Fuzzy Information Granules: a Compact, Transparent and Efficient Representation

This paper presents a method to construct information granules that provide a relevant description of experimental observations and, at the same time, are represented in a compact and semantically sound form. The method works by first granulating data through a fuzzy clustering algorithm, and then representing granules in form of fuzzy sets. Specifically, an optimal Gaussian functional form for the membership functions is derived by solving a constrained optimization problem on the membership values of the partition matrix returned by the clustering algorithm. The granules represented with Gaussian functional forms can be used to build a fuzzy inference system that performs inferences on the working environment. To illustrate the behavior of the proposed method a real-world information granulation problem has been used. Simulation results show that compact and robust fuzzy granules are attained, with the appreciable feature of being represented in a short functional form. In addition to the information granulation problem, a descriptive fuzzy model for a prediction benchmark has been developed to verify how much fuzzy granules identified form data through the proposed method are useful in providing good mapping properties. The obtained results are reported, supported by comparison with other works.