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Top-down induction of decision trees is the most popular technique for classification in the field of data mining and knowledge discovery. Quinlan developed the basic induction algorithm of decision trees, ID3 (1984), and extended to C4.5 (1993). There is a lot of research work for dealing with a single attribute decision-making node (so-called the first order decision) of decision trees. Murphy and Pazzani (1991) addressed about multiple attribute conditions at decision-making nodes. They show that higher order decision-making generates smaller decision trees and better accuracy. However, there always exist NP complete combinations of multiple-attribute decision-makings...