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Commutativity as prior knowledge in fuzzy modeling

机译：可交换性作为模糊建模的先验知识

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摘要

In fuzzy modeling (FM), the quantity and quality of the training set is crucial to properly grasp the behavior of the system being modeled. However, the available data are often not large enough or are deficiently distributed along the input space, not revealing the system behavior completely. In such cases, the consideration of any prior knowledge about the system can be decisive for the accuracy achieved by the fuzzy modeling. This paper faces with the integration of mathematical properties satisfied by a system as prior knowledge in FM, focusing on the commutativity property as a starting point. With this aim, several measures are developed to evaluate the commutativity in a fuzzy environment dealing with different elements involved in FM. Then, several approaches are proposed to measure the commutativity degrees of a fuzzy rule with respect to the training set and a simple method is presented to integrate these degrees into the FM task. The experimental results show the accuracy improvement gained by the proposed method.
机译：在模糊建模（FM）中，训练集的数量和质量对于正确掌握要建模的系统的行为至关重要。但是，可用数据通常不够大或沿着输入空间分布不充分，从而无法完全揭示系统行为。在这种情况下，对系统的任何先验知识的考虑对于通过模糊建模实现的准确性可能是决定性的。本文面对作为调频先验知识的系统所满足的数学特性的集成，并着重于以可交换性特性为起点。为此目的，开发了几种措施来评估在模糊环境中处理FM中涉及的不同元素的可交换性。然后，提出了几种方法来测量模糊规则相对于训练集的可交换度，并提出了一种简单的方法来将这些度集成到FM任务中。实验结果表明，该方法提高了精度。

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