A new distance measure and corresponding TOPSIS method for interval-valued intuitionistic fuzzy sets in multi-attribute decision-making

Ya Qin; Siti Rahayu Mohd. Hashim; Jumat Sulaiman; Ya Qin; Siti Rahayu Mohd. Hashim; Jumat Sulaiman

doi:10.3934/math.20231351

AIMS Mathematics

2023, Volume 8, Issue 11: 26459-26483. doi: 10.3934/math.20231351

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A new distance measure and corresponding TOPSIS method for interval-valued intuitionistic fuzzy sets in multi-attribute decision-making

1.
Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Kota Kinabalu, Sabah 88400, Malaysia
2.
School of Mathematics and Information Sciences, Numerical Simulation Key Laboratory of Sichuan Provincial Universities, Neijiang Normal University, Neijiang 641000, Sichuan Province, China

Received: 25 April 2023 Revised: 02 August 2023 Accepted: 22 August 2023 Published: 15 September 2023
MSC : 03B52, 03E72, 90B50

Strengthening the evaluation of teaching satisfaction plays a crucial role in guiding teachers to improve their teaching quality and competence, as well as in aiding educational institutions in the formulation of effective teaching reforms and plans. The evaluation process for teaching satisfaction is usually regarded as a typical multi-attribute decision-making (MADM) process, which inherently possesses uncertainty and fuzziness due to the subjective nature of human cognition. In order to improve the subtle discrimination of evaluation information data and enhance the accuracy of the evaluation results, we have developed an integrated MADM method by combining a new distance measure and an improved TOPSIS method for interval-valued intuitionistic fuzzy sets (IvIFSs). First, a novel distance measure for IvIFSs based on triangular divergence is proposed to capture the differences between two IvIFSs, and some properties of this distance measure are investigated. Then, the superiority of this new distance measure is compared with some existing distance measures. Afterward, an improved TOPSIS method is also established based on the proposed triangular distance under the interval-valued intuitionistic fuzzy setting. Besides, to illustrate the practicality of the new method, a numerical example is presentedto evaluate mathematics teaching satisfaction. Moreover, a comparative analysis that includes existing TOPSIS methods, is presented to demonstrate the superiority of the given method. The comparison outcomes show that the proposed technique can effectively discern uncertainties or subtle differences in IvIFSs, resulting in more accurate and comprehensive evaluation results for teaching satisfaction. Overall, the findings of this study emphasize the importance of incorporating the new distance measure in MADM. The proposed approach serves as a valuable tool for decision-makers to compare and evaluate alternatives effectively.
- multi-attribute decision-making,
- interval-valued intuitionistic fuzzy set,
- distance measure,
- TOPSIS,
- triangular divergence,
- teaching satisfaction evaluation
Citation: Ya Qin, Siti Rahayu Mohd. Hashim, Jumat Sulaiman. A new distance measure and corresponding TOPSIS method for interval-valued intuitionistic fuzzy sets in multi-attribute decision-making[J]. AIMS Mathematics, 2023, 8(11): 26459-26483. doi: 10.3934/math.20231351

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Abstract

Strengthening the evaluation of teaching satisfaction plays a crucial role in guiding teachers to improve their teaching quality and competence, as well as in aiding educational institutions in the formulation of effective teaching reforms and plans. The evaluation process for teaching satisfaction is usually regarded as a typical multi-attribute decision-making (MADM) process, which inherently possesses uncertainty and fuzziness due to the subjective nature of human cognition. In order to improve the subtle discrimination of evaluation information data and enhance the accuracy of the evaluation results, we have developed an integrated MADM method by combining a new distance measure and an improved TOPSIS method for interval-valued intuitionistic fuzzy sets (IvIFSs). First, a novel distance measure for IvIFSs based on triangular divergence is proposed to capture the differences between two IvIFSs, and some properties of this distance measure are investigated. Then, the superiority of this new distance measure is compared with some existing distance measures. Afterward, an improved TOPSIS method is also established based on the proposed triangular distance under the interval-valued intuitionistic fuzzy setting. Besides, to illustrate the practicality of the new method, a numerical example is presentedto evaluate mathematics teaching satisfaction. Moreover, a comparative analysis that includes existing TOPSIS methods, is presented to demonstrate the superiority of the given method. The comparison outcomes show that the proposed technique can effectively discern uncertainties or subtle differences in IvIFSs, resulting in more accurate and comprehensive evaluation results for teaching satisfaction. Overall, the findings of this study emphasize the importance of incorporating the new distance measure in MADM. The proposed approach serves as a valuable tool for decision-makers to compare and evaluate alternatives effectively.

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