Intuitionistic Fuzzy \(\tilde{\bar{X}} - \tilde {R}\) and \(\tilde{\bar{X}} - \tilde {S}\) Control Charts for Triangular Intuitionistic Fuzzy Numbers

This study proposes a novel methodology for constructing intuitionistic $\tilde{\overline{X}}-\tilde{R}$ and $\tilde{\overline{X}}-\tilde{S}$ control charts by incorporating a ranking method developed explicitly for triangular intuitionistic fuzzy numbers. Unlike traditional fuzzy control charts, the proposed model eliminates the need for defuzzification in the computation process. Instead, all decisions are derived directly through a fuzzy ranking approach, thereby preserving the integrity of the original fuzzy information and preventing information loss. This characteristic constitutes a key contribution of the study. To validate the practical applicability and effectiveness of the proposed methodology, real-world data collected from an engineering facility were utilized. The results were thoroughly analyzed through a real-world manufacturing case study. The application demonstrated that all samples, except for an assignable cause in one specific sub-range, were statistically in control. Most importantly, the proposed approach monitored the process variations without stripping away the inherent subjective hesitation of the decision-makers, thereby demonstrating its potential capability in handling structural uncertainty compared to traditional crisp methods.