## 4 Numerical Experiment for a Smart Apparel Industry
Before implementing the proposed method, it was necessary to create the MCDM model supporting the operation prioritization phase. In reply, seven job criteria or features (F1: job quantity; F2: customer type; F3: throughput; F4: monthly demand; F5: number of tardy jobs per product; F6: tardiness; and F7: number of remaining process steps) were identified. This set of criteria (Figure 7) was pointed out considering the pertinent scientific literature and the experts' opinion (5 production managers, 2 sales staff, the general manager, and the administrative director of the company). The experts have wide experience in production and demand management (>20 years); in addition, they have been related to the textile sector for more than 15 years and hold a professional degree in Business Administration/Industrial Engineering fields. The design of the hierarchy was led by two coauthors of this paper ([PERSON] and NJ) who have significant expertise and background in MCDM methods. The next step was to elicit the relative priorities of each job criterion in the global decision of selecting the highest priority operation. FAHP was implemented to deal with this task considering its advantage of calculating the importance of each decision element under uncertainty. The ambiguity was incorporated in this application to obtain more realistic results given the nature of human thought and reasoning; in this case, represented by paired judgments or comparisons. In particular, the experts used the five-point scale depicted in Table A4 (Appendix A) to establish how important criterion \(i\) is with respect to criterion \(j\) when choosing the highest priority operation in FJSP. The comparisons were collected through a survey designed in a Microsoft Excel spreadsheet. The matrixes of fuzzy judgments \(\widetilde{A}^{K}\) were derived for each expert using Equation (1). After this, the matrixes were aggregated by employing Equations (2) and (3). The resulting matrix \(\widetilde{A}\) is presented in Table A5 (Appendix A). Following this, the geometric means of the fuzzy comparisons (\(\widetilde{\tau}_{i}\)) were calculated for each decision element (job criterion or feature) by implementing Equation (4) (Table A6). Table A6 (Appendix A) also presents the fuzzy relative priorities of criteria (\(\widetilde{w}_{i}\)), which were achieved by using Equation (5). The fuzzy weights were then converted into crisp values using the center of area method (Equation (6)) (Table A6). These weights were normalized via applying Equation (7). The results revealed that tardiness (F6) was found to be the most important feature (GW = 0.414) when selecting the highest priority operation. This is supported by the fact that clients are more aware of being supplied in a timely manner, as previously agreed. Therefore, non-compliance with this critical factor of satisfaction may represent a potential loss of loyalty and future incomes. In fact, various competitors can take advantage of this weakness and subsequently increase their market share. This is also greatly related to the second aspect of importance in this application (number of tardy jobs per product--F5; GW= 0.203), which aims to reduce the dissatisfaction proportion of products with high expectations and background in the market. Another aspect of relevance is the throughput--F3 (GW = 0.200) of the references offered by the company. The throughput is defined as the amount of money earned by the company per time unit in the bottleneck resource; in other words, the speed at which the FJSS generates money for  
the firm [32; 33]. In this respect, the company is interested in prioritizing those products with high throughput, which would ensure better utilization of their resources. The rest of the criteria (monthly demand, number of remaining steps, and customer type) were not found to be highly significant (GW \(<\) 0.10) on the operation selection model.