Positive Extension Matrix The extension matrix method is that at first, we find the distinguishing between the positive examples and negative examples. The extension matrix is used to represent those distinguishes, and then according to those distinguishes, the examples are induced so that the proper assertions are obtained. The extension matrix clearly reflects the distinguishing between positive examples and negative examples. It is easy to find the heuristic of a problem relying on it. • Nowadays there are AE1, AE5 , AE9 and AE11 algorithms that are created by relying on the extension matrix. All those algorithms are creating the heuristics starting from the nature of the path. In the algorithms, a rule is simplest with AE11, and it obtains the simpler rule than the AQ15. The algorithm AE18 we proposed in the paper also belongs to the extension matrix. It is based on the positive extension matrix (PEM). It also creates heuristics to induce starting from the nature of the path. In the inducing the algorithm prior selects the required elements. • In order to optimize our positive matrix algorithm, this talk will presents the algorithm AE18 and makes comparisons with our experimental results