Document Type : Research Paper




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 a basis of local data sets. The individual
models are formed in a highly synergistic, collaborative manner. Given the fact that
fuzzy models are inherently granular constructs that dwell upon collections of
information granules – fuzzy sets, this observation implies a certain general
development process. There are two fundamental design issues of this style of
modeling, namely (a) a formation of information granules carried out on 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 fuzzy models involving information
granules of higher type such as e.g., type-2 fuzzy sets.


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