## 3 Evaluation Model of Current Situation of River and Lake Shoreline Planning and Utilization
### Improved Matter-Element Extension Evaluation Model
#### 3.2.2 Improved Matter-Element Extension Model  
Assuming that the name of the thing to be evaluated is N, the characteristic of the thing is C, and the characteristic value is V, then it is recorded as R = (N,C,V). The ordered triple composed of the three is called the basic matter-element. The current status of river and lake shoreline planning and utilization is defined as the basic matter-element R, then the level of the status quo is N, each evaluation index of the current situation is C, and the range of each evaluation index is V.  
(1) Evaluation level determination.  
The evaluation grade of the current situation of river and lake shoreline planning and utilization is divided into five levels, i.e., excellent, good, medium, little poor, and poor, which are expressed by S\({}^{\ast}\), S\({}^{\ast}\) = (S\({}^{\ast}\)1, S\({}^{\ast}\)2, S\({}^{\ast}\)3, S\({}^{\ast}\)4, S\({}^{\ast}\)5). The evaluation level and scoring criteria for the current situation of river and lake shoreline planning and utilization are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Evaluation Level** & **Excellent** & **Good** & **Medium** & **Little Poor** & **Poor** \\ \hline Score & (90, 100) & (80, 90) & (60, 80) & (40, 60) & (0, 40) \\ \hline \end{tabular}
\end{table}
Table 1: Evaluation grade and scoring standard of the current situation of river lake shoreline planning and utilization.  
(2) Determining the classical domain.  
\[R_{0}=(N_{08^{*}},\ C_{j},\ V_{08^{*}j})=\begin{bmatrix}N_{08^{*}}&c_{1}&<a_{08^{ *}1},&b_{08^{*}1}>\\ &c_{2}&<a_{08^{*}2},&b_{08^{*}2}>\\ &\vdots&&\vdots\\ &c_{j}&<a_{08^{*}j},&b_{08^{*}j}>\end{bmatrix} \tag{12}\]  
In Formula (12), \(R_{0}\) is the matter-element of the classical domain, \(N_{08^{*}}\) is the \(s^{*}\) evaluation level of the classical domain(\(s^{*}\) = 1, 2,..., 5), \(C_{j}\) is the status quo evaluation index, \(j\) = 1, 2,..., n, \(V_{08^{*}j}\) is the scoring standard of the \(s^{*}\)th evaluation level of the \(j\)th index in the classical domain, \(a_{08^{*}j}\), \(b_{08^{*}j}\) are the upper limit of the \(s^{*}\)th evaluation level scoring standard of the \(j\)th index and lower limit.  
(3) Determine the section field.  
\[RP=(NP,\ C_{j},\ VP)=\begin{bmatrix}NP&c_{1}&<ap_{1},&bp_{1}>\\ &c_{2}&<ap_{2},&bp_{2}>\\ &\vdots&&\vdots\\ &c_{n}&<ap_{j},&bp_{j}>\end{bmatrix} \tag{13}\]  
In Formula (13), \(RP\) is the matter-element of the node domain; \(NP\) is the individual to be measured for the status quo evaluation; \(ap\) and \(bp_{j}\) are the lower and upper values of the \(j\)th index, respectively.  
(4) Determine the matter element to be evaluated  
\[R_{k}=(N_{k},\ C_{j},\ V_{kj})=\begin{bmatrix}N_{k}&c_{1}&v_{1}\\ &c_{2}&v_{2}\\ &\vdots&\vdots\\ &c_{j}&v_{j}\end{bmatrix} \tag{14}\]  
In Formula (14), \(R_{k}\) is the matter element to be evaluated, \(N_{k}\) is the \(k\)th evaluation individual, \(k\) = 1, 2,..., m, and \(V_{kj}\) is the score of the \(j\)th evaluation index of the \(k\)th evaluation individual.  
(5) Standardized processing  
\[R^{\prime}_{0}=(N_{08^{*}},\ C_{j},\ V^{\prime}_{08^{*}j})=\begin{bmatrix}N_{ 08^{*}}&c_{1}&<\frac{a_{08^{*}1}}{bp_{1}},\frac{b_{08^{*}1}}{bp_{1}^{*}}>\\ &c_{2}&<\frac{a_{08^{*}2}}{bp_{2}},\frac{b_{08^{*}2}}{bp_{2}}>\\ &\vdots&&\vdots\\ &c_{j}&<\frac{a_{08^{*}j}}{bp_{j}},\frac{b_{08^{*}j}}{bp_{j}}>\end{bmatrix} \tag{15}\]  
\[R^{\prime}_{k}=(N_{k},\ C_{j},\ V_{kj})=\begin{bmatrix}N_{k}&c_{1}&\frac{v_{1 }}{bp_{1}}\\ &c_{2}&\frac{v_{2}}{bp_{2}}\\ &\vdots&\vdots\\ &c_{j}&\frac{v_{j}}{bp_{n}}\end{bmatrix} \tag{16}\]  
In Formulas (15) and (16), \(R^{\prime}_{0}\), \(R^{\prime}_{k}\) are divided into normalized classical matter-element and evaluation matter-element.  
(6) Calculation of closeness function values.  
The closeness function formula is as follows:  
\[H_{s^{*}}(v_{kj})=1-\frac{1}{n(n+1)}\sum_{j=1}^{n}D_{j}(v_{kj})\omega_{j} \tag{17}\]