Generating of Fuzzy Rule Bases with Gaussian Parameters Optimized via Fuzzy C-Mean and Ordinary Least Square

Abstract

The fuzzy rule bases has a central role in the fuzzy inference system. Generating of rule bases based on input-output data pairs by using Fuzzy C-Mean clustering (FCM) requires parameters setting of the membership function (mf). In the Gaussian mf, the mean and spread parameters must be determined. The outputs of FCM clustering include the cluster center and the partition matrix of each object. The value of cluster center can be used as the center parameter, but the spread parameter is usually determined as a constant value. The research proposes a method to determine spread parameter of Gaussian mf by using Ordinary Least Square (OLS) approach with using the partition matrix as the membership degree of each object in the cluster. The magnitude of cluster centers (n) of 3, 5, and 7 are considered as FCM input to cluster the weekly price of soybeans in East Java, Indonesia on the period of January 2014 to December 2017. Based on each cluster center, the optimal spread value of a Gaussian mf is obtained via OLS. This research succeeded in getting a spread values that could approach almost perfectly each element of the partition matrix