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Experts may adjust their assessments through communication and mutual influence, and this dynamic evolution relies on the spread of internal trust relationships. Due to differences in educational backgrounds and knowledge experiences, trust relationships among experts are often incomplete. To address such issues and reduce decision biases, this paper proposes a probabilistic linguistic multi-attribute group decision consensus model based on an incomplete social trust network (InSTN).

In this paper, we first define the new trust propagation operators based on the operations of Probability Language Term Set (PLTS) with algebraic t-conorm and t-norm, which are combined with trust aggregation operators to estimate InSTN. The adjustment coefficients are then determined through trust relations to quantify their impact on expert evaluation. Finally, the particle swarm algorithm (PSO) is used to optimize the expert evaluation to meet the consensus threshold.

This study demonstrates the feasibility of the method through the selection of treatment plans for complex cases. The proposed consensus model exhibits greater robustness and effectiveness compared to traditional methods, mainly due to the effective regulation of trust relations in the decision-making process, which reduces decision bias and inconsistencies.

This paper introduces a novel probabilistic linguistic multi-attribute swarm decision consensus model based on an InSTN. It proposes a redefined trust propagation and aggregation approach to estimate the InSTN. Moreover, the computational efficiency and decision consensus accuracy of the proposed model are enhanced by using PSO optimization.

The purpose of this paper is to study the pipe-type electromagnetic induction heating device under power frequency condition.

To reduce eddy current loss and improve heating efficiency, the structure of a pipe-type power-frequency electromagnetic heating device was optimized. Based on the maximum load flow formula, a parallel excitation winding structure is designed, and the distribution of electromagnetic field under four different powers is analyzed by simulation. Four heating modes were proposed according to the structure of diversion ring, inner wall and outer wall. Two heating modes with better heating effect were obtained by comprehensively considering the factors such as magnetic field distribution, thermal power and energy consumption.

The double-wall structure of the pipe-type electromagnetic heating device can make the heat source distribution more uniform, and the use of power-frequency power supply can increase security, the installation of diversion ring can make the heating more sufficient and the heating efficiency of the two heating methods selected according to the structural performance is more than 90%.

In view of the medium or high frequency of pipe-type electromagnetic heating device, it is necessary to configure high power electronic frequency conversion drive system, and eddy current can only be produced on the tube wall, resulting in uneven distribution of heat sources. A pipe-type power-frequency electromagnetic heating device with double-wall structure was proposed.

This study conducts a comparative analysis of the diversification effects of China's national carbon market (CEA) and the EU ETS Phase IV (EUA) within major commodity markets.

The study employs the TVP-VAR extension of the spillover index framework to scrutinize the information spillovers among the energy, agriculture, metal, and carbon markets. Subsequently, the study explores practical applications of these findings, emphasizing how investors can harness insights from information spillovers to refine their investment strategies.

First, the CEA provide ample opportunities for portfolio diversification between the energy, agriculture, and metal markets, a desirable feature that the EUA does not possess. Second, a portfolio comprising exclusively energy and carbon assets often exhibits the highest Sharpe ratio. Nevertheless, the inclusion of agricultural and metal commodities in a carbon-oriented portfolio may potentially compromise its performance. Finally, our results underscore the pronounced advantage of minimum spillover portfolios; particularly those that designed minimize net pairwise volatility spillover, in the context of China's national carbon market.

This study addresses the previously unexplored intersection of information spillovers and portfolio diversification in major commodity markets, with an emphasis on the role of CEA.

This study conducts an analysis of the interplay between governance quality, environmental expenditure of the government, and pollution emissions (measured as CO2 emissions) within the BRIC economies.

Utilizing the FMOLS model and marginal effects, we investigate the influence of governance quality and environmental expenditure on environmental quality (CO2 emissions) over the period 1996–2020. We took data for Brazil, Russia, India and China. We excluded South Africa due to its due to its small economic size relative to other BRIC economies, sluggish industrial growth and deteriorating foreign trade which gives contrast outliers to our data.

Results indicate that government investments in environmental protection contribute to a reduction in CO2 emissions. However, the effectiveness of these expenditures is contingent upon the quality of governance. This underscores the significance of robust governance for realizing meaningful reductions in air pollution through environmental spending. Further, increase in GDP per capita and the industrial sector's share of GDP are associated with a significant rise in CO2 emissions across BRIC economies. Conversely, FDI and trade openness exhibit a negative impact on CO2 emissions, with this effect gaining greater resilience when accounting for governance factors.

Like any other studies, the present study also suffers from some limitations. First, besides air quality, environmental quality encompasses multiple dimensions and various characteristics such as water purity, noise pollution, open space access, visual effects of buildings etc. But the present study included only CO2 (air quality) as a proxy of environmental quality due to various problems of data and methods. Second, CO2 (carbon dioxide) emission, which is the dependent variable in our model, is actually influenced by various quantitative and qualitative (both natural and man-made) factors. We included only nine independent variables. However, we could not include many variables due to lack of consistent data. Third, this study included only four countries – Brazil, Russia, India and China (BRIC) and excluded South Africa which is a member of the BRICS block due to its economic size, sluggish industrial growth and deteriorating foreign trade which gives contrast outliers to our data set of the four BRIC countries. Therefore, the future research may be carried out by addressing those issues for better understanding of the environmental problems, governance and policies thereon.

(i) Establish environmental governance committees – The four BRIC countries including South Africa should form a committee comprising government, civil society, and private sector representatives for comprehensive oversight and collaboration in environmental governance. (ii) Invest in capacity building for environmental institutions – Allocate resources to enhance environmental institutions' capacity through training, data improvement, and enforcement strengthening. (iii) Implement green procurement policies – Encourage green procurement in government agencies to drive demand for eco-friendly products and services, promoting sustainable practices. (iv) Incentivize green technology development – Offer tax credits or subsidies to stimulate green technology adoption, including renewable energy and sustainable agriculture. (v) Promote sustainable urban development – Prioritize sustainable urban strategies like public transportation investment and green space promotion to mitigate urbanizations' environmental impacts. (vi) Enhance cross-border cooperation – Foster collaboration on transboundary environmental issues among four BRIC nations including South Africa, including joint research and policy responses. (vii) Promote green finance and investment – Mobilize green finance to support sustainable development projects through instruments like green investment funds and bonds.

This study distinguishes itself by offering a unique analysis of both individual and combined effects of governance and environmental expenditure on environmental quality. Additionally, it encompasses various dimensions of governance, an aspect rarely explored in the BRIC countries.