Simplified fuzzy rule-based systems using non-parametric antecedents and relative data density

Abstract

In this paper a new method for definition of the antecedent/premise part of the fuzzy rule-based (FRB) systems is proposed. It removes the need to define the membership functions per variable using often artificial parametric functions such as triangular, Gaussian etc. Instead, it strictly follows the real data distribution and in this sense resembles particle filters. In addition, it is in a vector form and thus removes the need to use logical connectives such as AND/OR to aggregate the scalar variables. Finally, it uses the relative data density expressed in a form of a parameter-free (Cauchy type) kernel to derive the activation level of each rule; these are then fuzzily weighted to produce the overall output. This new simplified type of FRB can be seen as the next form after the two popular FRB system types, namely the Zadeh-Mamdani and Takagi-Sugeno. The new type of FRB has a much simplified antecedent part which is formed using data clouds. Data clouds are sets of data samples in the data space and differ from clusters significantly (they have no specific shape, boundaries, and parameters). An important specific of the activation level determined by relative density is that it takes directly into account the distance to all previous data samples, not just the mean or prototype as other methods do. The proposed simplified FRB types of systems can be applied to off-line, on-line as well as evolving (with adaptive system structure) versions of FRB and related neuro-fuzzy systems. They can also be applied to prediction, classification, and control problems. In this paper examples will be presented of an evolving FRB predictor and of a classifier of one rule per class type which will be compared with the traditional approaches primarily aiming proof of concept. More thorough investigation of the rich possibilities which this innovative technique offers will be presented in parallel publications.