熵产生率作为决策理论中不一致性的判据
Entropy production rate as a criterion for inconsistency in decision theory
摘要：
个人和群体的决策是复杂的，通常涉及从众多选项中选择一个合适的替代方案。评估成对比较将这些复杂的决策问题分解为易于处理的问题。成对比较矩阵（PCM）经常用于解决多准则决策（MCDM）问题，例如使用Saaty的层次分析法（AHP）框架。然而，使用PCM存在两个显著缺点。首先，人类以不一致的方式评估PCM。其次，并非大型PCM的所有条目都可以由人类决策者可靠地填充。我们解决这两个问题，首先建立一个新的PCM和时间不可逆马尔可夫过程之间的连接。具体来说，我们表明，每个PCM诱导一个家庭的耗散最大路径熵随机游动（MERW）的替代品。我们表明，只有“一致的”PCM对应于详细的平衡MERW。我们确定的非平衡熵产生的诱导MERW作为度量的不一致性的基础PCM。值得注意的是，熵产生满足所有最近制定的合理一致性指数的标准。我们还提出了一种方法，使用不完全填充PCM层次分析法。还讨论了未来的潜在途径。关键词：层次分析法，马尔可夫链，最大熵
英文摘要：
Individual and group decisions are complex, often involving choosing an apt alternative from a multitude of options. Evaluating pairwise comparisons breaks down such complex decision problems into tractable ones. Pairwise comparison matrices (PCMs) are regularly used to solve multiple-criteria decision-making (MCDM) problems, for example, using Saaty's analytic hierarchy process (AHP) framework. However, there are two significant drawbacks of using PCMs. First, humans evaluate PCMs in an inconsistent manner. Second, not all entries of a large PCM can be reliably filled by human decision makers. We address these two issues by first establishing a novel connection between PCMs and time-irreversible Markov processes. Specifically, we show that every PCM induces a family of dissipative maximum path entropy random walks (MERW) over the set of alternatives. We show that only `consistent' PCMs correspond to detailed balanced MERWs. We identify the non-equilibrium entropy production in the induced MERWs as a metric of inconsistency of the underlying PCMs. Notably, the entropy production satisfies all of the recently laid out criteria for reasonable consistency indices. We also propose an approach to use incompletely filled PCMs in AHP. Potential future avenues are discussed as well. keywords: analytic hierarchy process, markov chains, maximum entropy
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