Research on VIKOR group decision making using WOWA operator based on interval Pythagorean triangular fuzzy numbers

Jun Hu; Jie Wu; Mengzhe Wang; Jun Hu; Jie Wu; Mengzhe Wang

doi:10.3934/math.20231338

AIMS Mathematics

2023, Volume 8, Issue 11: 26237-26259. doi: 10.3934/math.20231338

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Research article

Research on VIKOR group decision making using WOWA operator based on interval Pythagorean triangular fuzzy numbers

1.
Huaiyin Normal University, Huai'an, Jiangsu, China
2.
Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China

Received: 10 August 2023 Revised: 24 August 2023 Accepted: 01 September 2023 Published: 13 September 2023
MSC : 47B92, 47B93, 47A13, 47N70

A new decision-making method based on interval Pythagorean triangular fuzzy numbers is proposed for fuzzy information decision-making problems, taking the advantages of interval Pythagorean fuzzy numbers and triangular fuzzy numbers into account. The VIse Kriterijumski Optimizacioni Racun (VIKOR) group decision-making method is based on the Weighted Ordered Weighted Average (WOWA) operator of interval Pythagorean triangular fuzzy numbers (IVPTFWOWA). First, this article provides the definition of the IVPTFWOWA operator and proves its degeneracy, idempotence, monotonicity, and boundedness. Second, the decision steps of the VIKOR decision method using the IVPTFWOWA operator are presented. Finally, the scientificity and effectiveness of the proposed method were verified through case studies and comparative discussions. The research results indicate that the following: (1) the IVPTFWOWA operator combines interval Pythagorean fuzzy numbers and triangular fuzzy numbers, complementing the shortcomings of the two fuzzy numbers, and can characterize fuzzy information on continuous geometry, thereby reducing decision errors caused by inaccurate and fuzzy information; (2) the VIKOR decision-making method based on the IVPTFWOWA operator applies comprehensive weights, fully considering the positional weights of the scheme attributes and the weights of raters, and fully utilizing the attribute features of decision-makers and cases; and (3) compared to other methods, there is a significant gap between the decision results obtained using this method, making it easier to identify the optimal solution.
- triangular fuzzy numbers,
- interval fuzziness,
- WOWA operator,
- VIKOR
Citation: Jun Hu, Jie Wu, Mengzhe Wang. Research on VIKOR group decision making using WOWA operator based on interval Pythagorean triangular fuzzy numbers[J]. AIMS Mathematics, 2023, 8(11): 26237-26259. doi: 10.3934/math.20231338

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Abstract

A new decision-making method based on interval Pythagorean triangular fuzzy numbers is proposed for fuzzy information decision-making problems, taking the advantages of interval Pythagorean fuzzy numbers and triangular fuzzy numbers into account. The VIse Kriterijumski Optimizacioni Racun (VIKOR) group decision-making method is based on the Weighted Ordered Weighted Average (WOWA) operator of interval Pythagorean triangular fuzzy numbers (IVPTFWOWA). First, this article provides the definition of the IVPTFWOWA operator and proves its degeneracy, idempotence, monotonicity, and boundedness. Second, the decision steps of the VIKOR decision method using the IVPTFWOWA operator are presented. Finally, the scientificity and effectiveness of the proposed method were verified through case studies and comparative discussions. The research results indicate that the following: (1) the IVPTFWOWA operator combines interval Pythagorean fuzzy numbers and triangular fuzzy numbers, complementing the shortcomings of the two fuzzy numbers, and can characterize fuzzy information on continuous geometry, thereby reducing decision errors caused by inaccurate and fuzzy information; (2) the VIKOR decision-making method based on the IVPTFWOWA operator applies comprehensive weights, fully considering the positional weights of the scheme attributes and the weights of raters, and fully utilizing the attribute features of decision-makers and cases; and (3) compared to other methods, there is a significant gap between the decision results obtained using this method, making it easier to identify the optimal solution.

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