Granular fuzzy models: Analysis, design, and evaluation

• We design, develop, and construct a granular fuzzy model that produces granular results instead of numeric values.
• Our method captures the diversity of data and handles the lack of numeric precision to be more reflective of reality.
• The model is formed by means of a fuzzy clustering algorithm known as conditional Fuzzy C-Means.
• The model is optimized by using Differential Evolution along with coverage criteria.
• The optimized model can be interpreted as a collection of “if–then” rules formed from the architecture.

The study is concerned with a design of granular fuzzy models. We exploit a concept of information granularity by developing a model coming as a network of intuitively structured collection of interval information granules described in the output space and a family of induced information granules (in the form of fuzzy sets) formed in the input space. In contrast to most fuzzy models encountered in the literature, the results produced by granular models are information granules rather than plain numeric entities. The design of the model concentrates on a construction of information granules that form a backbone of the overall construct. Interval information granules positioned in the output space are built by considering intervals of equal length, equal probability, and developing an optimized version of the intervals. The induced fuzzy information granules localized in the input space are realized by running a conditional Fuzzy C-Means (FCM). The performance of the model is assessed by considering criteria of coverage and information specificity (information granularity). Further optimization of the model is proposed along the line of an optimal re-distribution of input information granules induced by the individual interval information granules located in the output space. Experimental results involve some synthetic low-dimensional data and publicly available benchmark data sets.