Bridging Stochasticity and Fuzziness: Automated Construction of Triangular Fuzzy Numbers via LLM Temperature Sampling for Managerial Decision Support

Traditional fuzzy decision-making often relies on manual expert calibration, which is labor-intensive and susceptible to subjective bias. This study addresses these limitations by proposing a novel framework that transforms the intrinsic probabilistic outputs of Large Language Models (LLMs) into Triangular Fuzzy Numbers (TFNs). We introduce a multi-temperature sampling strategy coupled with weighted quantile aggregation and an adaptive interval adjustment mechanism to systematically map model stochasticity to fuzzy possibility distributions. Empirical validation on a structured prototype dataset demonstrates that the proposed method achieves high consistency with expert consensus, with GPT-4.2 exhibiting superior central accuracy and Gemini-2.5 excelling in uncertainty coverage. Furthermore, in complex unstructured scenarios involving business public opinion, the integration of Model Context Protocol (MCP) and Retrieval-Augmented Generation (RAG) significantly corrects cognitive biases and converges uncertainty boundaries. This research establishes a rigorous pathway from generative AI probabilities to fuzzy decision theory, offering a robust automated solution for quantitative risk assessment and intelligent decision support.