Integration of Multiple Fuzzy Decision Trees Based on Fuzzy Integral

Given a fuzzy information system, several important fuzzy attribute subsets can be found and each of them can have different contributions to decision-making. If only one of the fuzzy attribute subsets, which may be the most important one, is selected to induce decision rules, some useful information hidden in other important subsets for the decision-making will be lost unavoidably. To sufficiently make use of the information provided by every individual important fuzzy attribute subset in a fuzzy information system, a novel integration of multiple fuzzy decision trees is proposed. The method consists of three stages. First, several important fuzzy attribute subsets are found by fuzzy equivalent relation, and then a fuzzy decision tree for each important fuzzy attribute subset is generated using fuzzy ID3. The fuzzy integral is finally used as a fusion tool to integrate the generated decision trees, which combines together all outputs of the multiple fuzzy decision trees and forms the final decision result. An illustration is given to show the proposed fusion scheme. A numerical experiment on real data indicates that the proposed multiple tree induction is superior to the single tree induction based on the individual important fuzzy attribute subset.