DISTRIBUTED AND COLLABORATIVE FUZZY MODELING

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