Rule-based models via the axiomatic fuzzy set clustering and their granular aggregation

Abstract

Rule-based models have become a popular way to represent and analyze the main knowledge residing in data because of the increasing complexity and uncertainty. For extracting semantically sound rules in a multi-view perspective, a novel rule-based model combined with the axiomatic fuzzy set (AFS) algorithm is developed in distributed systems. Using the idea of the AFS algorithm, several clusters and accompanying fuzzy descriptions are formed in terms of data distribution; thereby, the input of rules exhibits well-defined semantics by the logic compound of the predefined linguistic terms. The output of the rule is approximated by the Takagi–Sugeno (T–S) model, in which an extended weighted least squares method is designed to optimize the parameter vectors simultaneously. In virtue of the diversity of these individual results, a granular aggregation procedure incorporates the weighted principle of justifiable granularity to summarize all the local results into compact and meaningful descriptors (information granules). Five experiments considering synthetic and publicly available datasets are carried out to demonstrate the performance of the proposed approach. In addition, the proposed approach is also shown effective in an application involving the credit dataset.