## 3 Evaluation Model Based on Intuitionistic Connection Cloud Model  
_Basic Principle and Evaluation Process_  
The basic principle of the evaluation model based on the intuitionistic connection cloud model is as follows. First, select the evaluation indicators and classification standards to construct the evaluation index system. Then, specify the numerical characteristic parameters of the intuitionistic connection cloud and generate the intuitionistic connection cloud. Next, investigate the weight assigned via the improved information entropy method based on the rough set and determine the intuitionistic connection degree of the sample to each grade. Finally, identify the shrinkage-swelling grade of the sample according to  
Figure 1: Comparisons of normal cloud, connection cloud, and intuitionistic cloud. the principle of maximum membership degree. The corresponding process is shown in Figure 2. And detailed steps are listed as follows. **Step 1:** Set up an evaluation index system of the shrinkage-swelling grade. The shrinkage-swelling mechanism of untreated and lime-treated expansive clays is complex, and there are many influencing factors. According to the references [10; 16] and the Chinese National Standards GB/50112 [17], five kinds of indexes, including the liquid limit \(C_{1}\), total shrinkage-swelling rate \(C_{2}\), plasticity index \(C_{3}\), natural water content \(C_{4}\), and free expansion rate \(C_{5}\), are selected as evaluation indicators, and the shrinkage-swelling property is divided into four grades: extreme high (I); high (II); moderate (III); and low (IV). The corresponding classification standard [16] is listed in Table 1.  
**Step 2:** Determine the weight of the evaluation index via the improved information entropy method based on the rough set. Since the rough set does not require any prior knowledge outside the dataset of the decision problem itself, it can effectively avoid human subjective errors [18] but ignore the cases where the weight of the index is 0. As we know, each index has a certain effect on the shrinkage-swelling property of soil, so their influence cannot be ignored in the evaluation process. To make full use of the objective information of sample data and take into account the impact of various attributes, this paper introduces an improved conditional information entropy \(I(D|C)\) method to distinguish index importance; that is, the corresponding weight \(\mathbf{w}\) of the evaluation index is as follows [18]:  
\[w(c_{i})=\frac{sig(c_{i})+I(D|c_{i})}{\sum\limits_{b\in C}[sig(b)+I(D|b)]}, \tag{5}\] \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Grade** & **Liquid Limit \(C_{1}\)\%** & \begin{tabular}{l} **Total Shrinkage-** \\ **Swelling Rate \(C_{2}\)/\%** \\ \end{tabular} & **Plasticity Index \(C_{3}\)** & \
\begin{tabular}{l} **Natural Water** \\ **Content \(C_{4}\)/\%** \\ \end{tabular} &
\begin{tabular}{l} **Free Expansion** \\ **Rate \(C_{5}\)/\%** \\ \end{tabular} \\ \hline Extreme High, I & 55–100 & 6–100 & 35–100 & 0–15 & 85–200 \\ High, II & 50–55 & 4–6 & 25–35 & 15–25 & 70–85 \\ Moderate, III & 45–50 & 2–4 & 18–25 & 25–35 & 55–70 \\ Low, IV & 40–45 & \(-\)2–2 & 0–18 & 35–100 & 0–55 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification standard for the shrinkage–swelling grade [16]. Figure 2: Flowchart for the shrinkage–swelling evaluation of untreated and lime-treated expansive clays. where \([u_{hm},\ 1-v_{hm}]\) is the membership interval of the index \(m\) of sample \(h\). To specify the connection degree of the sample to each grade, combined with the index weight vector \(\mathbf{w}\), the aggregated membership interval vector \(\mathbf{R}\) is obtained as follows:  
\[\mathbf{R}=\mathbf{M}\mathbf{w}^{\prime}, \tag{10}\]  
where \(\mathbf{w}^{\prime}\) is the transpose matrix of the matrix \(\mathbf{w}=[w_{1},\,\ldots,w_{m}]\). **Step 4**: Calculate the numerical characteristics of the intuitionistic connection cloud, generate \(N\) cloud droplets in a finite interval, and then specify the intuitionistic connection degree.