Bayesianize Fuzziness in the Statistical Analysis of Fuzzy Data

2025-01-31

AI Summary

Subjective assessments in social sciences—such as Likert-scale responses and fuzzy ratings—yield bounded fuzzy data for which rigorous regression inference remains underdeveloped. Method: This paper introduces the first Bayesian regression framework specifically designed for bounded fuzzy data. It models fuzzy observations as outcomes of a covariate-driven coarsening process applied to an underlying continuous latent variable, thereby unifying conditional probability modeling with Bayesian inference. Efficient approximate inference is achieved via a hybrid strategy combining Gibbs sampling and posterior quadratic approximation. Contribution/Results: Simulation and empirical studies demonstrate that the proposed method substantially improves parameter estimation accuracy, reliability of uncertainty quantification, and model interpretability. By bridging theoretical fuzzy statistics with practical requirements of social science research, the framework advances the empirical applicability of fuzzy statistical modeling.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based framework remains undeveloped. Hence, we propose a novel approach for analyzing bounded fuzzy variables within a regression framework. Building on the premise that fuzzy data result from a process analogous to statistical coarsening, we introduce a conditional probabilistic approach that links observed fuzzy statistics (e.g., mode, spread) to the underlying, unobserved statistical model, which depends on external covariates. The inferential problem is addressed using Approximate Bayesian methods, mainly through a Gibbs sampler incorporating a quadratic approximation of the posterior distribution. Simulation studies and applications involving external validations are employed to evaluate the effectiveness of the proposed approach for fuzzy data analysis. By reintegrating fuzzy data analysis into a more traditional statistical framework, this work provides a significant step toward enhancing the interpretability and applicability of fuzzy statistical methods in many applicative contexts.

Problem

• Develop regression framework for bounded fuzzy variables
• Link fuzzy statistics to underlying statistical model
• Enhance interpretability of fuzzy statistical methods

Innovation

• Bayesian approach for fuzzy data analysis
• Conditional probabilistic model for fuzzy statistics
• Gibbs sampler with quadratic approximation