In this paper certain interpretability criteria are taken into account in order to extract a set of linear inequality constraints for enhancing the fuzzy model interpretability. Among others, the criteria of model distinguishability, completeness, compactness, and fuzzy set sharing between rules are considered. To support distinguishability, the distances between fuzzy set centers are lower bounded and the widths are manipulated as to control the overlap between fuzzy sets. Sufficient conditions are given to satisfy the completeness criterion, whereas the compactness requirement is addressed by comparing models with different number of rules. Finally, fuzzy set sharing between rules is achieved through a model optimization procedure that involves fuzzy set merging. It turns out that the feasible region is a compact and convex set. The tradeoff between interpretability and accuracy is established by minimizing the model's square error over the feasible region through constrained particle swarm optimization. The method is tested using a number of high-dimensional datasets and conducting two kinds of experiments. The first focuses on interpretability. The second studies the accuracy by comparing the method to other algorithms that perform unconstrained optimization, using nonparametric statistics.

中文翻译：

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由约束粒子群优化实现的模糊建模的可解释性约束

本文考虑了某些可解释性标准，以提取一组线性不等式约束以增强模糊模型的可解释性。其中，考虑了模型可区分性、完整性、紧凑性和规则之间的模糊集共享等标准。为了支持可区分性，模糊集中心之间的距离是下界的，并且宽度被操纵以控制模糊集之间的重叠。给出了足够的条件来满足完整性标准，而紧凑性要求是通过比较具有不同规则数量的模型来解决的。最后，规则之间的模糊集共享是通过涉及模糊集合并的模型优化过程实现的。事实证明，可行域是一个紧凸集。可解释性和准确性之间的权衡是通过约束粒子群优化最小化模型在可行区域上的平方误差来建立的。该方法使用多个高维数据集进行了测试，并进行了两种实验。第一个重点是可解释性。第二种方法是通过将方法与其他执行无约束优化的算法进行比较，使用非参数统计来研究准确性。