Fuzzy cognitive maps (FCMs) play an important role in high-level reasoning but are limited in their ability to model complex systems with singularities. We are interested in systems that exhibit discontinuous behaviors as one or more of their internal node states approach a threshold. In a new approach to FCM dynamics, we define general classes of aggregation functions which “jump” to a boundary value when any input crosses a threshold, or when all inputs do. The threshold value is a context-dependent parameter which can be readily understood by subject matter experts. Aggregation functions are applied separately to positively and negatively causal antecedents to each node then combined to form the nodal state. This modeling is applied in Computing with Words (CWW) settings, in which link strengths and activation levels are elicited using vocabulary words represented by interval type-2 fuzzy membership functions. We illustrate the behaviors of these novel FCM systems in comparison with their nonsingularity versions.

中文翻译：

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通过模糊认知图中的词计算对复杂系统现象进行建模


模糊认知图 (FCM) 在高级推理中发挥着重要作用，但在对具有奇点的复杂系统进行建模的能力方面受到限制。我们感兴趣的是当一个或多个内部节点状态接近阈值时表现出不连续行为的系统。在 FCM 动力学的新方法中，我们定义了聚合函数的通用类，当任何输入超过阈值或所有输入都超过阈值时，这些函数会“跳转”到边界值。阈值是主题专家可以容易理解的上下文相关参数。聚合函数分别应用于每个节点的正向和负向因果前提，然后组合以形成节点状态。该建模应用于单词计算 (CWW) 设置，其中使用由区间类型 2 模糊隶属函数表示的词汇单词来得出链接强度和激活级别。我们将这些新颖的 FCM 系统与其非奇点版本进行比较来说明其行为。