## 5 Discussion
### Superiority of the Proposed Model  
The membership degree of the cloud model changes continuously in the interval \([0,1]\). The sample of connection degree closer to 1 has a greater possibility of belonging to the given grade, and the sample of connection degree closer to 0 presents a greater possibility that the sample does not belong to the given grade. Moreover, membership 0.5 is the mean  
Figure 4: The statistical characteristics of the free expansion rate \(C_{5}\): (**a**) measured values; (**b**) coefficient of variation; and (**c**) standard deviation.  
value of the membership interval [0, 1], which is the boundary point between belonging and not belonging; it is the fuzziest point. For example, as seen in Table 1, it is obvious that the threshold value 35 of index \(C_{3}\) between grade I and grade II is subordinate to both grade I and grade II, the degree of belonging to grade I and grade II is 0.5, and the ambiguity at this point is the highest. So, it is more likely that this point belongs to grade I and grade II. It can be seen from Figure 3e that the membership \(y(\)III\()\) and \(y(\)IV\()\) at this point are both 0.5 in the connection cloud model; so, the connection cloud model can well describe the transformation trend between adjacent grades. However, in the connection cloud model, if the indicator value \(x\) is the expected value, then \(y(x)=1\), which is an accurate representation and ignores the hesitant nature. In contrast, the intuitionistic connection cloud not only retains the advantages of connection cloud but also overcomes the above shortcoming such that the vertex of the intuitionistic connection degree is no longer a crisp value of 1 but fluctuates in an interval slightly less than 1. It is seen from Table 3 that the minimum reliability of the plasticity index is about 0.85, and the maximum intuitionistic connection degree is a random number uniformly generated between 0.85 and 1. Figure 3f is a demonstration of the above random uniform implementation. Thus, the intuitionistic connection cloud model can depict relationships between the interval-valued indexes and classification standards from membership, non-membership, and hesitation aspects, and can deal with multiple uncertainties without information loss or distortion relative to the normal cloud model and connection cloud model.  
The evaluation of the shrinkage-swelling grade is a complex problem with uncertainty indicators. The case study shows that the intuitionistic connection model can overcome the shortcomings of the conventional cloud models and has a better description of uncertainties. The model proposed here can significantly enhance reliability because it can consider hesitation characteristics of the interval-valued index. It has the following benefits over other methods.  
1. Compared with the normal cloud model, the intuitionistic connection cloud model offers a useful basis for the depiction of the certain and uncertain relationships between the interval-valued indexes with classification standards from three perspectives, namely, identity, discrepancy, and contrary aspects. Additionally, it overcomes the disadvantage of the requirement of normal distribution.
2. The proposed model without information loss or distortion can simultaneously express ambiguity, randomness, and hesitation; so, it has the capability to depict high uncertainty in the evaluation of the shrinkage-swelling grade of untreated and lime-treated expansive clays, enhancing the description of the evaluation result \"not one is not the other\".
3. The weights assigned according to the conditional information entropy method based on the rough set can effectively find the index importance. This weighting method can not only avoid prior knowledge and a large number of data requirements but also reduce the errors caused by human factors.