The study area was selected to be in the mainstream of the Haihe River, with a total of 3 monitoring stations and a monitoring water area of 330 hm². Each station was conducted in May, July, and September from 2016 to 2020. The latitude and longitude of the monitoring stations are listed in Table 1.

Table 1. The longitude and latitude of the station for the mainstream of Haihe River.

Water quality monitoring items: permanganate index, total nitrogen, total phosphorus, petroleum, dissolved oxygen. The sample collection and testing methods were implemented in accordance with TheSpecificationforEcological Environment MonitoringofFisheries—Part 1:General Rules ([10]).

One water sample was taken at each station, with a sampling depth of 0.5 m, and arithmetic mean values were calculated from the three monitoring stations for each month.

The entropy weight fuzzy comprehensive evaluation method was used to analyze and evaluate the water quality status of the mainstream of Haihe River.

2.3.1. Establish Evaluation Factor

Assume that the fuzzy subset composed of the actual measurement concentration results of themwater quality indicators participating in the evaluation in the evaluation index was:

U = { x 1 , x 2 , x 3 , ⋯ , x i , ⋯ , x m } , where x_i was the actual measurement result of the evaluation parameter i.

2.3.2. The Establishment of Fuzzy Evaluation Set

The evaluation set was a collection of all possible evaluation results for each evaluation object. The evaluation set of environmental quality was a collection ofnwater quality evaluation standard grades corresponding tomwater quality indicators, which can be expressed as:

V = { V 1 , V 2 , ⋯ , V j , ⋯ , V n } , where V_j is thenevaluation standard grades of the evaluation parameter x_i.

According to the Environmental Quality Standards for Surface Water ([11]), the surface water quality was divided into five grades. Therefore, the evaluation set is determined to be S = {I, II, III, IV, V}. The environmental quality grade standards for surface water were in Table 2.

Table 2. Quality standard for surface water mg/L.

2.3.3. Establish Fuzzy Relationship Matrix

After both X and V were given, by evaluating each pollution index, the fuzzy relationship between each pollution index and each evaluation standard was obtained, thereby establishing a fuzzy relationship matrix R:

In the formula: m is the number of evaluation factors, i = 1 , 2 , ⋯ , m ; n is the water grade, j = 1 , 2 , ⋯ , n .

If the water environment quality index is better with a small distribution, its membership function adopts a small-scale distribution (such as COD_Mn, etc.), Dissolved oxygen is just on the contrary. Larger value is preferred, and big distribution is used.

The method of establishing the membership function of the concentration of each evaluation index for the partial small distribution is as follows:

The membership function of the I-level water corresponding to the i-th index can be expressed as:

The membership function of the j-level water corresponding to the i-th index can be expressed as:

The membership function of the n-level water corresponding to the i-th index can be expressed as:

r_ij represents the measured value of the environmental factor of the i-th pollutant, which can be judged as the possibility of the j-th level of water environmental quality level, that is, the degree of subordination of the i-th index to the j-grade water environmental quality standard.

2.3.4. Determination of Weight

If the evaluation index and evaluation object are m and n respectively, the original matrix can be formed as: R ′ = ( r ′ i j ) m × n .

Standardize the data on the original matrix, and get:

r_ij is the standard value of the j-th evaluation object on the evaluation index, r_ij ϵ [0, 1]. Among them, for the big distribution factors, and get:

For the small distribution factors, and get:

2.3.5. Determination of Entropy

In the evaluation system where the evaluation index and evaluation object are m and n respectively, the entropy of the i-th index is defined as:

In the formula: i = 1 , 2 , ⋯ , m , f i j = r i j ∑ j = 1 n r i j , k = 1 ln n , and suppose that in the formula: f i j = 0 , f i j ln n = 0 .

2.3.6. The Definition of Entropy Weight

On the basis of the definition of entropy value, define the entropy weight of the i-th index, namely:

The measured average values of the physical and chemical factors in May, July, and September from 2016 to 2020 are shown in Table 3.

Table 3. Mean value of the physical and chemical factors.

The fuzzy relationship matrix R represents the membership degree of the actual measured value of each factor to each grade of water quality. For example, the water quality matrix of the mainstream of Haihe River in May 2016 is as follows:

Follow the same method to establish other fuzzy relationship matrix, and this paper will not list them one by one here.

Table 4. The entropy weight of every evaluation index.

The fuzzy relationship matrix and the entropy weight are combined to obtain the fuzzy comprehensive evaluation set of each evaluation object, which is defined as the following formula:

In the formula, K is the result of fuzzy comprehensive evaluation; W is the entropy weight obtained from Table 4; R is the fuzzy relationship matrix obtained from (10).

Table 5 shows the fuzzy comprehensive evaluation results of the water quality monitoring in the mainstream of Haihe River from 2016 to 2020.

Table 5. Results of the fuzzy synthetic evaluation.