Fuzzy Rule-Based Classification Systems for multi-class problems using binary decomposition strategies: On the influence of n-dimensional overlap functions in the Fuzzy Reasoning Method

• We study the influence of the usage of n-dimensional overlap functions to model the conjunction in Fuzzy Rule Based Classification Systems (FRBCSs).
• We analyze the behavior of these functions when using both decomposition strategies and baseline classifiers.
• We consider four well-known FRBCSs (CHI, SLAVE, FURIA, and FARC-HD) and One-vs-All (OVA) and One-vs-One (OVO) strategies.
• The benefits obtained from overlap functions strongly depend on the learning process and the rule structure of each algorithm.

Multi-class classification problems appear in a broad variety of real-world problems, e.g., medicine, genomics, bioinformatics, or computer vision. In this context, decomposition strategies are useful to increase the classification performance of classifiers. For this reason, in a previous work we proposed to improve the performance of FARC-HD (Fuzzy Association Rule-based Classification model for High-Dimensional problems) fuzzy classifier using One-vs-One (OVO) and One-vs-All (OVA) decomposition strategies. As a result of an exhaustive experimental analysis, we concluded that even though the usage of decomposition strategies was worth to be considered, further improvements could be achieved by introducing n-dimensional overlap functions instead of the product t-norm in the Fuzzy Reasoning Method (FRM). In this way, we can improve confidences for the subsequent processing performed in both OVO and OVA.In this paper, we want to conduct a broader study of the influence of the usage of n-dimensional overlap functions to model the conjunction in several Fuzzy Rule-Based Classification Systems (FRBCSs) in order to enhance their performance in multi-class classification problems applying decomposition techniques. To do so, we adapt the FRM of four well-known FRBCSs (CHI, SLAVE, FURIA, and FARC-HD itself). We will show that the benefits of the usage of n-dimensional overlap functions strongly depend on both the learning algorithm and the rule structure of each classifier, which explains why FARC-HD is the most suitable one for the usage of these functions.