用少1/2的比较次数,快速得到一致的决策判断结果
The Tournament Tree Method for preference elicitation in Multi-criteria decision-making
- 通过锦标赛树结构仅需m-1次比较完成评估
- 保证结果一致且避免专家认知负担过重
- 适合需要高效决策支持的工程与管理场景
成对比较方法如模糊偏好关系和Saaty乘法偏好关系广泛用于多准则决策中的专家判断建模。然而,其应用受限于完成 $m(m-1)/2$ 次比较带来的高认知负荷、不一致风险及推导一致价值尺度的计算复杂性。本文提出锦标赛树方法(Tournament Tree Method, TTM),一种新型的获取与评估框架,仅需 $m-1$ 次成对比较即可获得完整、互反且一致的比较矩阵。该方法包含三个阶段:(i) 使用精简的目标化比较进行专家判断收集,(ii) 构建一致的成对比较矩阵,(iii) 从所得矩阵推导全局价值尺度。所提方法通过设计确保一致性,最小化认知努力,并将偏好建模的维度从 $m(m-1)/2$ 降低至 $m$ 个参数。此外,该方法兼容经典扑克牌法,可处理区间与比率尺度。我们还开发了基于网络的工具,验证其在真实决策场景中的实用性。
原文摘要 · Abstract (English)
Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high cognitive load required to complete $m(m-1)/2$ comparisons, the risk of inconsistency, and the computational complexity of deriving consistent value scales. This paper proposes the Tournament Tree Method (TTM), a novel elicitation and evaluation framework that overcomes these limitations. The TTM requires only $m-1$ pairwise comparisons to obtain a complete, reciprocal, and consistent comparison matrix. The method consists of three phases: (i) elicitation of expert judgments using a reduced set of targeted comparisons, (ii) construction of the consistent pairwise comparison matrix, and (iii) derivation of a global value scale from the resulting matrix. The proposed approach ensures consistency by design, minimizes cognitive effort, and reduces the dimensionality of preference modeling from $m(m-1)/2$ to $m$ parameters. Furthermore, it is compatible with the classical Deck of Cards method, and thus it can handle interval and ratio scales. We have also developed a web-based tool that demonstrates its practical applicability in real decision-making scenarios.
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