As an extension of fuzzy numbers, the concept of Z-number is a more appropriate formal structure to describe uncertain and partially reliable information. As a result of its representation capability, it can receive better classification results. However, there is still a gap in the application of Z-numbers to classification problems due to their high computation complexity. To take advantage of the Z-number, we design a system to make Z-numbers apply to classification problems. We decided to solve the problem on the basis of Z-neural network(ZNN), which we developed. First we tested the problem data about dental disease on the basis of traditional ANN to check if there are conflicts in data. The initial rules for ZNN were produced on the basis of fuzzy clustering. Various experiments of clustering were done. An optimal number of clusters found was 5 for data about dental disease. If-Then initial fuzzy rules (5 rules) were generated with 7 input variables each described by 5 linguistic terms. For better results 4 output variables were used (one for each dental disease) each with two linguistic terms. It is possible to use one output, but the training in this case was not successful. ZNN was trained to produce optimal Z-terms for If-Then rules. The aim of this paper is to construct a basic Z-number-valued rule-based classification system (ZRBCS). We define the basic form of the Z-number-valued if–then rule: If input pattern is antecedent Z-numbers then consequent class.