Development of Unified Learning Paradigm for Fuzzy Pattern Classification Systems

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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.