# Prediction of MAG Welding Formation Based on Fuzzy Interpolation Reasoning
## 1 Introduction  
Welding technology is an important production and processing method in industrial production. Due to its low cost, high efficiency and reliable connection, it is widely used in the metal connections of marine production. However, welding is a highly nonlinear, time-varying and multicoupling typically complex process; thus, it is difficult to describe accurately by a model. Usually, the quality of welded joints is directly affected by the welding input parameters, as the selection of welding process parameters has a significant impact on the quality of welded joints. At present, the determination of welding process parameters and the prediction of welding formation quality rely more on the experience and subjective judgment of professional and skilled welders. Fuzzy logic can perform well in such situations. In [1; 2; 3; 4], fuzzy logic was used to predict the weld-forming quality and achieved good results. However, the weld-forming prediction model based on traditional fuzzy inference methods has certain limitations. For sparse fuzzy rule bases with incomplete knowledge, traditional fuzzy reasoning methods (like the widely used Mamdani inference method) cannot obtain effective results. It is very meaningful to seek a method for predicting welding formation in a sparse rule base of the welding process. Uncertain information is inevitable in practical applications. One of the challenges for intelligent systems is how to effectively handle uncertainty to achieve more accurate decision-making. So far, there have been many effective studies on uncertain information, like intuitionistic fuzzy sets [5; 6], extension of intuitionistic fuzzy sets [7], complex decision-making [8; 9], evidential reasoning [10; 11], and fuzzy set theory [12]. Since the theory of fuzzy sets was put forward in 1965, it has gradually become a powerful tool to manage the problems of fuzziness and uncertainty, especially for systems based on fuzzy rules, which have been applied in many fields and work effectively [13; 14]. The most widely used fuzzy system is the inference system based on fuzzy rules. Fuzzy inference is an important part of intelligent systems such as fuzzy control, fuzzy expert systems and fuzzy decision support systems. However, traditional fuzzy inference techniques require that any input value must fire at least one fuzzy rule in the rule base, so that the fuzzy inference systemcan operate normally. However, in the process of industrial production, significant time and energy are required to construct a complete rule base that completely covers the entire input domain. However, due to incomplete knowledge, it is not easy to build a complete rule base. When the rule antecedents in the rule base cannot match the given observations, the traditional fuzzy reasoning method will not derive the inference consequence. [PERSON] and [PERSON] [15] proposed the fuzzy rule interpolation method (FRI) in 1993 to solve the above problems, which provides a new way for reasoning under sparse rule bases. In recent years, some fuzzy interpolation reasoning methods applicable to sparse rule bases have been proposed. These interpolation reasoning methods can be summarized into two forms: one is fuzzy rule-interpolation reasoning based on nontransformation methods, and the other is interpolation reasoning based on intermediate rule transformation. The KH method is the earliest nontransformation type of fuzzy rule-interpolation reasoning, but in some cases the reasoning result is not convex. [PERSON] et al. [16] proposed an improved method to ensure the convexity of inference conclusions by using similar transfer inference. [PERSON] et al. [17] improved the method of rule interpolation based on \(\alpha\)-cut set to avoid abnormal consequences. [PERSON] et al. [18] proposed an interpolation reasoning method based on geometric similarity according to the proportion of the geometric area enclosed by the input facts and rule antecedents. [PERSON] et al.