通过实验验证最优成对比较图模式，提升决策效率。
An experimental approach: The graph of graphs
- 基于6种颜色的成对比较实验，构建最优比较图序列。
- 实测结果与模拟数据高度一致，验证了最优模式有效性。
- 提供可视化图表与Java工具，便于实际应用。
决策问题与偏好建模中的关键挑战在于如何设计最少且最有效的成对比较。本文通过色彩选择实验，研究最优成对比较模式及其序列。实验在国际标准化感官测试间内进行，使用色彩校准平板，评估红、绿、蓝、品红、青绿、黄六种颜色，采用成对比较和直接评价两种方式。共收集301名参与者生成的成对比较矩阵（PCMs），利用对数最小二乘法计算权重。所有能形成连通表示图的比较模式均基于完整数据进行评估。结果表明，实测得到的比较矩阵元素分布与文献中模拟结果高度相似；所获经验最优比较模式在先前模拟中也表现为最佳或次佳，其比较序列完全一致。为增强实用性，论文提出“图中之图”概念，并展示各模式对应的表示图，同时以表格和Java应用程序形式给出具体推荐方案。
原文摘要 · Abstract (English)
One of the essential issues in decision problems and preference modeling is the number of comparisons and their pattern to ask from the decision maker. We focus on the optimal patterns of pairwise comparisons and the sequence including the most (close to) optimal cases based on the results of a color selection experiment. In the test, six colors (red, green, blue, magenta, turquoise, yellow) were evaluated with pairwise comparisons as well as in a direct manner, on color-calibrated tablets in ISO standardized sensory test booths of a sensory laboratory. All the possible patterns of comparisons resulting in a connected representing graph were evaluated against the complete data based on 301 individual's pairwise comparison matrices (PCMs) using the logarithmic least squares weight calculation technique. It is shown that the empirical results, i.e., the empirical distributions of the elements of PCMs, are quite similar to the former simulated outcomes from the literature. The obtained empirically optimal patterns of comparisons were the best or the second best in the former simulations as well, while the sequence of comparisons that contains the most (close to) optimal patterns is exactly the same. In order to enhance the applicability of the results, besides the presentation of graph of graphs, and the representing graphs of the patterns that describe the proposed sequence of comparisons themselves, the recommendations are also detailed in a table format as well as in a Java application.
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