A Compact Gaussian Representation of Fuzzy Information Granules

—In this paper we propose a new method to represent information granules by Gaussian functional forms. First, the fuzzy granules are extracted from data by a fuzzy clustering algorithm. Then, they are properly represented by Gaussian functions determined by solving a constrained quadratic programming problem on membership values returned by the clustering algorithm. Simulation results show that compact and robust fuzzy granules are attained, with the appreciable feature of being represented in a short functional form. I. INTRODUCTION uzzy information granulation is the process of discovering pieces of information, called information granules, expressed in terms of fuzzy theory [1], [2], [3]. The attained granules can be successively used in Fuzzy Information Systems (FIS) to perform inferences on the working environment. Fuzzy clustering is a general unsupervised method to induce fuzzy granules (i.e. clusters) that represent groups of observations that are " close " in the sense of some predefined metric. Many fuzzy clustering algorithms return a prototype vector and a partition matrix that contains the membership values of each observation to each cluster [4]. Such partition matrix needs large memory requirements, since its space complexity is linear in the number of observations and in the number of clusters. Moreover, the partition matrix does not convey any direct information about fuzzy memberships of new data. For these reasons, when a FIS is built on the derived clusters, only prototype information is usually used to define the fuzzy granules, while the partition matrix is partially or totally ignored. When Gaussian functions are adopted to represent fuzzy granules, one problem is choosing the widths of membership