AI 中文总结
研究针对alpha-FBWM问题，提出Linear alpha-FBWM及Linear alpha-PFBWM，通过线性规划确定准则权重，引入OPV度量评估偏好，经数值示例和实际案例验证，该方法能减少专家评估，是复杂工业决策的有效工具。
AI 中文摘要
为解决基于α-截集区间的模糊最佳-最差方法（alpha-FBWM）中的计算强度和清晰权重限制问题，本研究提出基于线性α-截集区间的模糊最佳-最差方法（Linear alpha-FBWM）。通过将非线性优化转化为单一线性规划模型，直接确定三角模糊数形式的准则权重以保留不确定性。引入基于突出效应的序贯偏好违反（OPV）度量来评估权重与决策者初始模糊偏好的一致性。数值示例表明Linear alpha-FBWM减少了逻辑违反，与原始alpha-FBWM相当或更优。为有效处理大规模数据集，扩展为基于线性α-截集区间的简约模糊最佳-最差方法（Linear alpha-PFBWM）。通过文献示例和跨国涂料公司在古吉拉特邦的20个备选方案的实际仓库选址案例研究验证了该框架，其减少了所需专家评估，证明是复杂工业决策的高效、可靠且可扩展工具。
英文摘要
To address computational intensity and crisp weight limitations in the alpha-cut intervals based Fuzzy Best-Worst Method (alpha-FBWM), this research proposes the Linear alpha-cut intervals based Fuzzy Best-Worst Method (Linear alpha-FBWM). By reformulating the non-linear optimization into a single linear programming model, the framework directly determines criteria weights as Triangular Fuzzy Numbers (TFNs) to retain uncertainty. To evaluate weight alignment with decision-makers' initial fuzzy preferences, an Ordinal Preference Violation (OPV) metric is introduced based on the prominence effect. Numerical examples demonstrate that Linear alpha-FBWM minimizes logical violations and matches or outperforms the original alpha-FBWM. To efficiently handle large-scale datasets, we extend this into the Linear alpha-cut intervals based Parsimonious Fuzzy Best-Worst Method (Linear alpha-PFBWM), embedding the linear formulation. This model allows initial alternative ratings as fuzzy numbers and computes non-reference alternative priorities via fuzzy interpolation without early defuzzification. The framework is validated using a literature example and a real-world warehouse selection case study involving 20 alternatives across Gujarat for a multinational paint firm. The integrated approach reduced the required expert evaluations from 185 to 20 initial ratings and 35 pairwise comparisons. This 81.08% reduction in pairwise comparisons proves the framework to be an efficient, reliable, and scalable tool for complex industrial decision-making.
Comments32 pages, 2 figures
