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To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension of natural language. Although many numbers are in fact Z-numbers, their higher computational complexity often prevents their recognition as such. In order to reduce computational complexity, this paper reviews the development and research direction of Z-numbers and deduces the operational rules for symmetric triangular Z-numbers. We first transform them into classical fuzzy numbers. Using linear programming, the extension principle of Zadeh, the convolution formula, and fuzzy number algorithms, we determine the operational rules for the basic operations of symmetric triangular Z-numbers, which are number-multiplication, addition, subtraction, multiplication, power, and division. Our operational rules reduce the complexity of calculation, improve computational efficiency, and effectively reduce the information difference while being applicable to other complex operations. This paper innovatively combines Z-numbers with classical fuzzy numbers in Z-number operations, and as such represents a continuation and innovation of the research on the operational laws of Z-numbers. [ABSTRACT FROM AUTHOR]

Sustainable development is a practical path to optimize industrial structures and enhance investment efficiency. Investigating risk contagion within ESG industries is a crucial step towards reducing systemic risks and fostering the green evolution of the economy. This research constructs ESG industry indices, taking into account the possibility of extreme tail risks, and employs VaR and CoVaR as measures of tail risk. The TENET network approach is integrated to to capture the structural evolution and direction of information flow among ESG industries, employing information entropy to quantify the topological characteristics of the network model, exploring the risk transmission paths and evolution patterns of ESG industries in an extreme tail risk event. Finally, Mantel tests are conducted to examine the existence of significant risk spillover effects between ESG and traditional industries. The research finds strong correlations among ESG industry indices during stock market crash, Sino–US trade frictions, and the COVID-19 pandemic, with industries such as the COAL, CMP, COM, RT, and RE playing key roles in risk transmission within the network, transmitting risks to other industries. Affected by systemic risk, the information entropy of the TENET network significantly decreases, reducing market information uncertainty and leading market participants to adopt more uniform investment strategies, thus diminishing the diversity of market behaviors. ESG industries show resilience in the face of extreme risks, demonstrating a lack of significant risk contagion with traditional industries. [ABSTRACT FROM AUTHOR]

Shannon entropy is used to measure information uncertainty, while the information dimension is used to measure information complexity. Given two probability distributions, the difference can be measured by relative entropy. However, the existing relative entropy does not consider the effect of information dimension. To improve the existing entropy, a new relative entropy is presented in this paper. The information fractal dimension is considered in the proposed relative entropy. The new relative entropy is more generalized than the initial relative entropy. When dimension is not considered, it will degenerate to the initial relative entropy. Another interesting point is that the new relative entropy may have negative values when calculating. The physical meaning is still under exploration. Finally, some application examples are provided to exemplify the utilization of the proposed relative entropy. [ABSTRACT FROM AUTHOR]

In group decision making (GDM), due to complexity of various factors, decision makers (DMs) often provide incomplete preference relations (PRs) in preference matrix. Interval-valued probabilistic uncertain linguistic term set (IVPULTS) is a flexible and accurate tool to depict evaluation information of experts. In this paper, we mainly propose a new concept pertaining to interval-valued probabilistic uncertain linguistic preference relation (IVPULPR) that applies the IVPULTS to preference relations. Firstly, some new basic theoretical concepts of IVPULTS are developed including ordered IVPULTS, normalization method and new expectation function. Secondly, we establish several goal programming models to estimate the unknown elements in incomplete IVPULPR and propose the expected additive consistency of IVPULPR. To improve the consistency level, two optimization models are constructed based on the idea of minimum adjustment. Thirdly, we derive the experts' weights in terms of information uncertainty, where a new method to measure information uncertainty of IVPULTS is proposed. For the sake of improving group consensus, we construct a group consensus index (GCI) and two optimization models depending on the adjustment mechanism of expert weight. Finally, a complete GDM framework with incomplete IVPULPR is devised based on the analysis of IVPULPR consistency and group consensus. Through an experiment analysis by using an UCI dataset, we find that the proposed GDM model can not only precisely express fuzzy preference information of DMs, but also ensure achievement of acceptable consistency and group consensus under the condition of not changing the initial preference as much as possible. [ABSTRACT FROM AUTHOR]

• The general membership functions of four types thresholds for the grades on attribute eigenvalue are proposed. • The trust information uncertainty degree in social network is researched. • A new method to generate the incomplete social network based on the trust information uncertainty degree and variable weight function is proposed. • A novel multi-objective decision optimization model for network security situation grade assessment under multi-source information is proposed. Grade assessment of network security situation is summarized as a typical multi-index grade assessment problem. However, the existed methods for grade assessment of network security situation do not consider multi-source information such as the trust information among experts, the preference information among companies and heterogeneous information of companies. The above problems are unable to be solved through traditional assessment methods. The aim of this paper is to establish a novel multi-objective decision model for the grade assessment of network security situation under multi-source information. On the basis of describing the grade assessment problem of network security situation, the membership functions of four-type thresholds for the grades on attribute eigenvalue are put forward. Two trust information uncertainty degrees in social network are defined, and the trust transfer operator based on trust information uncertainty degree and multi-path trust integration method based on the variable weight function is proposed. Afterwards, a new method to generate the incomplete social network is used to identify the weights of experts. Then, a multi-objective decision grade assessment optimization model is further established to obtain the network security situation grades and grade discrimination based on the two-tuple linguistic operator. The proposed method provides a theoretical basis for constructing and testing the grade assessment of network security situation. Meanwhile, it develops the grade assessment system of advanced network security situation and improves the ability to protect network security. [ABSTRACT FROM AUTHOR]

Long-term development in computer manufacturing is crucial to satisfying the demands for the software and hardware needed for artificial intelligence (AI) computation. However, the computer manufacturing sector is highly energy-intensive and resource-consuming, making company sustainability an issue. The framework developed in this study incorporates 15 sustainability criteria focusing predominantly on the economy, society, environment, and risk perspectives. A novel hybrid approach that integrates the ISVTNN (interval single-valued trapezoidal neutrosophic number), DEMATEL (decision-making trial and evaluation laboratory), and PGRA (probability-based grey relational analysis) techniques is proposed. This approach is applied to evaluate the interdependent weights of the criteria for a comprehensive calculation of the performance of the evaluated companies based on probabilities. The inclusion of ISVTNNs allows not only for the broader consideration of information uncertainty but also for more effective integration of experts' judgments. To verify the robustness of the proposed model, three sensitivity analyses were conducted. The results show no significant changes in the rankings of the evaluated companies, demonstrating the stability and reliability of the model. The proposed framework and methodology can serve as the foundation for assessing the sustainable performance of companies in the electronics manufacturing industry. This study indirectly strengthens the backbone of the AI system, by improving sustainability assessment in the computer manufacturing sector (which is integral to the foundation for AI computation). In the AI-driven era, it can be expected that hardware demands will skyrocket, making sustainable manufacturing the linchpin for long-term operational success, resilience, and industry growth. • Developed a novel group decision-making approach for assessing corporate sustainability performance. • Integrated ISVTNN to measure uncertainty and effectively amalgamate expert opinions. • The proposed ISVTNN PGRA retains fuzziness, calculating through probabilistic means. • Demonstrated approach efficacy across six electronics manufacturing enterprises. • Sensitivity analysis underscores the approach's robustness. [ABSTRACT FROM AUTHOR]

The construction and building industry (CBI) is considered one of the major carbon emission contributors to the environment and faces various social and technical challenges in implementing decarbonized and circular economy (DCE) practices. Resource optimization can be achieved using the CBI product circularity and carbon offset mechanisms for greater business sustainability. In past studies, DCE practices have been loosely considered for improving the sustainability performance of emerging economies’ CBI. To fill this gap, this study uniquely focuses on CBI practices on DCE in consideration of socio-technical system (STS) availability because STS plays a vital role in adopting DCE practices. The proposed research framework is based on STS theory to measure the inter-influence of socio-technical challenges in achieving decarbonized and circular CBI. The STS-based framework consists of six dimensions namely: goals of circular construction (GCC), people barriers (PB), cultural barriers (CB), infrastructural barriers (IB), technological barriers (TB), and construction process and procedural barriers (CPB). The main STS dimensions are further divided into 26 sub-dimensions to assess interinfluencing mapping. The proposed framework is analyzed using integrated grey information uncertainty theory with decision-making trial and evaluation laboratory (DEMATEL), and interpretive structural modelling (ISM), i.e., grey-DISM. The grey-DISM method measures the driving power and dependence of the interdependencies of the decarbonized circularity barriers of the Indian CBI. Fifteen industry experts participated in the data survey, and their participation consistency was more than 95%. Barriers IB and CPB were found to be the major and minor challenges in implementing DCE in CBI. The findings of this research reported that lack of decarbonized and CE-based infrastructure hinders the adoption of DCE practices. This paper’s results also highlight the construction design dependency on infrastructure and machinery and low DCE practice perceptions for improving circularity in CBI. The entire decision model is divided into three levels of hierarchical mapping, which helps construction practitioners and policymakers develop strategic planning for improving DCE practices in CBI. The paper also presented managerial and policy implications for CBI practitioners and policymakers. [ABSTRACT FROM AUTHOR]