Development of Unified Learning Paradigm for Fuzzy Pattern Classification Systems

在我们之前的项目中，我们开发了几个模糊模式分类系统。在本项目中，我们将模糊系统系统化，并开发了统一的学习范式，具体如下：多维隶属函数的发展：在多维输入空间中，我们发展了（截断）锥体隶属函数（截断）多面体锥体隶属函数、钟形隶属函数，并分析了隶属函数对类边界的影响。统一学习范式的发展：通过解析计算当隶属函数的斜率或位置发生变化时识别率变化的点，我们计算出识别率最大化的区间。然后我们调整斜率和/或隶属函数的位置，使它们处于这些区间内。该方法直接最大化了训练数据的识别率。我们用几个基准数据集评估了我们的方法。基于多面体区域的模糊分类器的开发：从初始凸包开始，每次增加一个基准来修改凸包。也就是说，如果基准点在凸包中，我们什么都不做。但如果它在凸壳之外，我们修改凸壳，使基准点是修改后的凸壳的一个顶点。性能评估：我们针对几个基准数据集评估了我们开发的模糊系统和传统系统，并证明了我们的系统比传统系统的有效性。

In our previous project we have developed several fuzzy pattern classification systems. In this project, we systemized fuzzy systems and developed unified learning paradigms as follows :1. Development of Multi-dimensional Membership Functions : In the multi-dimensional input space, we developed (truncated) pyramidal membership functions (truncated) polyhedral pyramidal membership functions, bell-shaped membership functions, and analyzed the effect of membership functions on class boundaries.2. Development of Unified Learning Paradigm : By analytically calculating the points where the recognition rate changes when the slopes or locations of the membership function are changed, we calculate the intervals that maximize the recognition rate. Then we tune slopes and/or locations of the membership functions so that they are in those intervals. By this method, the recognition rate of the training data is directly maximized. We evaluated our method for several benchmark data sets.3. Development of a Fuzzy Classifier with Polyhedral Regions : Starting from an initial convex hull, we modify the convex hull adding one datum at a time. Namely, if the datum is in the convex hull, we do nothing. But if it is outside of the convex hull, we modify the convex hull so that the datum is a vertex of the modified convex hull.4. Performance Evaluation: We evaluated the fuzzy systems we have developed and the conventional systems for several benchmark data sets, and demonstrated the effectiveness of our systems over conventional ones.