摘 要：随着复杂决策问题的日益增多，传统精确数学方法在处理不确定性信息时逐渐显现出局限性，而模糊数学为解决这一问题提供了有效工具。本研究旨在探索模糊数学理论在决策支持系统中的应用潜力，通过构建基于模糊集和模糊逻辑的决策模型，提升系统对不确定性和模糊性信息的处理能力。研究采用理论分析与实证验证相结合的方法，首先将模糊综合评价法引入多属性决策场景，随后设计了一种改进型模糊推理算法以优化决策过程。实验结果表明，该方法能够显著提高决策支持系统的准确性和适应性，尤其是在面对模糊边界和主观偏好时表现出更强的鲁棒性。本研究的主要创新点在于提出了一种融合专家知识与数据驱动的模糊决策框架，为实际应用场景中的复杂决策问题提供了新思路，其贡献在于拓展了模糊数学的应用范围，并为智能化决策支持系统的发展奠定了理论基础。
关键词：模糊数学；决策支持系统；模糊综合评价；改进型模糊推理算法；专家知识与数据驱动
An Exploration of Fuzzy Mathematics in Decision Support Systems
英文人名
Directive teacher:×××
Abstract：With the increasing number of complex decision-making problems, traditional precise mathematical methods have gradually revealed limitations in dealing with uncertain information, while fuzzy mathematics provides an effective tool for addressing this issue. This study aims to explore the application potential of fuzzy mathematics theory in decision support systems by constructing decision models based on fuzzy sets and fuzzy logic to enhance the system's ability to handle uncertainty and fuzziness. A combination of theoretical analysis and empirical validation is employed, initially introducing fuzzy comprehensive evaluation into multi-attribute decision-making scenarios and subsequently designing an improved fuzzy inference algorithm to optimize the decision process. The experimental results demonstrate that this approach can significantly improve the accuracy and adaptability of decision support systems, particularly exhibiting stronger robustness when confronting fuzzy boundaries and subjective preferences. The primary innovation of this research lies in proposing a fuzzy decision-making fr amework that integrates expert knowledge with data-driven approaches, offering new insights into complex decision-making problems in practical application contexts. Its contribution extends the application scope of fuzzy mathematics and lays a theoretical foundation for the development of intelligent decision support systems.
Keywords: Fuzzy Mathematics；Decision Support System；Fuzzy Comprehensive Evaluation；Improved Fuzzy Inference Algorithm；Expert Knowledge And Data Driven
目 录
引言 1
一、模糊数学基础与决策支持系统概述 1
(一)模糊数学基本概念 1
(二)决策支持系统的核心功能 2
(三)模糊数学在 2
二、模糊集合理论在决策建模中的应用 3
(一)决策问题的模糊化处理 3
(二)模糊集合在多目标决策中的作用 3
(三)模糊推理机制对决策模型的支持 4
三、模糊逻辑在不确定性决策中的实现 4
(一)不确定性决策的特点与挑战 4
(二)模糊逻辑对不确定性的刻画能力 5
(三)基于模糊逻辑的决策算法设计 5
四、模糊数学在实际决策支持系统中的案例研究 5
(一)案例背景与需求分析 6
(二)模糊方法在具体场景中的应用 6
(三)应用效果评估与改进建议 7
结论 7
参考文献 8
致谢 8
