Despite the impressive few-shot performance of in-context learning (ICL) in knowledge-based visual question answering (VQA), existing research often prioritizes addressing the image information gap in VQA, while placing less emphasis on organizing appropriate demonstrations (e.g., in-context examples) to support this task. Recent studies, however, have shown that ICL performance is sensitive to the organization of demonstrations. To address this, we introduce axiomatic fuzzy set (AFS) theory into knowledge-based VQA, leveraging its unsupervised and interpretable nature to effectively organize demonstrations by describing each candidate with semantic concepts, thereby enhancing both the understanding and trustworthiness of the decision-making process. In this article, we propose AFSPrompt, a train-free example selection and ranking framework based on AFS theory for knowledge-based VQA tasks. After filtering irrelevant examples using multimodal embeddings, we apply AFS logic to integrate comparison information from candidates with multidimensional features. Furthermore, to reduce reliance on large-scale language model APIs such as OpenAI and facilitate model deployment, we employ a smaller 7B LLM as the knowledge engine to answer questions based on the optimized prompt. Through extensive evaluations of two datasets, we demonstrate the effectiveness of AFSPrompt within a lightweight pipeline for knowledge-based VQA tasks. Our code is publicly available at https://github.com/afs001/AFSPrompt.