面向多指标成本控制的熵权–模糊综合评价模型：隶属度构造、加权合成与数值验证

An Entropy-Weighted Fuzzy Comprehensive Evaluation Model for Multi-Indicator Cost Measurement: Membership Construction, Weighted Synthesis and Numerical Verification

摘要: 针对多指标成本控制评价中存在的边界模糊、量纲冲突及信息重叠问题，构建了一种基于熵权–模糊综合评价的定量测度模型。首先，建立包含生产成本、期间费用与营运效率的三层评价指标体系；其次，采用极差标准化法消除量纲差异，引入熵权法依据指标数据离散程度客观赋权，避免主观赋权的随意性；进而，构造基于半梯形分布的隶属度函数生成模糊关系矩阵，并选用M (•,+)加权平均合成算子进行模糊合成，将多指标评价问题转化为可计算的数值综合得分。以美的集团2021~2025年财务数据为数值算例，测算得到各年度综合评价值分别为86.00、83.30、84.23、79.50、79.43，结果表明该模型能有效融合冲突指标、输出统一的量化结论。进一步引入业务修正权重进行稳健性检验，两组得分排序一致，验证了模型对权重设定的鲁棒性。本文为模糊数学在多指标财务评价领域的应用提供了可复用的建模框架与数值验证范例。

Abstract: To address the issues of ambiguous boundaries, dimensional conflicts, and information overlap in multi-indicator cost control evaluation, this study constructs a quantitative measurement model based on the entropy-weighted fuzzy comprehensive evaluation method. First, a three-tier indicator system encompassing production costs, period costs, and operational effi-ciency is established. Second, the range-standardization method is employed to eliminate di-mensional discrepancies, and the entropy weight method is introduced to objectively assign weights based on the dispersion of indicator data, thereby avoiding the arbitrariness of subjec-tive weighting. Subsequently, membership functions based on a semi-trapezoidal distribution are constructed to generate a fuzzy relation matrix, and the M (•,+) weighted average synthesis operator is applied to perform fuzzy synthesis, transforming the multi-indicator evaluation problem into a computable numerical composite score. Using the financial data of Midea Group from 2021 to 2025 as a numerical example, the composite evaluation scores for each year are calculated as 86.00, 83.30, 84.23, 79.50, and 79.43, respectively. The results demonstrate that the model effectively integrates conflicting indicators and yields unified quantitative conclusions. Furthermore, business-adjusted weights are introduced for robustness testing; the ranking re-sults of the two sets are consistent, confirming the model’s tolerance to weight specifications. This paper provides a reusable modeling framework and numerical verification paradigm for the application of fuzzy mathematics in multi-indicator financial evaluation.