# Prediction of MAG Welding Formation Based on Fuzzy Interpolation Reasoning
## 1 Introduction
[19] proposed a fuzzy LaGrange's interpolation reasoning method based on geometric parameters according to slope. Relying on transforming intermediate rules, such as those given in [PERSON] and [PERSON] [20,21], [PERSON] et al. [22], [PERSON] et al. [23] and [PERSON] et al. [24], have been popularly studied and widely applied, despite their relative recency. [PERSON] and [PERSON] [20, 21] used the gravity feature of membership function graph to construct intermediate rules, then used scale and move transformations to obtain the reasoning consequences. [PERSON] et al. [25] selected a subset of rules from the sparse rule base with an embedded rule-weighting scheme for the automatic assembling of the intermediate rule. [PERSON] et al. [26] measured and subsequently added certain interpolated rules that are deemed of high value into the sparse rule base. In addition, some interpolation methods [25,27] using the weighted rule-interpolation scheme, which generates attribute weights given a sparse rule base and integrates them into nonweighted FRI for classification and prediction. Through continuous development, some methods were successfully applied to control and prediction [28, 29, 30, 31]. Most of the above methods have some shortcomings, and some of the reasoning results of these methods will lead to nonconvex Fuzzy set [15], poor applicability [19], and high computational complexity [20,21]. The distance and similarity of fuzzy sets are important concepts to judge the degree of difference between two fuzzy sets. In the existing research, the fuzzy set distance is mostly defined based on the cut set and representative value of the fuzzy set, which simplifies the calculation of the fuzzy set distance, but may lead to an insufficient description of the distance reflecting the whole fuzzy set. Therefore, this paper defines the distance of fuzzy sets by normalizing the Euclidean distance. The intermediate rules are constructed by calculating the distance between the observed values and the fuzzy sets of adjacent rules. The final inference conclusion is determined according to the similarity of fuzzy sets. This method can obtain inference conclusions that satisfy the normality and convexity of fuzzy sets, and are also applicable to different types of Fuzzy sets. It is of great significance to improve the interpolation inference method system. Welding is an important process in industrial production. Due to the complexity of its process mechanism, it is difficult to describe through precise mathematical models. At present, the prediction, decision-making, and control of welding processes are usually completed by the experience and knowledge of experts and technicians. For this type of knowledge, it is more appropriate to use fuzzy language to describe it. The establishment of welding process parameter models usually requires a large number of prior experiments to complete. For the widely used fuzzy inference model--Mamdani fuzzy inference model--the inference process requires a complete rules base. It is difficult to construct a welding formation prediction model using such inference models. The more rules reflect the relationship between welding process parameters and welding formation quality, the more parameter experiments are required to establish the rules. The fuzzy interpolation inference method does not require a complete rules base to achieve inference. To address the above issues, we propose a welding formation prediction method based on fuzzy interpolation inference, and provide an idea for achieving efficient and convenient welding formation prediction. More importantly, fuzzy interpolation reasoning has better application prospects for achieving welding process parameter designs and real-time control of welding formation. The paper is organized as follows. For completeness, Section 2 reviews the KH methods and HS methods. Section 3 describes the new interpolative reasoning method. Section 4 provides an application example of MAG welding formation prediction. Finally, in Section 5, we discuss our conclusions.