A multivariate framework for measuring international mobility in tertiary education with neutrosophic sentiment assessment

International mobility of tertiary education is vital for countries engaged in innovative educational research and those wishing to stay ahead in the field. However, cross-national comparisons face a challenge in methodology induced by the phenomenon's multi-dimensionality. This study analyzes the international mobility of tertiary education in 29 countries from 2013 to 2020 using international students as a percentage of enrollment as a primary dependent variable. The goal is to evaluate trends across nations and subsequently propose a composite index of the multi-dimensional phenomenon. A variety of multivariate analytical techniques were employed; for example, STATIS (Structuring de Tableaux À Trois) Statistics Indices determined a composite structure across countries over time, while hierarchical cluster analysis revealed four clusters of countries with distinguished trends of international mobility in tertiary education. Results confirm the existence of significant trends across time for international students' percentage structure, with 2017 and 2020 being essential years. Our main finding is the International Mobility in Tertiary Education Index (IMIET), determined with four dimensions: baseline, dynamism, coherence, and regional differentiation. For example, Latin America and Asia present low levels of baseline and dynamism, which limits their international competitiveness potential; at the regional level, Oceania excels in IMIET segments like dynamism and coherence, suggesting the related public policies developed there in recent years. Additionally, a neutrosophic sentiments assessment allows for a qualitative evaluation of international scholars via truth indeterminacy and falsity components to provide more in-depth assessments of International Mobility trends while exploring qualitative satisfaction, research impediments, and expectations in indeterminacy.