This article presents the Euler-Maclaurin expansions of the hypersingular integrals $\int_{a}^{b}\frac{g(x)}{|x-t|^{m+1}}dx$ and $\int_{a}^{b}% \frac{g(x)}{(x-t)^{m+1}}dx$ with arbitrary singular point $t$ and arbitrary non-negative integer $m$. These general expansions are applicable to a large range of hypersingular integrals, including both popular hypersingular integrals discussed in the literature and other important ones which have not been addressed yet. The corresponding mid-rectangular formulas and extrapolations, which can be calculated in fairly straightforward ways, are investigated. Numerical examples are provided to illustrate the features of the numerical methods and verify the theoretical conclusions.

For interval-valued intuitionistic fuzzy sets featuring complementary symmetry in evaluation relations, this paper proposes a novel, complete fuzzy multi-attribute group decision-making (MAGDM) method that optimizes both expert weights and attribute weights. First, an optimization model is constructed to determine expert weights by minimizing the cumulative difference between individual evaluations and the overall consistent evaluations derived from all experts. Second, based on the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), the improved closeness index for evaluating each alternative is obtained. Finally, leveraging entropy theory, a concise and interpretable optimization model is established to determine the attribute weight. This weight is then incorporated into the closeness index to enable the ranking of alternatives. Integrating these features, the complete fuzzy MAGDM algorithm is formulated, effectively combining the strengths of subjective and objective weighting approaches. To conclude, the feasibility and effectiveness of the proposed method are thoroughly verified and compared through detailed examination of two real-world cases.

This paper presents a new approach based on optimization model to determine the weights of experts in the multi-attribute group decision. Firstly, by minimizing the sum of differences between individual evaluations and the overall consistent evaluations of all experts, a new optimization model is established for determining expert weights. Then, rigorous proof of the unique existence of solution is analyzed in detail, and the sequential least squares quadratic programming algorithm is adopted to solve the optimization model. Finally, the reasonableness of the new approach is verified by numerical experiments, i.e., the smaller the difference between the individual evaluations and the overall consistent evaluations, the larger the weights assigned to the corresponding individual.

Given the evaluation data of all the experts in multi-attribute group decision making, this paper establishes an optimization model for learning and determining expert weights based on minimizing the sum of the differences between the individual evaluation and the overall consistent evaluation results. The paper proves the uniqueness of the solution of the optimization model and rigorously proves that the expert weights obtained by the model have “perfect rationality”, i.e., the weights are inversely proportional to the distance to the “overall consistent scoring point”. Based on the above characteristics, the optimization problem is further transformed into solving a system of nonlinear equations to obtain the expert weights. Finally, numerical experiments are conducted to verify the rationality of the model and the feasibility of transforming the problem into a system of nonlinear equations. Numerical experiments demonstrate that the deviation metric for the expert weights produced by our optimization model is significantly lower than that obtained under equal weighting or the entropy weight method, and it approaches zero. Within numerical tolerance, this confirms the model’s “perfect rationality”. Furthermore, the weights determined by solving the corresponding nonlinear equations coincide exactly with the optimization solution, indicating that a dedicated algorithm grounded in perfect rationality can directly solve the model.

As a core surface facility in natural gas development, the operational efficiency of a gas gathering and transportation system depends largely on the precise configuration of its parameters. However, the complex structure of such a system and the large number of components make real-time data acquisition and accurate monitoring difficult under all operating conditions, so numerical simulation has become the standard way to represent its behavior. At present, the input parameters of professional simulation software still rely heavily on manual empirical settings, and parameter accuracy is therefore difficult to guarantee. If the manually set parameters deviate significantly from the actual operating conditions, the reliability of the simulation results is seriously compromised and subsequent decisions may be misleading. To address this problem, the present work uses Pipesim as the simulation platform and formulates parameter calibration as a weighted least-squares optimization problem. For a network with a fixed topology, the key component parameters are calibrated jointly. The objective is to minimize the deviation between the simulated and the field-measured values of the selected operating variables; pressure and flow rate are used in the case study, while the temperature term is retained in the general formulation. The Pipesim solver is proprietary and does not expose analytical derivatives of its outputs with respect to the calibrated parameters, so the model is solved with particle swarm optimization (PSO) combined with a continuation-projection encoding that handles continuous, discrete-gear and Boolean parameters. On the network examined here, the proposed procedure reduces the calibration effort and outperforms manual tuning in both accuracy and time. It therefore provides a practical reference for the design and operation management of gas gathering and transportation systems.