As a novel architecture of a fuzzy decision tree constructed on fuzzy rules, the fuzzy rule-based decision tree (FRDT) achieved better performance in terms of both classification accuracy and the size of the resulted decision tree than other classical decision trees such as C4.5, LADtree, BFtree, SimpleCart and NBTree. The concept of Z-number extends the classical fuzzy number to model both uncertain and partial reliable information. Z-numbers have significant potential in rule-based systems due to their strong representation capability. This paper designs a Z-number-valued rule-based decision tree (ZRDT) and provides the learning algorithm. Firstly, the information gain is used to replace the fuzzy confidence in FRDT to select features in each rule. Additionally, we use the negative samples to generate the second fuzzy numbers that adjust the first fuzzy numbers and improve the model's fit to the training data. The proposed ZRDT is compared with the FRDT with three different parameter values and two classical decision trees, PUBLIC and C4.5, and a decision tree ensemble method, AdaBoost.NC, in terms of classification effect and size of decision trees. Based on statistical tests, the proposed ZRDT has the highest classification performance with the smallest size for the produced decision tree.

Information that people rely on is often uncertain and partially reliable. Zadeh introduced the concept of Z-numbers as a more adequate formal construct for describing uncertain and partially reliable information. Most existing applications of Z-numbers involve discrete ones due to the high complexity of calculating continuous ones. However, the continuous form is the most common form of information in the real world. Simplifying continuous Z-number calculations is significant for practical applications. There are two reasons for the complexity of continuous Z-number calculations: the use of normal distributions and the inconsistency between the meaning and definition of Z-numbers. In this paper, we extend the triangular distribution as the hidden probability density function of triangular Z-numbers. We add a new parameter to the triangular distribution to influence its convexity and concavity, and then expand the value's domain of the probability measure. Finally, we implement the basic operations of triangular Z-numbers based on the extended triangular distribution. The suggested method is illustrated with numerical examples, and we compare its computational complexity and the entropy (uncertainty) of the resulting Z-number to the traditional method. The comparison shows that our method has lower computational complexity, higher precision and lower uncertainty in the results.

Recent multi-criteria group decision making methods focus their analysis on the experts preferences. They do not take into account the reasons why each expert has provided a specific set of preferences. In this paper, a method that introduces novel measures capable of explaining the reasons behind experts decisions is presented. A novel concept, the arguments are presented. They represent the experts have for maintaining a certain position in the debate. Several measures related to the arguments are proposed. These new argumentation measures, along with consensus measures, help us to get a clear idea about how and why a specific resolution has been reached. They help us to determine which is the most influential expert, that is, the expert whose contributions to the debate have inspired the rest. Also, the proposed method allows us to determine which are the arguments that most of the experts have followed. A clear overview about how the debate is evolving in terms of arguments is also provided. The novel presented analysis indicate how the experts change their opinions in every round and what was the reason for it, which changes have occurred between rounds and they also provide global analysis results.