Decision tree is a widely used technique to discover patterns from consistent data set. But if the data set is inconsistent, where there are groups of examples (objects) with equal values of conditional attributes but different decisions (values of the decision attribute), then to discover the essential patterns or knowledge from the data set is challenging. We consider three approaches (generalized, most common and many-valued decision) to handle such inconsistency. We created different greedy algorithms using various types of impurity and uncertainty measures to construct decision trees. We compared the three approaches based on the decision tree properties of the depth, average depth and number of nodes. Based on the result of the comparison, we choose to work with the many-valued decision approach. Now to determine which greedy algorithms are efficient, we compared them based on the optimization and classification results. It was found that some greedy algorithms (Mult_ws_entSort , and Mult_ws_entML) are good for both optimization and classification.