Analyzing public attitudes on social media is crucial for opinion-mining systems. Stance detection aims to identify the attitude of an opinionated text towards a given target. Despite advances in conventional stance detection methods, handling sentences with ambiguous stances remains a significant challenge. Meanwhile, fuzzy logic theory can improve knowledge representation under uncertainty, but learning logical rules from samples requires a large corpus of annotated data, which is impractical for stance detection tasks involving numerous targets. Inspired by the impressive zero-shot performance of large language models (LLM) on commonsense reasoning tasks, we propose the LLM-enhanced Fuzzy Logic Fusion (LLM-FLF) Framework, which synergizes the strengths of LLMs and fuzzy logic to improve performance in complex reasoning tasks. LLM-FLF consists of two main components: Logical Schema Graph construction and Logic-integrated fuzzy relational graph convolutional network. Our approach achieves state-of-the-art results across zero-shot, cross-target, and in-target settings. Notably, it demonstrates a substantial performance gain, outperforming the best baseline methods by 5.1% and 5.5% on Semeval-2016 and VAST benchmark datasets in the most challenging zero-shot scenario.