Methodological Development and Empirical Validation for TCC of Cities Through Hybrid SEM–FAHP–FCE Framework

The quantitative measurement of TCC at tourist cities involves considerable methodological complexities. Conventional evaluation methods based on fixed numerical criteria are frequently insufficient since tourism systems are characterized by unclear information, gradual shifts, and subjective experiences. To address these methodological constraints, this study develops and implements a hybrid FAHP-weighted Fuzzy Comprehensive Evaluation (FCE) framework to estimate TCC. The framework incorporates four critical indicators, visitor density, waste generation, infrastructure load, visitor perception, reflecting the physical, environmental, infrastructural, and socio-cultural dimensions of tourism development. These indicators are assessed using a structured analytical procedure integrating fuzzification, expert-derived weighting through the fuzzy analytic hierarchy process, fuzzy comprehensive evaluation, and centroid defuzzification. This study presents a hybrid SEM–FAHP–FCE framework, which is a multi-method integrated decision model that combines SEM (structural equation modeling) for visitor perception and behavioral drivers, FAHP (fuzzy analytic hierarchy process) for expert-based indicator weighting and FCE (fuzzy comprehensive evaluation) for final carrying capacity assessment under uncertainty. This combined methodology offers a more adaptive and empirically grounded assessment of TCC by synthesizing quantitative conditions with qualitative stakeholder perceptions within a unified evaluative model. The framework is validated through empirical application to Vrindavan, Uttar Pradesh, one of India’s most visited destinations, across eight study sites and two seasonal conditions (normal and festival-peak). Primary data collection comprises 300 visitor count observation units and field data, i.e., visitor count, waste generation and infrastructure details. The defuzzified FAHP–FCE results for each site (W = 3.94, 3.33, 2.44, 1.95, 3.66, 1.87, 1.86 and 2.71) reveal that major pilgrimage nodes exhibit scores approaching the upper bound of the evaluation scale, indicating that tourism pressure has significantly exceeded carrying capacity during peak periods. This study establishes proof-of-concept for the FAHP–FCE framework as a standardized, replicable instrument for evidence-based TCC governance at tourism cities.