Commonly used weight assignment methods can be divided into subjective, objective, and combinatorial weighting methods. The most typical and commonly used subjective weighting method is the analytic hierarchy process (AHP) method [2
]; however, it has high requirements for the professional ability of the users, causing the weight calculation result to be unstable, which should be verified through a consistency test. These shortcomings are all due to the method’s subjectivity [4
]. However, objective weighting methods, such as the entropy weight method (EWM) [5
] and over-standard multiple (OSM) method [9
], avoid this problem due to their specific calculation rules. As a commonly used objective weighting method, EWM has stable weight calculation results, and its weight value can reflect the amount of useful information represented by the data of each indicator; however, it cannot reflect the degree of pollution of each indicator [10
]. Additionally, the EWM is also highly suitable for multi-sample evaluation, which can avoid repeated calculations and conserve workload. In 2006, Zou et al. used the EWM and a fuzzy evaluation method to calculate the water quality in the Three Gorges Reservoir area, and their results showed that the method greatly predigested the fuzzy synthetic evaluation process [12
]. However, the method cannot provide the weight value of each indicator to a single sample; rather, it can only provide the comprehensive weight of each indicator to multiple samples. The weight calculation result of the OSM method can reflect the pollution degree of each indicator, calculate the single weight value of each indicator for each sample, and fully represent the respective data characteristics of each sample. However, separately calculating the weights of each indicator within each sample may cause notable differences in the weights of each indicator in different samples, which cannot accurately reflect the overall characteristics of the data [13
]. According to the above analysis results, both subjective and objective weighting methods have some shortcomings. Researchers have made many improvements to resolve these issues. In 2012, Yang considered the dual effects of toxicology and excessive concentration to improve the traditional entropy method [14
]. In 2018, Yang improved the traditional EWM based on the relative entropy theory, allowing a more comprehensive understanding of the response indicators’ dipartite degrees and pollution conditions [15
]. In 2019, the projection pursuit classification (PP) was adopted by Wang to calculate the objective weight, reduce human factors, and balance the subjective uncertainty and randomness of the AHP [16
]. However, the combinatorial weighting method is the most commonly used improved method, which combines various weighting methods for calculation. This combinatorial weighting method, which is constructed from various weighting methods, is more comprehensive and compensates for the shortcomings of each method as much as possible. To effectively utilize the advantages of the combinatorial weighting method, researchers have attempted to develop combinatorial methods and forms. For example, in 2014, Jun et al. evaluated the water quality at monitoring sections in four dry seasons based on the application of the AHP and entropy weight methods and used fuzzy comprehensive evaluation to obtain the quadratic combination weight of each index method. The results showed that this method avoided the subjective differences observed in the expert score method, meeting the target weight and the effective degree of credibility [17
]. In 2016, considering the disadvantages of the subjective and objective weighted methods, a combined weighted index method was proposed by Yan et al., called the geometric mean weighted method, to assign weights to drinking water indices in order to make the weight distribution more scientific, reasonable, and robust [18
]. In 2018, Hu et al. combined AHP and entropy methods and used the dynamic adjustment of the S-type function to increase the influence of standard exceeded pollutants, which resolved the issues of looseness and strictness of the average pollution index and single-factor evaluation methods, respectively [1
]. In 2020, Wu et al. used the Shannon entropy theory, a fuzzy comprehensive method, and the AHP to provide reasonable weights for ECC evaluation modeling by combining subjective and objective weights [19
]. Most existing combination weighting methods use a combination of subjective (AHP) and objective (EWM) weighting methods. Although this method has the advantages of both subjective and objective weighting methods, the evaluation results are still unstable due to the subjectivity of the subjective weighting method adopted. To avoid this problem, an amendment rule is introduced to replace the function of the subjective weighting method in this study. Amendment rules are expressed as formulas and affect the objective evaluation results based on the amendment data used, which were the single-factor evaluation results that reflect the pollution degree of each indicator in each sample in this study; thus, the influence of this method on the weight value can be determined by the pollution degree of each indicator. The higher the pollution degree of the indicator, the greater the magnifying effect of the amendment rule on its objective weight. If the users have their own views on the influencing factors of the combined weights, the influencing factors of the objective weights can be changed by altering the amendment data. The “amendment rule” affects the result of the combinatorial weighting method from “artificially given” to “formula calculation” in the subjective weighting method, greatly reducing the subjectivity. Additionally, for time-series samples, if the pollution degree is selected as the factor affecting the combination weight, the weight value should not be constant but change with changes in the pollution degree of the sample. Therefore, the OSM method is introduced to calculate the local weight of each indicator in each sample in this study. The comprehensive weight obtained by EWM and the amendment rule, and the local weight of each sample obtained by the OSM method are weighted, and global and local weight values (hereinafter referred to as the ESO weight) are obtained, which can reflect the degree by which the standard is exceeded and dispersion of the sample. The weight value obtained by this method (hereinafter referred to as the ESO method) is highly comprehensive and robust; thus, it is high-quality. The main objectives of this study were as follows: 1. To introduce the improved weight assignment method, i.e., the ESO method, and combine it with the fuzzy synthetic evaluation method (FSEM) to evaluate the water quality of Chagan Lake and determine whether it meets the water quality standards of the 13th Five-Year Plan; 2. To compare the ESO method to traditional weighting methods, such as the EWM, OSM, and single-factor evaluation method, thereby demonstrating its advantages and progressiveness.
Chagan Lake, the largest natural lake in Jilin Province, plays an important role in the ecological environment of the area and was approved as a nature reserve by the State Council in 2007. However, the retreat of farmland threatens the water quality of Chagan Lake. To elucidate whether Chagan Lake meets the class III provincial water quality target of the “13th Five-Year Plan”, ten years of water quality monitoring data were collected from the center of Chagan Lake between 2007 and 2016, and the combination weighting method proposed in this study was used to evaluate the water quality of Chagan Lake.