Hierarchical Architectures of Fuzzy Models: From Type-1 fuzzy sets to Information Granules of Higher Type

Complex phenomena are perceived from different perspectives, diversified conceptual points of view and at various levels of granularity. Symbolic and sub-symbolic processing becomes an inherently visible computing practice. Distributed nature of perception becomes reflected in topologies of multi-agent systems. All of these facets challenge the well-established paradigms of system modeling including fuzzy models and neural networks. In spite of the diversity of existing architectures and underlying algorithms, a vast majority of fuzzy models adheres to the surprisingly homogeneous principles of Granular Computing, that are associated with the processing of granular information. In this study, being cognizant of this underpinning, we concentrate on the architectures and fundamentals supporting the reconciliation and characterization of a family of fuzzy models aimed at the representation of the same system (phenomenon) from different cognitive perspectives. The variety of points of view is reflected in different levels of granularity (specificity) of fuzzy sets present in individual models as well as different feature (attribute) spaces being used in the individual models. We discuss a way in which type-2 fuzzy sets come to the play as a result of the overall characterization. An effective way of determining of such fuzzy sets is presented. Further studies on the interpretability of fuzzy sets at the level of linguistic valuation are presented and with this regard where it is shown how these can be carried out in the setting of type-2 fuzzy sets. The question of logic operators constructed in presence of a large number of fuzzy sets is raised along with a proposal of statistically grounded logic operators, which capture some characteristics of membership degrees to be processed.