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

arXiv: https://arxiv.org/abs/2509.22054 · HTML: https://mlsanity.com/paper/2509.22054/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Meta-Prompting: Enhancing Language Models with Task-Agnostic Scaffolding](https://mlsanity.com/paper/2401.12954/) (2024)
- [AutoHint: Automatic Prompt Optimization with Hint Generation](https://mlsanity.com/paper/2307.07415/) (2023)
- [Affective Computing in the Era of Large Language Models: A Survey from the NLP Perspective](https://mlsanity.com/paper/2408.04638/) (2024)
- [Zero-Shot Chain-of-Thought Reasoning Guided by Evolutionary Algorithms in Large Language Models](https://mlsanity.com/paper/2402.05376/) (2024)
- [Recent Advancement of Emotion Cognition in Large Language Models](https://mlsanity.com/paper/2409.13354/) (2024)
- [PromptExp: Multi-granularity Prompt Explanation of Large Language Models](https://mlsanity.com/paper/2410.13073/) (2024)
- [Implicit Sentiment Analysis Based on Chain of Thought Prompting](https://mlsanity.com/paper/2408.12157/) (2024)

## Built on by (most cited first, 2 of 2)

- [Chain-of-Trajectories: Unlocking the Intrinsic Generative Optimality of Diffusion Models via Graph-Theoretic Planning](https://mlsanity.com/paper/2603.14704/) (2026)
- [From Prompt Optimization to Multi-Dimensional Credibility Evaluation: Enhancing Trustworthiness of Chinese LLM-Generated Liver MRI Reports -- with Preliminary Extension to Lung Cancer](https://mlsanity.com/paper/2510.23008/) (2025)

## Abstract (arXiv)

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.