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A new approach to MADM problem using interval-valued hesitant Fermatean fuzzy Hamacher operators and statistical
Xiuqin Ma1,2, Xuli Niu1, Hongwu Qin3,4
1College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730020, Gansu, China.
Scientific Reports
|March 19, 2025
Summary
This study introduces a new method for assessing water ecological civilization construction (WECC) using interval-valued hesitant Fermatean fuzzy sets. The approach enhances decision-making by improving attribute weight calculation and aggregation operators for greater accuracy and efficiency.
Area of Science:
- Environmental Science
- Decision Science
- Fuzzy Mathematics
Background:
- Water ecological civilization construction (WECC) is crucial but faces assessment uncertainties.
- Existing multiple-attribute decision-making (MADM) methods struggle with WECC assessment due to data redundancy and inefficiency.
- Current aggregation operators often overlook attribute importance and order.
Purpose of the Study:
- To develop a novel MADM model for WECC assessment that addresses existing limitations.
- To introduce an efficient objective weight calculation method using statistical variance (SV).
- To propose new interval-valued hesitant Fermatean fuzzy (IVHFF) Hamacher aggregation operators (AOs) that account for attribute significance and order.
Main Methods:
- Utilized interval-valued hesitant Fermatean fuzzy sets (IVHFFS) for uncertainty handling in MADM.
- Developed a statistical variance (SV) method for objective attribute weight calculation under IVHFFSs.
- Proposed novel IVHFF Hamacher aggregation operators, including ordered and hybrid variants.
- Constructed a new MADM model integrating SV weights and IVHFF Hamacher AOs.
Main Results:
- The proposed SV weight calculation method reduces data redundancy and improves computational efficiency.
- The new IVHFF Hamacher AOs effectively incorporate attribute importance and their ordered positions.
- The developed MADM model demonstrated superior performance in WECC assessment compared to existing methods.
- Comparative studies confirmed the robustness and effectiveness of the proposed approach.
Conclusions:
- The novel MADM model provides a more accurate and efficient approach to WECC assessment.
- The integration of SV weights and IVHFF Hamacher AOs offers a significant advancement in handling complex decision-making under uncertainty.
- This research contributes to improving the scientific basis for WECC and related environmental management strategies.
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