A large-scale group decision making model with a clustering algorithm based on a locality sensitive hash function

With the development of science and technology, an expanding array of decision-makers across various fields, including engineering and medicine, have been participating in collaborative decision-making for complex scenarios, such as earthquake relief and disease containment. The rapidly changing dynamics of real-world decision-making and the high complexity of consensus reaching among decision-makers require the development of more sophisticated models to handle these challenges. Considering the diversity and stability of group categories, this study proposes a large-scale group decision-making model based on a locality sensitive hash function. First, the volatility of attributes in real scenarios is considered, and a time-series decision matrix is constructed based on the average growth rates to make the results closer to reality. Then, hash functions are used to map the decision opinions to different dimensions and express the similarity through the Hamming distance, yielding clustering results with high stability and cohesion. To determine whether the decision-making group can reach a consensus, this study conducts hypothesis testing, adopting the idea of small probability counterfactuals to provide objective and fair standards for threshold judgment. Finally, through the case study and comparative analysis, it is proved that the proposed method improved 26.4% and 4.2% under the criteria of integrated cohesion and global consensus degree, respectively, with better clustering effect.