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

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.

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 parameterized fuzzy membership distributions governed by a single effective uncertainty ratio, constructs a correlation structure in the five-dimensional 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).

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 fewer cross-loadings and a more differentiated loading pattern in this empirical case under the adopted exploratory specification. From an information-theoretic perspective, FE-EFA produces higher entropy (average = 0.8688) and low Jensen-Shannon divergence (average = 0.0133), suggesting a limited redistribution of ordinal information without substantially altering the overall distributional structure. Entropy-adjusted weighting further reveals systematic shifts in indicator importance across key dimensions.

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 suggesting a more differentiated organization of latent constructs and indicator-level representations in this empirical context. The proposed approach provides an exploratory representation-level extension for perception-based evaluation and decision support in tramway cultural tourism development and related contexts.