## 2 Theory
### Intuitionistic Connection Cloud Model
Combined with the numerical characteristic parameters of the connection cloud model, an intuitionistic connection degree \(z(x)\) is given as  
\[z(x)=\beta\cdot\exp\left(-\frac{9}{2}\bigg{|}\frac{x-Ex}{3 En^{\prime}}\bigg{|} ^{k}\right), \tag{4}\]  
where \(\beta\) is a random number satisfying uniform distribution \(U\left[u,1-v\right]\). If \(u=1,\ v=0\), the intuitionistic connection cloud degenerates into a connection cloud. As denoted above, the cloud drop generation algorithm for intuitionistic connection cloud is depicted as follows:  
1. Initialization of numbers of cloud drops and the lower limitations of the possible values of the membership degree and non-membership degree corresponding to \(Ex\). 2. Generation of random numbers \(En^{\prime}\) from the normal distribution with entropy \(En\) and hyper entropy \(He\). 3. Generation of random numbers \(x_{m}\) satisfying the normal distribution of expectation \(Ex\) and standard deviation \(En^{\prime}\). 4. Generation of random numbers \(\beta\) following the uniform distribution of lower limitation \(u\) and upper limitation \(1-v\). 5. Specification of the intuitionistic connection degree of cloud drops through Equation (4). A corresponding drop is obtained as (\(x_{m}\), \(z(x_{m})\)). 6. Repeat 2 to 5 steps until all cloud drops are obtained. To illustrate the advantages of an intuitionistic connection cloud, Figure 1 uses an example to reflect the theoretical optimization process from the normal cloud to the connection cloud and then to the intuitionistic connection cloud. The classification standard interval of the known value to be evaluated is [6; 12]. The numerical characteristics of the normal cloud and the connection cloud are (\(Ex\), \(En\), \(He\)) = (9.0, 3.0, 0.01) and (\(Ex\), \(En\), \(He\), \(\xi\), \(k\)) = (9.0, 3.0, 0.01, 9.0, 1.70), and the corresponding cloud map is obtained after generating 1000 cloud droplets. However, at the classification thresholds \(x\) = 6 and 12, there is both the possibility of belonging to the adjacent grades and the possibility of not belonging to the adjacent grades; the membership degree should be assigned to 0.5 at these two points. It can be seen from Figure 1 that the connection degree of the two boundary values 6 and 12 in the connection cloud is equal to 0.5, but the degree of certainty in the normal cloud is not equal to 0.5. Therefore, the connection cloud truly reflects the certainty and uncertainty at the thresholds and its conversion trend, which effectively compensates for the defects of the normal cloud. On the other hand, the membership at the \(Ex\) of the connection cloud and norm model is a crisp value 1. This cannot express the hesitation properties. To better deal with the non-membership and hesitation properties of some fuzzy concepts [12], the intuitionistic cloud model incorporates the concept of the hesitancy degree. In Figure 1, let \(\beta\)-\(U\) [0.9, 1]; according to definition 3, the intuitionistic connection degree in the intuitionistic connection cloud is no longer the crisp value of 1 when \(x\) takes the mathematical expectation value of 9; instead, it fluctuates in the range of 0.9-1.0. Therefore, compared with the connection cloud and normal cloud, the intuitionistic connection cloud can more effectively capture uncertainty and realize the objective description of the degree of non-membership and hesitation.