## 1 Introduction  
Today, non-conventional methods are increasingly used in the processing of sheet materials. Increasing the quality and precision of these machining systems reduces the need for multiple rework operations while achieving satisfactory accuracy, productivity, and economy [1]. The selection of the appropriate cutting process is an important activity from the point of view of investment efficiency in the development of the product or process [2]. From the aspect of machining performances such as surface quality, machining time--productivity and accuracy, the selection of suitable machine tools is the real challenge of today's production [3]. Among non-conventional machining methods, plasma arc machining (PAM), laser beam machining (LBM), and abrasive waterjet machining (AWJM) are most commonly used to cut steel sheets of various thicknesses [4]. Each of these methods has its advantages and disadvantages in terms of machining quality, dimensional accuracy, machining time, and more. For example, the main advantages of PAM are the efficient speed of material removal and the ability to cut different thicknesses, even up to 150 mm. It can be concluded that the productivity of this process is at a high level. In practice, PAM is considered a rough machining process due to the high concentration of energy on a small area [5]. This leads to irregular cut edges and a high value for kerf width, which ultimately results in a poor surface finish and low dimensional accuracy. Compared with the general plasma method, LBM has some obvious advantages. For example, when cutting thin steel sheets, LBM has a much higher cutting speed than plasma [6]. Dimensional accuracy is also better because the laser produces a much smaller width of cut on the workpiece [7]. However, the laser also has disadvantages. The main ones are the high cost of the equipment and the poor surface quality when cutting thicker steel sheets [8]. The aforementioned machining is mainly based on the thermal effect, i.e., the material removal from the workpiece is achieved by melting. This high heat has a negative effect on the integrity of the workpiece surface. On the other hand, AWJM is a cold process. Therefore, it is irreplaceable when a machined surface without thermal influence is required [9]. Compared to the previous two processes (PAM and LBM), the cutting speed of AWJM is relatively low, especially when cutting thicker materials. In general, it is quite difficult to make a decision on which process is best in terms of accuracy, surface quality and productivity. In these cases, decision support systems are used to make the right choice. Poor decision making in cutting process selection can lead to serious problems in production. The process of selecting the machine for the specific operation in question is an important issue for any manufacturing company [10]. This is because irregular selection of cutting process can have a negative impact on technological parameters [11]. In general, these problems can have a negative impact on the overall effect of a production system. Technological parameters directly depend on the type of cutting process selected. However, making the right choice is a difficult process that requires a certain level of expertise and experience. To make a correct decision, a large amount of data must be analyzed, especially as many input/output factors as possible [12]. Selecting a cutting process is usually a difficult decision for engineers because there are many qualitative and quantitative characteristics that must be considered when selecting a suitable cutting process. To solve problems in this field, researchers have often used various methods based on multiple criteria, such as Analytic Hierarchy Process (AHP) [13], Multi criterion optimization and compromise solution (VIKOR) [14], Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) [15], Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) [16], and Analytical Network Process (ANP) [17].