A Spanning Tree-Induced Method to Derive Weights From Fuzzy Preference Relations: A Monte Carlo Simulation-Based Investigation
提出一种基于图论生成树的模糊偏好关系权重推导方法，能提取所有可能权重向量并计算总体权重，同时定义新的不一致性度量，适用于不完整偏好关系，蒙特卡洛模拟验证了其优势。
Deriving the priority weights from fuzzy preference relations (FPRs) forms an interesting, promising, and practically oriented research topic. Using the spanning tree tool present in graph theory, we develop a spanning tree-induced method (SPIM) to induce the weight vectors from preference information. The essence of this method is to extract all possible “key combinations” from an FPR and then compute all possible weight vectors. The arithmetic mean (AM) and geometric mean (GM) of these weight vectors are the overall weight vectors of the FPR. Based on the accumulation of squared deviations between the overall weight vector and all possible weight vectors, we define a new measure of inconsistency. The SPIM exhibits three essential characteristics; this method not only produces all possible weight vectors but also identifies their sources. Consequently, this approach can further facilitate the inconsistency analysis, and this method can be directly applied to incomplete FPRs without estimating missing elements. Additionally, we prove the mathematical equivalence of the GM of weight vectors derived from all spanning trees to that of the logarithmic least-squares method (LLSM). Without loss of generality, we adopt the Monte Carlo simulations and report a comparison analysis to provide strong evidence for the advantages and effectiveness of our proposed method.