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A Methodology for Building of Interval and General Type-2 Fuzzy Systems Based on the Principle of Justifiable Granularity
Oscar Castillo, Juan R. Castro and Patricia Melin

In this article a design methodology for Mamdani interval and general type-2 fuzzy systems with center-of-sets type reduction is presented. The methodology utilizes descriptive statistics, fuzzy c means clustering and granular computing theory, to define 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 the type-2 membership functions and characterize its JFOU. Second, we use the data structure of the justifiable information granule to characterize and parameterize the asymmetric type-2 membership functions of the fuzzy system. 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 repositories of automated learning, measuring R2adj and RMSE to evaluate the reliability of the proposed methodology, while maintaining the justifiable uncertainty of the model.

Keywords: Interval type-2 fuzzy systems, general type-2 fuzzy systems, principle of justifiable granularity, justifiable footprint of uncertainty

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