This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME.

The blended educational method has become a common way of teaching and learning in the post-COVID-19 era. However, the related research on the selection model for the blended design teaching service quality solution is still an important research gap during this period. Therefore, this study proposed a hybrid method of fuzzy analytic network process (FANP) and technique for order preference by similarity to ideal solution (TOPSIS) to analyse the dimensions, indicators and alternatives of blended design teaching service quality. As for the findings of this research, the dimension of assurance is the most vital factor, followed by responsiveness, reliability and empathy. Meanwhile, this research discovered that the top three significant alternatives are “Employees are trustworthy”, “Safe transaction mechanism and environment” and “Personalised needs of customers”. Also, we found that dimensions utilised to evaluate the quality of education service are similar whether in the post COVID-19 era, in the COVID-19 epidemic or prior to the COVID-19 pandemic. The main contribution of this study is to establish a multi-criteria decision-making (MCDM) model for the ranking of the blended design teaching service quality index and solution under a fuzzy environment. Finally, the research findings of this study have a guiding role, thereby becoming a guide for the industries related to hybrid design education to maintain good service quality in similar scenarios in the future.

We consider a family of explicit Runge–Kutta pairs of orders six and five without any additional property (reduced truncation errors, Hamiltonian preservation, symplecticness, etc.). This family offers five parameters that someone chooses freely. Then, we train them in order for the presented method to furnish the best results on a couple of Kepler orbits, a certain interval and tolerance. Consequently, we observe an efficient performance on a wide range of orbital problems (i.e., Kepler for a variety of eccentricities, perturbed Kepler with various disturbances, Arenstorf and Pleiades). About $1.8$ digits of accuracy is gained on average over conventional pairs, which is truly remarkable for methods coming from the same family and order.

The United Nations established 17 sustainable development goals (SDGs) in 2015, but research on these goals in the visual design industry remains limited. This study introduces a hybrid approach, combining fuzzy analytical hierarchy process (FAHP) and grey rational analysis (GRA) to assess sustainable factors from the perspectives of both service providers and consumers. In the FAHP model, consumers and visual design professionals had similar views on the ranking of dimensions and indicators. Both reported that the most important dimension for visual design sustainability is the environment. However, the perspective of consumers differed from that of visual design practitioners in the GRA model, as consumers argued that the social aspect has the greatest impact on visual design sustainability, while practitioners believed that the environmental aspect is the most important. The main contribution of the study is to emphasise that the hybrid multi-criteria decision-making (MCDM) mode can help the visual design industry align its services to consumer expectations. A systematic and objective model that presents practical insights relevant to industry is offered by this model. It also serves as a valuable reference for future research in similar areas.

Online education has been still a common way for teaching and learning in the post epidemic era. However, the related research on service quality for the online Yue kiln celadon art education industry is still a vital research gap during this period. Thus, a hybrid method of FANP and GRA is proposed in this study to analyse and evaluate the key factors for providing and maintaining high service quality of online Yue kiln celadon art education industry in the post coronavirus era. In this research, whether in the model of FANP and GRA, factors such as safety mechanism of transaction and education, personnel quality, and the ability of customer need handling are essential conditions for providing excellent service quality in the post-COVID-19 era. The main contribution of this study is to propose an integrated method of FANP and GRA to calculate and rank potential solutions of online Yue kiln celadon art education service quality in the post-COVID-19 era under fuzzy environment and discrete conditions. Finally, the research findings of this study have a guiding role, thereby becoming a guide for the industries related to online Yue kiln celadon art education to maintain good service quality in similar scenarios in the future.

Achieving sustainable development in the ceramic industry necessitates aligning production practices with evolving consumer expectations and the UN Sustainable Development Goals (SDGs). This study evaluates sustainability practices from a customer perspective, aiming to foster more sustainable manufacturing within the China’s product manufacturing sector. We introduce a novel hybrid fuzzy multi-criteria decision-making (MCDM) framework by integrating the Fuzzy Full Consistency Method (FUCOM-F) and Fuzzy Measurement of Alternatives and Ranking according to COmpromise Solution (FMARCOS). This approach, leveraging expert evaluations with linguistic fuzzy numbers, rigorously determines the importance of various sustainability criteria (aligned with SDGs) and ranks potential sustainable alternatives for the ceramic industry. Our findings demonstrate the framework’s robustness in assessing consumer priorities for sustainability, highlighting “Environment” and “Humanity” as the most critical dimensions from the consumer viewpoint. Furthermore, “The Branding of Cultural and Creative Industries” and “Sustainable Materials Use and Environmental Impact Reduction” emerged as the top-ranked solutions. This research offers significant managerial implications for ceramic product manufacturer, managers, and policymakers by providing a structured approach to prioritise sustainability initiatives that resonate with consumer values. Ultimately, it guides the industry towards sustainable pro- duction pathways, bridging the gap between awareness and facilitating a transition to more sustainable manufacturing models and public policies, with relevance for the ceramic product manufacturing sector and beyond.