Entropy-Based Uncertainty-Aware Exploratory Factor Analysis for Ordinal Data: Application to Tramway Cultural Tourism Evaluation

Background: Perception-based evaluation using Likert-scale survey data is widely applied in tourism and transport research, yet conventional point-valued encoding imposes artificial precision and overlooks ambiguity between adjacent ordinal categories. This limitation is particularly relevant in experiential contexts, where subjective judgments often involve transitional evaluations. Methods: This study develops a parameterized fuzzy–entropy exploratory factor analysis (FE-EFA) framework for uncertainty-aware analysis of ordinal perception data. The approach transforms ordinal responses into fuzzy membership distributions, constructs a correlation structure in membership space, and incorporates Shannon entropy and Jensen–Shannon divergence to characterize distributional dispersion and representation differences. The framework is applied to survey data from Chengdu Tramway Line 2 (N = 1242; 32 indicators). Results: Under the Kaiser criterion (eigenvalues > 1), conventional EFA yields a seven-factor structure, whereas FE-EFA identifies an additional eighth factor located near the retention boundary. Under a unified factor specification, both approaches preserve a consistent high-level structure, while FE-EFA shows clearer factor separation, fewer cross-loadings, and more coherent indicator clustering. From an information-theoretic perspective, FE-EFA produces higher entropy (average = 0.8688) and moderate Jensen–Shannon divergence (average = 0.0133), indicating a controlled redistribution of ordinal information rather than structural distortion. Entropy-informed weighting further reveals systematic shifts in indicator importance across key dimensions. Conclusions: The FE-EFA framework extends conventional Likert-scale analysis by introducing an uncertainty-aware representation layer prior to factor extraction. It preserves overall structural stability while improving the resolution of latent constructs and the sensitivity of indicator representation. The proposed approach provides a practical and theoretically grounded basis for perception-based evaluation and decision support in tramway cultural-tourism development and related contexts.