Fuzzy decision tree (FDT) is an extension of decision tree. Fuzzy classification rules can be extracted by FDT from fuzzy decision tables with fuzzy conditional attributes and fuzzy decision attributes. However, it is very time consuming for fuzzifying conditional attributes, and fuzzification of conditional attributes will inevitably lead to information loss. In order to deal with this problem, based on tolerance rough fuzzy set, this paper proposed an algorithm named TRFDT (Tolerance Rough Fuzzy Decision Tree) and theoretically proved that the proposed algorithm is convergent with a very large probability. TRFDT can directly handle fuzzy decision tables with continuous-valued conditional attributes and fuzzy decision attributes. Accordingly, TRFDT has fast learning speed and good generalization ability, which have been experimentally proved by comparing TRFDT with two state-of-the-art approaches fuzzy ID3 and FDT-YS.
