Fuzzy descriptive models:an interactive framework of information granularity

In this paper, we introduce and discuss an important class of endeavors of fuzzy modeling, such as fuzzy descriptive models. In a nutshell, the objective of fuzzy descriptive models is to provide with a sound, comprehensible, and relevant description of experimental data at a general level of relationships revealed there. The elements of such models called descriptors are inherently information granules as the notion of granularity goes hand-in-hand with the interpretability of the resulting constructs (information granules). This paper elaborates on the use of the language of fuzzy sets that are viewed as generic models of information granules. The development of the information granules is carried out in an interactive manner in which a designer can inspect a structure in a data set in a visual fashion. Such visualization is possible through a suitable visualization vehicle provided by self-organizing maps. The role of the designer is to choose from some already visualized regions of the self-organizing map characterized by a high level of data homogeneity. We provide a new algorithm of constructing membership functions of the information granules (fuzzy sets). In addition to some synthetic data, the study includes a comprehensive descriptive modeling of highly dimensional electrocardiogram data.