type 2 pythagorean fuzzy todim approach for sensible decision making with unknown weights in the presence of hesitancy |
| topic | pythagorean fuzzy set sensible decision-making todim type-2 fuzzy set mcdm |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231556?viewType=HTML |
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