Machine learning methods based on probabilistic decision tree under the multi-valued preference environment

In the classification calculation, the data are sometimes not unique and there are different values and probabilities. Then, it is meaningful to develop the appropriate methods to make classification decision. To solve this issue, this paper proposes the machine learning methods based on a probabilistic decision tree (DT) under the multi-valued preference environment and the probabilistic multi-valued preference environment respectively for the different classification aims. First, this paper develops a data pre-processing method to deal with the weight and quantity matching under the multi-valued preference environment. In this method, we use the least common multiple and weight assignments to balance the probability of each preference. Then, based on the training data, this paper introduces the entropy method to further optimize the DT model under the multi-valued preference environment. After that, the corresponding calculation rules and probability classifications are given. In addition, considering the different numbers and probabilities of the preferences, this paper also uses the entropy method to develop the DT model under the probabilistic multi-valued preference environment. Furthermore, the calculation rules and probability classifications are similarly derived. At last, we demonstrate the feasibility of the machine learning methods and the DT models under the above two preference environments based on the illustrated examples.