Distributed and collaborative fuzzy modeling

In this study, we introduce and study a concept of distributed fuzzy modeling. Fuzzy modeling encountered so far is predominantly of a centralized nature by being focused on the use of a single data set. In contrast to this style of modeling, the proposed paradigm of distributed and collaborative modeling is concerned with distributed models which are constructed in a highly collaborative fashion. In a nutshell, distributed models reconcile and aggregate findings of the individual fuzzy models produced on 2 basis of local data sets. The individual models are formed in a highly synergistic, collaborative manner. Given the fact that fuzzy models arc inherently granular constructs that dwell upon collections of information granules - fuzzy sets, this observation implies a certain general development process. There arc two fundamental design issues of this style of modeling, namely (a) a formation of information granules carried out oil a basis of locally available data and their collaborative refinement, and (b) construction of local models with the use of properly established collaborative linkages. We discuss the underlying general concepts and then elaborate on their detailed development. Information granulation is realized in terms of fuzzy clustering. Local models emerge in the form of rule-based systems. The paper elaborates on a number of mechanisms of collaboration offering two general categories of so-called horizontal and vertical clustering. The study also addresses an issue of collaboration in cases when such interaction involves information granules formed at different levels of specificity (granularity). It is shown how various algorithms of collaboration lead to the emergence of fuzz), models involving information granules of higher type such as e.g., type-2 fuzzy sets.