A Quantitative Explainability Quality Index Framework for Visual XAI in Fuzzy Group Decision-Making for Supply Chain Facility Localization

Visual explainable artificial intelligence (XAI) is an important mechanism for connecting analytically complex decision models with practitioners who must interpret and act upon their outputs in industrial supply chains. In facility localization problems, wafer foundries and other capital-intensive manufacturers must evaluate geographically dispersed candidate sites against multiple uncertain criteria. The ability to communicate fuzzy group decision-making (FGDM) outcomes in a transparent, interpretable form has direct operational relevance. The literature has introduced hanging gradient bar charts, gradient bidirectional scatterplots, and traceable aggregation charts as visual XAI instruments for semiconductor supply chain localization that show substantial reductions in interpretation error versus conventional plots. However, the quantitative assessment of explanation quality itself remains underdeveloped. To address such a gap, this research proposes a quantitative explainability quality index (XQI) that formalizes visual explanation quality in FGDM as a composite measurable construct. XQI integrates two complementary layers: (1) An objective explainability layer (OEI), consisting of normalized fuzzy interpretation deviation, response time, ranking fidelity, and interpretation accuracy, and (2) a subjective explainability layer (SEI), consisting of perceived understanding, perceived transparency, decision confidence, and cognitive load. Trust, acceptance, and decision quality are downstream outcome constructs rather than components of the index. A weighted linear combination of OEI and SEI produces a single index for systematic, reproducible comparison across competing visualization designs. A structural equation model is specified as a planned validation mechanism for examining how explanation quality may relate to trust, acceptance, and downstream decision quality. The proposed validation framework includes a semiconductor facility localization scenario, three visualization conditions, and a planned participant pool of 150–240 supply chain managers, engineers, and graduate students. The XQI framework transforms visual XAI from a descriptive communication aid into a testable decision-support construct, thereby addressing a key evaluation gap in the FGDM visualization literature.