Z-number-valued Rule-Based Classification System

Abstract

The fuzzy rule-based classification system (FRBCS) is a popular tool for classification problems due to its interpretability and comprehensibility. As an extension of fuzzy numbers, the concept of Z-number is a more appropriate formal structure to describe uncertain and partially reliable information. A Z-number is an ordered pair of fuzzy numbers, where the second fuzzy number describes the reliability of the first one. 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 simple way to make Z-numbers apply to classification problems. Use the second fuzzy number to adjust the first fuzzy number to fit the training data. Then we create a kind of Z-number-valued if–then rule by extending the fuzzy if–then rule. In addition, a Z-number-valued rule-based classification system (ZRBCS) is developed, including two main processes: rule generation and new pattern classification. The developed system can cover more information than the classic fuzzy rule-based system, which can improve classification effects. The proposed ZRBCS is compared with classical FRBCS with/without certain degrees and three classical classification algorithms. According to statistical tests, ZRBCS is superior to FRBCS and two other algorithms.