## 6 Conclusions  
This study addresses for the first time FJSSP in fuzzy environments considering parameters and constraints of real production systems such as sequence-dependent setup times, due windows, recirculation, and consideration of earliness and tardiness in objective functions. Due to the complexity of the FJSSP, it is necessary to use artificial intelligence techniques such as genetic algorithms, which provide satisfactory solutions in reasonable computation times. One of the main contributions of this article is the proposal of a genetic algorithm and four heuristics since they represent one of the first approaches to tackle the FJSSP considering the realistic conditions presented in this study and applied to a fabric finishing production system.  
When comparing the results of the proposed genetic algorithm with different heuristics, it was possible to verify that, in all cases, the proposed methodology exceeded the performance of the heuristics by more than 30%, which shows the effectiveness of the proposed algorithm. Additionally, the GA provides satisfactory solutions regarding the possibility and number of tardy jobs. Moreover, the computing time of the genetic algorithm is viable for operating environments; therefore, it can be used daily in flexible job shop systems once the production orders are available. These results showed that the proposed genetic algorithm provides the best solutions for the FJSSP, outperforming heuristics widely used in production systems. Consequently, this study reduces the penalties related to earliness and tardiness and flexible job shop systems, increasing customer service and storage costs, inventory obsolescence, and lost sales.  
Despite the contributions of the study, it still has some flaws. In the future, datasets such as BRdata [44], Kacem data [45], BCdata [46], and HUdata [47] can be used to test the efficiency and effectiveness of the proposed GA, and compare its performance with other metaheuristics such as ACO, ABC, AIS, NS, SA, TS, PSO, hybrid metaheuristics, and other evolutionary algorithms. Likewise, future studies could include orthogonal experiments for parameter tuning for both the genetic algorithm and the metaheuristics used as benchmarks. Future works could consider changes in work speed, limitations in transportation and storage within the production system, machine downtime, and stockout probabilities. Moreover, the proposed algorithm could be complemented with a local search algorithm to improve the fitness of the chromosomes and reduce the number of iterations necessary to find a satisfactory solution.  
Conceptualization, E.A.C. and E.R.-V.; methodology, E.A.C., E.R.-V. and J.A.C.; software, E.A.C.; validation, E.R.-V., J.A.C. and R.G.-M.; formal analysis, E.A.C. and J.A.C.; investigation, E.A.C.; resources, R.G.-M.; data curation, E.A.C.; writing--original draft preparation, E.A.C. and J.A.C.; writing--review and editing, J.A.C. and E.A.C.; visualization, E.R.-V. and P.C.; project administration, E.A.C.; funding acquisition, R.G.-M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data will be accessible upon request.  
The authors declare no conflict of interest.