Designing Distributed Fuzzy Rule-Based Models

In the design of fuzzy rule-based models, in the presence of high-dimensional data, we are faced with conceptual and algorithmic challenges. Conceptually, as the dimensionality of data increases, the notion of distance starts to be questionable, resulting in the well-known concentration effect. This has a direct detrimental effect given the fact that the distance is used in fuzzy clustering, using which the condition parts of the rules are being formed. Computationally, with the increase of dimensionality, the computing overhead becomes significant and has to be carefully addressed. In this article, we advocate a construction of distributed fuzzy rule-based models, where instead of a single monolithic (multivariable) rule-based model, we construct a collection of low-dimensional (in particular, 1- or 2-D) rule-based models and aggregate their results through some linear transformations. A suite of experimental studies realized using publicly available data are reported along with a comparative analysis engaging accuracy criteria and computing overhead. Interestingly, building distributed models exhibits some tangible benefits over the construction of the monolithic rule-based models. In terms of accuracy and computing costs, the gains of 1-D rule-based models with optimal linkage matrix (on average) are around 43.46% and 98.85%, respectively.