The ability in providing result that is consistent with actual ranking remains the major concern in group decision making environment. The main aim of this paper is to introduce a novel modification of TOPSIS method to facilitate multi criteria decision making problems based on the concept of Z-numbers called Z-TOPSIS. The proposed method is adequate and intuitive in giving meaningful structure for formalizing information of a decision making problem, as it takes into account the decision makers' reliability. This study also provides bridge with some established knowledge in fuzzy sets to certain extend as to strengthen the concept of ranking alternatives using Znumbers. To ensure practicality and effectiveness of proposed method, stock selection problem is studied. The ranking based on proposed method is validated comparatively using spearman rho rank correlation. Based on the analysis, the proposed method outperforms the established TOPSIS methods in term of ranking performance.

The new concept of a Z-number has been recently introduced in decision making analysis. This concept is capable of effectively dealing with uncertainty in information about a decision. As this concept is relatively new in fuzzy sets, its underlying theoretical aspects have not been established yet. In this paper, a multi-layer methodology for ranking Z-numbers is proposed for the first time. This methodology consists of two layers: Z-number conversion as the first layer and fuzzy number ranking as the second layer. In this study, the conversion methodology of Z-numbers into fuzzy numbers is extended to conversion into standardised generalised fuzzy number so that the methodology is applicable to both positive and negative data values. The methodology is validated by means of thorough comparison with some established ranking methods for consistency purposes. This methodology is considered as a generic decision making procedure, especially when Z-numbers are applied to real decision making problems.

A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review.

Connected and autonomous vehicles, along with the expanding Internet of Vehicles (IoV), are increasingly exposed to complex and evolving cyberattacks. Consequently, Intrusion Detection Systems (IDS) have become a vital component of modern vehicular cybersecurity. Federated Learning (FL) enables multiple vehicles to collaboratively train detection models while keeping their local data private, providing a decentralized alternative to traditional centralized learning. Despite these advantages, FL-based IDS frameworks remain vulnerable to attacks. To address this vulnerability, we propose an explainable federated intrusion detection framework that enhances both the security and interpretability of IDS in connected vehicles. The framework employs a Deep Neural Network (DNN) within a federated setting and integrates explainability through the Shapley Additive Explanations (SHAP) method. This Explainable Artificial Intelligence (XAI) component identifies the most influential network features contributing to detection decisions and assists in recognizing anomalies arising from malicious or corrupted clients. Experimental validation on the CICEVSE2024 and CICIoV2024 vehicular datasets demonstrates that the proposed system achieves high detection accuracy. Moreover, the XAI module improves transparency and enables analysts to verify and understand the model’s decision-making process. Compared with both centralized IDS models and conventional federated approaches without explainability, the proposed system delivers comparable performance, stronger resilience to attacks, and significantly enhanced interpretability. Overall, this work demonstrates that integrating FL with XAI provides a privacy-preserving and trustworthy approach for intrusion detection in connected vehicular networks.

Due to the vast and rapid increase in the size of data, data mining has been an increasingly important tool for the purpose of knowledge discovery to prevent the presence of rich data but poor knowledge. In this context, machine learning can be seen as a powerful approach to achieve intelligent data mining. In practice, machine learning is also an intelligent approach for predictive modelling. Rule learning methods, a special type of machine learning methods, can be used to build a rule based system as a special type of expert systems for both knowledge discovery and predictive modelling. A rule based system may be represented through different structures. The techniques for representing rules are known as rule representation, which is significant for knowledge discovery in relation to the interpretability of the model, as well as for predictive modelling with regard to efficiency in predicting unseen instances. This paper justifies the significance of rule representation and presents several existing representation techniques. Two types of novel networked topologies for rule representation are developed against existing techniques. This paper also includes complexity analysis of the networked topologies in order to show their advantages comparing with the existing techniques in terms of model interpretability and computational efficiency.

In this work, the fuzzy property is described by means of the Z-number as the coefficients and variables of the fuzzy equations. This alteration for the fuzzy equation is appropriate for system modeling with Z-number parameters. In this paper, the fuzzy equation with Z-number coefficients and variables is tended to be used as the models for the uncertain systems. The modeling issue related to the uncertain system is to obtain the Z-number coefficients and variables of the fuzzy equation. Nevertheless, it is extremely hard to get the Z-number coefficients of the fuzzy equations.