# A Classification Model Based on Interval Rule Inference Network with Interpretability
## 1 Introduction  
Classification problems have long been a key component of machine learning in many fields. In view of the nonlinearity, complexity, and uncertainty of the real world, a variety of classification methods have been proposed that perform well in solving classification problems. However, many classification methods, especially neural networks, achieve superior performance at the expense of low interpretability. In recent years, there has been a surge of interest in interpretable machine learning techniques [1, 2, 3, 4]. To address the opacity issue in the decision making of many classification methods, researchers have begun to explore integrating expert knowledge into classifiers [5]. Rule-based classification systems, which integrate expert knowledge and provide high interpretability, have become a prominent artificial intelligence technology [6]. However,when designing and implementing a rule-based classification system, due to the diversity of input data and the complex uncertainty of the real world, the system will inevitably face challenges such as fuzziness, incompleteness, and uncertainty [7,8]. To tackle these challenges, [PERSON] et al. [9] proposed the belief-rule-based inference methodology using the evidential reasoning approach (RIMER). This method establishes rules using belief distributions to effectively handle various types of uncertain knowledge. Subsequently, [PERSON] et al. [10] further expanded the BRB and proposed the extended belief rule base (EBRB). The EBRB embeds belief degrees in antecedent attributes as well as the results of each rule to handle uncertainty more efficiently. However, neither the EBRB nor the BRB consider interval uncertainty, so it cannot effectively handle interval uncertainty caused by interval values, interval belief degrees, and interval reference values. To solve this problem, some researchers have conducted various studies in recent years. Aiming at the interval uncertainty caused by interval reference values, [PERSON] et al. [11] introduced the generalized belief rule base, where grade intervals are used to express consequents, effectively solving the interval uncertainty problem caused by the reference value of the antecedent attribute. Aiming at the interval uncertainty caused by interval values and interval belief degree, [PERSON] et al. [12] extended the ER method to the interval ER method, which effectively dealt with uncertainty, including the interval belief degree and interval value. [PERSON] et al. [7] introduced an interval belief rule-based system (IBRBS) that considers interval data, interval belief degrees, and interval reference values, addressing the overall interval uncertainty. [PERSON] et al. [13] proposed an interval-valued belief rule-based inference method using the evidential reasoning approach (IRIMER). The IRIMER embeds interval-valued belief degrees in both the antecedents and consequents of each rule, allowing it to represent uncertain information or knowledge more flexibly and reasonably than previous belief rule bases. However, although these methods can effectively deal with interval uncertainty, these systems are all set by experts manually. When the data scales or data dimensions increase, there are a large number of parameters in the IBRB system, which inevitably increases the number of parameters. The complexity creates the risk of subjective fallacy. Therefore, determining how to determine these parameters has become a key issue in IBRB research. To date, research on the automatic generation of IBRB is still insufficient. In other rule-based systems, there are some methods for automatic generation, which provide research ideas for building methods for automatically generating IBRBs. [PERSON] et al. [14] proposed a student performance prediction model based on a belief rule base with automatic construction, where the accuracy of the model is improved by optimizing the parameters using the P-CMA-ES algorithm. [PERSON] et al.