The Linear Diophantine Fuzzy Z-Numbers Set: Development and Application to Decision Making in Textile Engineering Using the Bonferroni Mean Operator

In this research, we introduce a novel approach to multi-attribute decision making by defining the Linear Diophantine Fuzzy Z-number set and generalizing the Bonferroni mean operator to this framework. Fuzzy Z-numbers are known for their ability to handle imprecise information by considering both a restriction (fuzzy number) and a reliability (degree of confidence). By extending these to linear Diophantine fuzzy sets, we incorporate more complex relationships between attributes, allowing for a deeper exploration of decision scenarios that involve uncertainty and interdependencies. The proposed generalized Bonferroni mean operator captures interactions between multiple attributes, providing a more robust aggregation mechanism in decision-making processes. We have applied this methodology to a real-world problem in textile engineering, selecting the best fabrics for designing new cricket uniforms. Textile selection involves multiple conflicting criteria such as durability, comfort, moisture absorption, and aesthetics. Our method handles these complexities efficiently to allow decision-makers to compare fabrics in an uncertain environment while taking trade-offs between different criteria into account. It can potentially lead to skills applications that match a variety of manufacturing industries, where one of the key factors for function and competitiveness is the efficient use of materials. The designed framework is capable of improving decision-making and providing a more sophisticated framework for evaluation of alternatives under uncertainty which has implications in both fuzzy logic theory and textile engineering fields.