Induction of tolerance rough fuzzy decision tree

The fuzzy ID3 is tailored for inducing fuzzy decision trees from the fuzzy decision tables with fuzzy condition attributes and fuzzy decision attribute. In fuzzy ID3, average fuzzy classification entropy is used as heuristic for selecting the expanded attributes, while fuzzy confidence degree is used as termination conditions of leaf nodes. When fuzzy ID3 is applied to induce fuzzy decision tree from fuzzy decision tables with continuous-valued conditional attributes and fuzzy-valued decision attribute, it is necessary for fuzzy ID3 to fuzzify the continuous-valued conditional attributes, but it is difficult to determine the fuzzy membership degree. In this paper, an induction method of fuzzy decision trees named TRFDT is proposed, TRFDT can directly induce fuzzy decision tree from fuzzy decision tables with continuous-valued conditional attributes and fuzzy-valued decision attribute. Tolerance rough fuzzy dependence is employed to select expanded attributes, Kosko fuzzy entropy is used as termination condition of leaf nodes. An example is presented to illustrate the induction process of fuzzy decision tree.