Modeling with linguistic entities and linguistic descriptors: a perspective of granular computing

In this study, we are concerned with the formation of interpretable descriptors of dependencies existing in experimental data and realized in the form of linguistic entities (information granules). We elaborate on a way of bridging numerically inclined fuzzy models (in which information granules are built on a basis of experimental data and described through numeric membership functions) and a qualitative way of system modeling (originating from symbol-based modeling). Proceeding with the principles of fuzzy modeling (especially, those residing with rule-based architectures), their numerical constructs of fuzzy sets-information granules are augmented with viable interpretation mechanisms abstracted from the detailed membership functions. In this regard, a linguistic view of the outcomes of fuzzy clustering (realized in terms of fuzzy C-means) are revisited and supplied with an interpretation at a higher level of abstraction. The buildup of the qualitative descriptors embraces two essential aspects of abstraction, namely (a) an abstraction of linguistic terms realized on the basis of membership functions (fuzzy sets) and (b) an abstraction of relationships completed on the basis of detailed functional dependencies present in the fuzzy model (say, the rules of the model). Two categories of problems are studied in detail along with their applications, namely a linguistic description of time series and a linguistic description of linearization tasks. Both of them are illustrated with a number of experimental studies.