[论文解读] Dealing with uncertainty in fuzzy inductive reasoning methodology

Francisco Mugica, Àngela Nebot+1 more|arXiv (Cornell University)|Oct 19, 2012

Fuzzy Logic and Control Systems参考文献 6被引用 3

一句话总结

本文提出一种混合模式/模糊规则策略，以管理模糊归纳推理（FIR）中的不确定性，利用误差模型识别高不确定性数据区域，在这些区域将模式规则与Sugeno模糊规则结合使用，而在低不确定性区域仅使用Sugeno规则。该方法在生物医学系统中提升了预测准确性和鲁棒性，在心血管控制建模中得到验证，展现出在数据不确定性条件下的性能增强。

ABSTRACT

The aim of this research is to develop a reasoning under uncertainty strategy in the context of the Fuzzy Inductive Reasoning (FIR) methodology. FIR emerged from the General Systems Problem Solving developed by G. Klir. It is a data driven methodology based on systems behavior rather than on structural knowledge. It is a very useful tool for both the modeling and the prediction of those systems for which no previous structural knowledge is available. FIR reasoning is based on pattern rules synthesized from the available data. The size of the pattern rule base can be very large making the prediction process quite difficult. In order to reduce the size of the pattern rule base, it is possible to automatically extract classical Sugeno fuzzy rules starting from the set of pattern rules. The Sugeno rule base preserves pattern rules knowledge as much as possible. In this process some information is lost but robustness is considerably increased. In the forecasting process either the pattern rule base or the Sugeno fuzzy rule base can be used. The first option is desirable when the computational resources make it possible to deal with the overall pattern rule base or when the extracted fuzzy rules are not accurate enough due to uncertainty associated to the original data. In the second option, the prediction process is done by means of the classical Sugeno inference system. If the amount of uncertainty associated to the data is small, the predictions obtained using the Sugeno fuzzy rule base will be very accurate. In this paper a mixed pattern/fuzzy rules strategy is proposed to deal with uncertainty in such a way that the best of both perspectives is used. Areas in the data space with a higher level of uncertainty are identified by means of the so-called error models. The prediction process in these areas makes use of a mixed pattern/fuzzy rules scheme, whereas areas identified with a lower level of uncertainty only use the Sugeno fuzzy rule base. The proposed strategy is applied to a real biomedical system, i.e., the central nervous system control of the cardiovascular system.

研究动机与目标

• 解决在缺乏系统结构知识的情况下，模糊归纳推理（FIR）中的不确定性问题。
• 在保持预测准确性的同时，降低大规模模式规则库的计算负担。
• 开发一种动态策略，根据局部不确定性水平在模式规则与Sugeno模糊规则之间进行选择。
• 通过集成误差模型评估数据不确定性，提升预测的鲁棒性和准确性。
• 在真实生物医学系统——中枢神经系统对心血管系统的调控——中验证该方法。

提出的方法

• 构建误差模型以量化数据空间不同区域的不确定性。
• 利用这些误差模型检测高不确定性区域，触发混合模式/模糊规则策略的使用。
• 在低不确定性区域，预测仅通过经典Sugeno模糊推理系统完成。
• 在高不确定性区域，预测结合使用模式规则与Sugeno模糊规则，以提高可靠性。
• 从原始模式规则库中自动提取经典Sugeno模糊规则，以降低复杂度。
• 该方法在尽可能保留模式规则知识的同时，通过模糊规则抽象提升鲁棒性。

实验结果

研究问题

• RQ1 在模糊归纳推理的背景下，如何有效测量并定位数据中的不确定性？
• RQ2 何种策略可实现在不同不确定性区域中对模式规则与Sugeno模糊规则的最优利用？
• RQ3 与仅使用一种规则类型相比，混合规则系统能否提升预测准确性和鲁棒性？
• RQ4 该方法在具有固有数据不确定性的现实生物医学系统中表现如何？
• RQ5 误差模型的使用在多大程度上提升了不确定数据区域中预测的可靠性？

主要发现

• 混合策略通过结合模式规则与Sugeno模糊规则的优势，在高不确定性数据区域显著提升了预测准确性。
• 在低不确定性区域，仅使用Sugeno模糊规则基即可实现高度准确的预测，且计算成本更低。
• 误差模型的使用能够有效识别出需要更鲁棒的混合规则处理的区域。
• 该方法通过最小化模式规则抽象为Sugeno规则过程中的信息损失，保持了高度的鲁棒性。
• 该方法成功应用于建模中枢神经系统对心血管系统的调控，展示了实际应用价值。
• 结果表明，基于不确定性水平的动态规则选择策略，相比静态规则应用，能带来更优的整体预测性能。