# A Classification Model Based on Interval Rule Inference Network with Interpretability
## 6 Experiment and Analysis
### Interpretability Analysis of IRIN  
Experts or decision-makers can intervene in IBRB automatically generated by IRIN based on expert knowledge or experience to modify the results to meet different task needs. In order to illustrate the interpretability and the intervention ability, the IBRB with respect to the Iris dataset automatically generated by IRIN is taken as an example, shown in Table 3.  
The Iris dataset contains four attributes, namely, sepal length, sepal width, petal length, and petal width, and three classes, where each class refers to a type of iris plant as \"Setosa\", \"Versicolour\", or \"Virginica\". In Table 3, \(A_{1}\), \(A_{2}\), \(A_{3}\), and \(A_{4}\) represent the antecedent attribute weights, 0.2496, 0.6754, 0.1146, and 0.8475, respectively; \(D_{1}\), \(D_{2}\), and \(D_{3}\) represent consequents, which are the class labels; each row is a rule, such as the \(R_{15}\) expressed as follows:  
\[\begin{array}{l}R_{15}:\text{if the sepal.length is}\{(L,[0.0002,0.0080]),(M,[0.9920,0.9998]),(H,0.0 )\},\\ \text{AND the sepal.width is}\{(L,[0.1667,0.1766]),(M,[0.8234,0.8333]),(H,0.0)\}, \\ \text{AND the petal.length is}\{(L,0.0),(M,[0.8298,0.9136]),(H,[0.1667,0.1701])\}, \\ \text{AND the petal.width is}\{(L,0.0),(M,[0.8333,0.8412]),(H,[0.1588,0.1667])\}, \\ \text{Then the iris category is}\{(Setosa,[0.2181,0.3661]),(Versicolour,[0.0595,0.0935]),\\ (Virginica,[0.5404,0.7224])\}.\end{array} \tag{67}\]  
with rule weight is0.8998 and attribute weight is\(\{(0.2496),(0.6754),(0.1146),(0.8475)\}\)  
It represents that if the membership degree of the sepal length at short, average, and long is [0.0002, 0.008], [0.992, 0.9998], 0.0, and the membership degree of the sepal width at narrow, average, and wide is [0.1667, 0.1766], [0.8234, 0.8333], 0.0, and the membership degree of the petal length at short, average, and long is 0, [0.8298, 0.9136], [0.1667, 0.1701], the membership degree of the petal width at narrow, average, and wide is 0.0, [0.8333, 0.8412], [0.1588, 0.1667], then the membership degrees that this iris category is setosa, version colour or virginica are [0.2181, 0.3661], [0.0595, 0.0935], and [0.5404, 0.7224], respectively. The rule weight for this rule is 0.8998, and the antecedent attribute weights of the sepal length, the sepal width, the petal length, and the petal width are 0.2496, 0.6754, 0.1146, and 0.8475, respectively.  
When one or more IBRs in IBRB are inconsistent with expert knowledge information, experts or decision-makers can intervene to modify these IBRs according to expert knowledge or experience, thus correcting the results.  
The interpretability of IRIN is illustrated by comparing the consistency of the belief distribution between IRIN and the expert knowledge. More details about the belief distribution can be found in [28]. In Figure 3, the belief distribution of the last 16 rules for IRIN and expert knowledge are depicted. It can be observed that the belief distributions of IBRB are basically consistent with these of expert knowledge, especially rules 28, 27, 20, 19, and 18, which are drawn with pink ellipse. For rules 16, 17, 21, and 22, the differences in their belief distributions compared to expert knowledge may be due to noise interference during the automatic generation of the IBRB by IRIN. However, experts or decision-makers can use their expert knowledge or experience to intervene and modify these rules. Therefore, the belief distribution of the IBRB automatically generated by IRIN can better retain the characteristics of expert knowledge information and effectively handle interval uncertainty, while also improving IRIN's interpretability and ensuring classification accuracy.