A new type of simplified fuzzy rule-based system

Abstract Over the last quarter of a century, two types of fuzzy rule-based (FRB) systems dominated, namely Mamdani and Takagi–Sugeno type. They use the same type of scalar fuzzy sets defined per input variable in their antecedent part which are aggregated at the inference stage by t-norms or co-norms representing logical AND/OR operations. In this paper, we propose a significantly simplified alternative to define the antecedent part of FRB systems by data Clouds and density distribution. This new type of FRB systems goes further in the conceptual and computational simplification while preserving the best features (flexibility, modularity, and human intelligibility) of its predecessors. The proposed concept offers alternative non-parametric form of the rules antecedents, which fully reflects the real data distribution and does not require any explicit aggregation operations and scalar membership functions to be imposed. Instead, it derives the fuzzy membership of a particular data sample to a Cloud by the data density distribution of the data associated with that Cloud. Contrast this to the clustering which is parametric data space decomposition/partitioning where the fuzzy membership to a cluster is measured by the distance to the cluster centre/prototype ignoring all the data that form that cluster or approximating their distribution. The proposed new approach takes into account fully and exactly the spatial distribution and similarity of all the real data by proposing an innovative and much simplified form of the antecedent part. In this paper, we provide several numerical examples aiming to illustrate the concept. Keywords: fuzzy rule-based systemsMamdani and Takagi–Sugeno fuzzy systemsrecursive least square estimationdata density and distributionclustering Notes 1. yager@panix.com Additional informationNotes on contributorsRonald Yager 1