## 1 Introduction
This improved the accuracy of group decision-making outcomes for electricity sales packages to a certain extent and provided ideas for package recommendations. However, different customers' evaluations and cognition of electricity sales packages are different. The above indirect decision-making method only considers a situation where customers are familiar with all the attributes of electricity sales packages and ignores the hesitant and ambiguous state of customers' evaluations [14], that is, the hesitant and ambiguous feature of customers' electricity sales package evaluation information [15]. Moreover, there exists significant variance in the evaluation feedback provided by different customers regarding the same electricity sales package. Even among customers with similar electricity consumption characteristics, substantial differences emerge in their evaluations of identical packages. Therefore, in order to minimize the errors of the group decision-making results for electricity sales packages, it is necessary to consider the consensus-reaching process during group decision making on electricity sales packages [16; 17]. In the consensus-reaching process, it is crucial to minimize the differences between customers' original and adjusted evaluation information [18; 19; 20]. Therefore, it is important to consider the hesitant fuzzy characteristics of customers' evaluation information for electricity sales packages. Based on the consensus rule of minimum adjustment distance, studying the multi-attribute group decision-making method can improve the accuracy of package recommendations and enhance customer satisfaction. In addition, customer clustering also plays an important role in the accuracy of electricity sales package group decision making. The electricity sales company can match target customers with historical similar customers based on the electricity consumption characteristics of the target customers. By leveraging the group decision-making results of historically similar customers, the company can recommend electricity sales packages to the target customers. The density clustering algorithm is a commonly used clustering algorithm that does not require the use of distance as a metric but determines the cluster structure based on the closeness of the sample distribution. Ordering points to identify the clustering structure (OPTICS) was proposed as a clustering method based on any radius and threshold in [21]. It generated a cluster-ordered reachable graph with implicitly included parameters, leaving it up to users to select the clustering result as needed. This process often resulted in significant inconvenience for users. Then, a method for enhancing the density computation called the residual error-based density peak clustering algorithm (REDPC) was proposed in [22], which utilized the residuals of neighborhood data points to compute local density. This algorithm aimed to enhance the variability in density peaks. However, this method encountered the issue of collateral misclustering. Based on the above density clustering algorithm research, this paper will propose TSDC, which improves the customer clustering accuracy. In total, a multi-attribute group decision-making method for electricity sales packages based on TSDC and minimum adjustment distance consensus will be proposed in this paper. The main contributions of the paper are listed as follows:  
1. A sample customer clustering method is proposed, the TSDC algorithm, avoiding the randomness, subjectivity, and associated errors existing in the current density clustering algorithm, which can improve the accuracy of identifying similar customers to the target customer. 2.