Constrained Optimization of Fuzzy Decision Trees

This paper proposes to build and optimize Takagi-Sugeno-like fuzzy regression trees with constraints aiming at preserving the interpretability of the rules. For this purpose, we state five requirements and deduce some conditions such as membership functions shared by the rules and strong fuzzy partitions on input variable domains. The membership functions are automatically placed thanks to an evolutionary strategy. We propose also a heuristics in order to find a sub-optimal structure of the tree.