Fuzzy Reasoning Chain ( FRC ): An Innovative Reasoning Framework from Fuzziness to Clarity (2025)

Abstract: With the rapid advancement of large language models (LLMs), natural language processing (NLP) has achieved remarkable progress. Nonetheless, significant challenges remain in handling texts with ambiguity, polysemy, or uncertainty. We introduce the Fuzzy Reasoning Chain (FRC) framework, which integrates LLM semantic priors with continuous fuzzy membership degrees, creating an explicit interaction between probability-based reasoning and fuzzy membership reasoning. This transition allows ambiguous inputs to be gradually transformed into clear and interpretable decisions while capturing conflicting or uncertain signals that traditional probability-based methods cannot. We validate FRC on sentiment analysis tasks, where both theoretical analysis and empirical results show that it ensures stable reasoning and facilitates knowledge transfer across different model scales. These findings indicate that FRC provides a general mechanism for managing subtle and ambiguous expressions with improved interpretability and robustness.

## introduction with the rapid advancement of large-scale language models (llms) @xcite , natural language processing (nlp) has achieved remarkable progress across various domains. however, reasoning with texts that exhibit ambiguity, polysemy, and uncertainty remains a significant challenge. in tasks such as sentiment analysis, ethical judgment, and security review, texts often contain complex emotions, such as "though dissatisfied, still acceptable.", which convey both negative sentiment and a degree of acceptance. this complexity makes traditional approaches, based on fixed labels or static rules, inadequate for capturing the multidimensional semantics @xcite . current fuzzy reasoning approaches quantify ambiguity through membership degrees; however, their reliance on manually defined rules limits their adaptability to dynamic and evolving contexts @xcite . although chain-of-thought (cot) reasoning enhances transparency, its discrete decision-making process often struggles with complex texts, such as those containing sarcasm and contradictions @xcite @xcite . consequently, both fuzzy reasoning and cot methods face limitations when addressing fuzzy and uncertain texts, underscoring the need for a more adaptive, stable, and transparent reasoning framework. in this paper, we propose the fuzzy reasoning chain (frc) framework to address challenges arising from ambiguous and uncertain text, as illustrated in fig. 1 . frc follows the standard step-by-step reasoning procedure typical of sentiment analysis and extends conventional chain-of-thought approaches by replacing discrete probability assignments with continuous fuzzy membership degrees. this transition from probability-based reasoning to fuzzy membership-based reasoning, which we refer to as the probability-to-membership collision, is the core methodological innovation. by capturing conflicting and ambiguous signals that probabilities alone cannot express, frc enables a more nuanced and robust representation of sentiment while naturally identifying "other" or unspecified categories. this fuzzy-to-clear reasoning paradigm ensures stability and transparency. we analyze the convergence behavior of frc and corroborate its practical utility through comprehensive experiments, demonstrating its effectiveness on complex, fuzzy texts and potential for reasoning transfer across model scales. the main contributions of frc are as follows: ## fuzzy reasoning chain in this section, we introduce the fuzzy reasoning chain (frc) framework, which addresses the unclear reasoning in traditional chain-of-thought (cot) methods and the rigidity of fixed-rule fuzzy reasoning, providing a fuzzy-to-clear inference approach. a comparison between cot and frc is shown in fig. 1 , where frc refines sentiment analysis through fuzzy membership degrees, facilitating a smoother transition from fuzzy to clear sentiment analysis. observations of llms @xcite @xcite reveal key characteristics in the generated semantic membership degrees, particularly in sentiment analysis: based on these characteristics, frc consists of three main steps: continuous membership degree, multi-granular semantic parsing, and global decision fusion. ## convergence analysis this section presents the convergence properties of the frc framework, focusing on three key characteristics: approximate robustness, conditional monotonicity, and dynamic completeness. these properties contribute to the stability and interpretability of sentiment analysis results, even when the input data is uncertain or imprecise. ## experiments to validate the effectiveness of the fuzzy reasoning chain (frc) framework in sentiment analysis, we conduct experiments on both english and chinese datasets. the evaluation focuses on robustness, monotonicity, and classification performance in comparison with cotbased and direct prompting methods. ## conclusion in this work, we propose the fuzzy reasoning chain (frc) framework to address the challenge of reasoning over ambiguous and uncertain texts. frc extends conventional probability-based reasoning by integrating continuous fuzzy membership degrees, providing a structured mechanism for translating fuzzy information into interpretable decisions. we provide a preliminary exploration of the framework's properties, and empirical results demonstrate its effectiveness on sentiment analysis tasks. the transition from probabilities to membership degrees allows frc to capture conflicting or uncertain signals that traditional approaches cannot, and also facilitates knowledge transfer between models of different scales. future work may explore applying frc to other fuzzy reasoning tasks such as security review and ethical judgment, integrating richer external knowledge sources, and further improving robustness and efficiency for practical deployments.