# Fuzzy MCDM Methodology for Analysis of Fibre Laser Cutting Process
At the same time, the existence of noise factors further affects cutting process variability and the resulting process performance [5], making it very difficult to select a particular combination of process parameters for each specific sheet material type and thickness. Moreover, as noted by [PERSON] et al. [6], in the laser cutting process, planning decisions include the consideration of the effect of multi-dimensional parameters on different preselected criteria and desirable process outputs. A comprehensive review related to the analysis of the effects of laser cutting parameters on different criteria in laser cutting of metals is available [7]. Nonetheless, the trial and error method is frequently seen as an acceptable approach for selecting laser cutting conditions during the manufacturing process [8]. However, although it may be sufficient for usual production requirements, it cannot efficiently handle multiple requirements, in terms of achieving particular process performance values, of different importance at the same time. Moreover, not only may the selection of laser cutting conditions be time-consuming and costly, but an inadequate selection of laser cutting conditions may also lead to different quality defects such as dorsal formation, wide heat affected zone, kerf taper, pittings, etc. [3]. In order to overcome these issues and select a particular combination of laser cutting parameters with respect to single or multiple criteria, different scientific/engineering approaches have been proposed, such as [PERSON]'s robust design methodology [9; 10; 11], empirical modelling and optimization [12; 13; 14; 15], artificial intelligence methods [16; 17; 18; 19; 20], fuzzy logic [21; 22; 23; 24] and multi-criteria decision-making (MCDM) methodology [8; 25; 26; 27; 28; 29; 30]. Given the limited application of MCDM methodology for analysis and assessment of laser cutting conditions, along with certain limitations, such as difficulty in determining the exact quantitative values of criteria weights in situations where criteria weights, as determined by a panel of decision makers, may vary, as well as handling uncertain attribute values, the present study promotes the use of fuzzy MCDM methodology for the analysis of the fibre laser cutting process, assessment of alternative cutting conditions and selection of favourable cutting conditions. Within the proposed framework, an attempt has been made to compare applied fuzzy MCDM methods, such as fuzzy TOPSIS, fuzzy WASP and fuzzy ARAS methods, by using [PERSON]'s tau-b and [PERSON]'s rho tests to analyse the ranking consistency of alternatives. In addition, a mathematical model is proposed to approximate the fuzzy decision-making rule so as to gain insight into the significance of process parameters and to identify the process window with the most favourable laser cutting conditions. It is believed that the proposed methodology can provide a more objective and robust analysis. Experimental data for the development of the fuzzy MCDM model was acquired using a Box-Behnken design with different combinations of three laser cutting parameters (focus position, cutting speed and oxygen pressure). Kerf width on a straight cut, kerf width on a curved cut, surface roughness and surface productivity were considered the relevant criteria for the assessment of cutting conditions in fibre laser cutting of mild steel using oxygen as the assist gas.