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This study aims to solve the problem of repair path planning between multiple small-size defects in the field of additive manufacturing (AM) repair by using Python-based ant colony algorithm (ACO). The optimal parameter combination scheme is obtained by discussing the influencing factors of parameters in the ACO.

The effects of the information heuristic factor α, the expected heuristic factor ß and the pheromone volatile factor ρ on the simulation results were investigated by designing a three-factor and three-level orthogonal experiment. The fast convergence of ACO in finding the optimal solution of multiple small-size defect repair path problem is proved by comparing the simulation results with those of genetic algorithm (GA) on the same data set.

The ACO can effectively solve the repair path planning problem between multiple small-size defects by optimizing the parameters. In the case of 50 defect locations, the simulation results of the ACO with optimized parameters are 159.8 iterations and 3,688 average path lengths, while the GA has 4,027.2 average path lengths under the same data set and the same number of iterations, and by comparison, it is proved that the ACO can find the optimal solution quickly in the small-size defects repair path planning problem, which greatly improves the efficiency of defect repair.

The parameter-optimized ACO can be quickly applied to the planning problem of repair paths between multiple small-size defects in the field of AM repair, which can better improve the defect repair efficiency and reduce the waste of resources.

The purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.

The uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if‐part fuzzy sets in the case of single‐input and single‐output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.

The since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.

From the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.

For engineers, the sinc‐shaped membership function is a good choice to improve their fuzzy systems in real applications.

The uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.

This paper aims to explore the mechanism of the slip phenomenon at macro/micro scales, and analyze the effect of slip on fluid flow and heat transfer, to reduce drag and enhance heat transfer.

The improved tangential momentum accommodation coefficient scheme incorporated with Navier’s slip model is introduced to the discrete unified gas kinetic scheme as a slip boundary condition. Numerical tests are simulated using the D2Q9 model with a code written in C++.

Velocity contour with slip at high Re is similar to that without slip at low Re. For flow around a square cylinder, the drag is reduced effectively and the vortex shedding frequency is reduced. For flow around a delta wing, drag is reduced and lift is increased significantly. For Cu/water nanofluid in a channel with surface mounted blocks, drag can be reduced greatly by slip and the highest value of drag reduction (DR) (67.63%) can be obtained. The highest value of the increase in averaged Nu (11.78%) is obtained by slip at Re = 40 with volume fraction φ=0.01, which shows that super-hydrophobic surface can enhance heat transfer by slip.

The present study introduces and proposes an effective and superior method for the numerical simulation of fluid/nanofluid slip flow, which has active guidance meaning and applied value to the engineering practice of DR, heat transfer, flow control and performance improvement.

To address the various irregularities that occurred during the development of China’s electricity market, particularly the issue of collusive pricing between upstream and downstream firms.

This study constructs a tripartite evolutionary game model involving government regulators, grid operators and power producers to address electricity market pricing chaos. By analyzing the stable strategies within each subject’s evolutionary game, adjustments to the relevant parameters are made to achieve a stable state of strategy selection.

The findings of this study indicate the following: (1) Enhancing the government’s rewards and punishments, increasing speculation and rent-seeking costs for grid operators and modifying tariff sales revenue can promote the integrity of grid operators. (2) Establishing reasonable incentives and penalties can effectively mitigate rent-seeking behaviors resulting from collusive pricing in the power industry. (3) Strengthening the accountability of higher authorities to government regulators and adjusting incentives for grid operators to comply and generators to refrain from rent-seeking behavior can increase the likelihood of rigorous inspections by government regulators.

This study elucidates the impact of factors such as the cost of speculation and sales revenue of grid operators, the cost of rent-seeking by power producers and the strength of rewards and punishments by government departments on the power sector. Adjusting these factors can significantly influence the stability of the three-party evolutionary game, providing valuable insights into the regulatory mechanisms of the power industry.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.