## 2 Theory
### Intuitionistic Connection Cloud Model  
The normal cloud model can transform qualitative concepts into quantitative data; thus, it is widely used in the analysis of uncertainty problems. However, it still has some defects. First, the cloud droplets mapped by the normal cloud generator are established in an infinite interval, which makes it difficult to describe the actual distribution of the evaluation index in the finite interval. Second, the actual distribution of the evaluation index sometimes struggles to meet the assumption of normal distribution. Finally, the common interaction among uncertainties in the classification problem is ignored, so the conversion trend of the evaluation results at the grading threshold cannot be effectively reflected. These shortcomings limit the application scope of the normal cloud and may cause deviations between the results and the actual situation. To make up for these defects of the normal cloud, [PERSON] et al. improved the normal cloud model by using the connection number theory and proposed a new connection cloud model [10]. Connection number theory developed from the principle of set pair analysis can analyze uncertain problems from the perspectives of identity, discrepancy, and contrary aspects. Definition 2: Let \(\mathbf{P}\) be a quantitative domain and \(\mathbf{Q}\) be a qualitative concept of \(\mathbf{P}\). If \(x\in\mathbf{P}\) is a random event of concept \(\mathbf{Q}\) and satisfies \(x\)-N(Ex, \((Ent^{\prime})^{2}\)), \(Ent^{\prime}\)\(\sim\)N(En, He\({}^{2}\)), then the distribution of \(x\) in the universe \(\mathbf{P}\) is called the connection cloud, and each \(x\) is a simulated cloud droplet. Similar to the certainty in the normal cloud, the membership degree of the cloud droplet \(x\) in the connection cloud is called the connection degree \(y(x)\), and its mathematic model is as follows [11]:  
\[y(x)=\exp\left(-\frac{9}{2}\bigg{|}\frac{x-Ex}{3 En^{\prime}}\bigg{|}^{k}\right), \tag{3}\]  
where \(En^{\prime}\) denotes random numbers following normal distribution based on entropy \(En\) and hyper entropy \(He\); and \(k\) is the order of the connection cloud. When \(k=2\), the connection cloud will degenerate into a normal cloud. The connection cloud model considers the actual distribution characteristics of evaluation indexes and describes the relationship between certainty and uncertainty relationships of information, the relationship between indexes and grades, and the conversion trend between adjacent grades. These advantages enable the connection cloud to be widely used in various fields. However, like normal clouds, it still does not deal well with the problem of non-subordination and the hesitation of fuzzy concepts. It can be seen from Equation (3) that when the value of the simulated cloud droplet \(x\) is equal to the mathematical expectation \(Ex\) of the cloud, its connection degree is equal to 1, which does not fully reflect the hesitant characteristics of some fuzzy random concepts [10]; that is, in some cases, the membership of any element of the discussed region cannot be accurately determined, and it is therefore impossible to find the elements that entirely belong to the ambiguous and uncertain classification set. The above drawbacks can be addressed by intuitionistic fuzzy sets, which allow membership to oscillate randomly in an interval rather than being fixed on a crisp number. Therefore, this paper proposes a new intuitionistic connection cloud model using intuitionistic fuzzy sets. Definition 3: Define \(x\) (\(x\in\mathbf{P}\)) as a one-time implementation of \(\mathbf{Q}\) in the region \(\mathbf{P}\). To achieve this, the connection degree is no longer equal to a fixed value of 1 corresponding to \(x=Ex\) but a uniform random number for the connection cloud model. The membership degree \(u\) and non-membership degree \(v\) with the condition \(0\leq u+v\leq 1\) are introduced to express the hesitancy degree of the connection degree.