Bipolar linear Diophantine fuzzy EDAS for multi-attribute group decision-making

The formation of new properties for Bipolar Linear Diophantine Fuzzy Set (\( { {\mathcal{BLDFS}}}\)) enhances the evaluation procedure by including control parameters and meticulously accumulating positive as well as negative opinions. While previous approaches encounter difficulties in accurately grasping uncertainties, the design and development of a novel Bipolar Linear Diophantine Fuzzy Evaluation based on Distance from Average Solution (\( { {\mathcal{BLDFEDAS}}}\)) approach aim to bridge the gap in the existing research. An application of implementing this approach is presented by case analysis on choosing the best Forensic Decision Intelligence (\( { {\mathcal{FDI}}}\)) system, as the significance of forensic science in the court system has yet to be demonstrated. Further, a novel Bipolar Linear Diophantine Fuzzy Multi-Attributive Border Approximation Area Comparison (\( { {\mathcal{BLDFMABAC}}}\)) methodology is provided to uplift the effectiveness of results by \( { {\mathcal{BLDFEDAS}}}\). By rigorously incorporating control parameters and bipolarity, the field substantially progresses and establishes a robust framework for tackling ambiguity in decision support systems.