A new approach to MADM problem using interval-valued hesitant Fermatean fuzzy Hamacher operators and statistical variance.

Water ecological civilization construction (WECC) is regarded as the core and cornerstone of ecological civilization construction. However, a lot of uncertainty is involved in assessing the WECC level, which presents serious and intricate difficulties for the related multiple- attribute decision-making (MADM) processes. The interval-valued hesitant Fermatean fuzzy set (IVHFFS) is a powerful tool for handling uncertainty in MADM issues. However, in the existing MADM approaches, attribute weight calculation involves high data redundancy and low computational efficiency. The existing aggregation operators ignore the importance of the attributes and their ordered positions. In order to solve these problems, in this paper, we propose a novel MADM model using interval-valued hesitant Fermatean fuzzy (IVHFF) Hamacher aggregation operator (AO) and statistical variance (SV) weight calculation. Firstly, the SV weight calculation method is given under IVHFFSs, aiming to computing objective weights of attributes. This greatly reduces data redundancy and improves the computational complexity. Secondly, we propose some IVHFF Hamacher AOs, such as IVHFF Hamacher (ordered) weighted averaging operator, IVHFF Hamacher (ordered) weighted geometric operator, IVHFF Hamacher hybrid averaging operator and geometric operator which consider the significance of the attributes and their ordered positions. Thirdly, a new MADM model based on the above information AOs and SV weight calculation is proposed. Finally, a comparative study on the real-world application for WECC and randomly generated data sets is also carried out to further demonstrate that our method outperforms the existing methods.