Z-Number Generation Model and Its Application in a Rule-Based Classification System

Abstract

Due to their unique structure and powerful capability to handle uncertainty and partial reliability of information, Z-numbers have achieved significant success in various fields. Zadeh previously asserted that a Z-number can be regarded as a summary of probability distributions. Researchers have proposed various methods for determining the underlying probability distributions from a given Z-number. Conversely, can a Z-number be used to summarize a set of probability distributions? This problem remains unexplored. In this article, we propose a nonlinear model, termed Maximum Expected Minimum Entropy (MEME), for generating a Z-number from a set of probability distributions. Through this model, Z-numbers can be generated directly from data without requiring expert knowledge. Additionally, we applied the MEME model to classification problems, introducing a novel if-then rule form, termed Z-valuation if-then rules. These rules replace the deterministic consequent part of a fuzzy rule with an uncertain Z-valuation, thereby further summarizing the uncertain information in the rule’s consequent. Based on the Z-valuation rules, we propose a Z-valuation rule-based (ZVRB) classification system, which aims to enhance decision-making processes in scenarios where uncertainty plays a key role. To validate the effectiveness of the ZVRB classification system, we conducted two experiments comparing it with both classic and advanced nonfuzzy classifiers as well as fuzzy classification systems. The results show that the ZVRB model is superior to the other comparative classifiers in terms of classification performance.