Pattern trees induction: A new machine learning method

Fuzzy classification is one of the most important applications in fuzzy set and fuzzy-logic-related research. Its goal is to find a set of fuzzy rules that form a classification model. Most of the existing fuzzy rule induction methods (e.g., the fuzzy decision trees (FDTs) induction method) focus on searching rules consisting of triangular norms (t-norms) (i.e., and) only, but not triangular conorms (t-conorms) or) explicitly. This may lead to the omission of generating important rules that involve t-conorms explicitly. This paper proposes a type of tree termed pattern trees (PTs) that makes use of different aggregations, including both t-norms and t-conorms. Like decision trees, PTs are an effective tool for classification applications. This paper discusses the difference between decision trees and PTs, and also shows that the subsethood-based method (SBM) and the weighted-subsethood-based method (WSBM) are two specific cases of PT induction. A novel PT induction method is proposed using similarity measure and fuzzy aggregations. The comparison to other classification methods including SBM, WSBM, C4.5, nearest neighbor, support vector machine, and FDT induction shows that: 1) PTs can obtain high accuracy rates in classifications; 2) PTs are robust to overfitting; and 3) PTs, especially simple pattern trees (SPTs), maintain compact tree structures.