Comparison of Fuzzy Functions with Fuzzy Rule Base Approaches

“Fuzzy Functions” are proposed to be determined separately by two regression estimation models: the least squares estimation (LSE), and Support Vector Machines for Regression (SVR), techniques for the development of fuzzy system models. LSE model tries to estimate the fuzzy function parameters linearly in the original space, whereas SVR algorithm maps the data samples into higher dimensional feature space and estimates a linear fuzzy function in the feature space. The membership values of input vectors are calculated using FCM algorithm or any variation of it. They are then used with scalar input variables by the LSE and SVR techniques to determine “Fuzzy Functions” for each cluster identified by FCM. “Fuzzy Functions” estimated with LSE and SVR methodologies are proposed as alternate representations and reasoning schemas to the fuzzy rule base approaches. We show with three case studies that the new approaches give better results in comparison to well-known fuzzy rule base approaches, i.e., Takagi-Sugeno [28] and Sugeno-Yasukawa [27] in test cases.