A methodology for building interval type‐3 fuzzy systems based on the principle of justifiable granularity

Abstract

In this article a design methodology for Mamdani interval type-3 fuzzy systems with center-of-sets type reduction is outlined. The methodology utilizes statistical measures, fuzzy c-means clustering and granular computing, to establish the justifiable footprint of uncertainty (JFOU) of the fuzzy granules, as explainable semantic abstractions that form the fuzzy model. The design methodology is presented in three general steps, first we use the principle of justifiable granularity to build a diagram of the justifiable information granule that contains a data structure with the descriptive measures of the experimental evidence of the data set. These measures are obtained from the partition matrix of the utilized clustering process, and these measures are used to evaluate the parameters of membership functions and characterize their JFOU. Second, we use the data structure of the justifiable information granule to characterize and parameterize the asymmetric interval type-3 membership functions. Lastly, the main procedure to obtain all the justifiable information fuzzy granules that define the knowledge base and the inference process of the fuzzy model is presented. Experiments were made with synthetic and real benchmark data from automated learning repositories, computing R adj 2 ${R}_{\mathrm{adj}}^{2}$ and root-mean-squared error to measure the reliability of the methodology, while keeping the justifiable uncertainty of the model.