The interpolation of Thiele-type continued fractions is thought of as the traditional rational interpolation and plays a significant role in numerical analysis and image interpolation. Different to the classical method, a novel type of bivariate Thiele-like rational interpolation continued fractions with parameters is proposed to efficiently address the interpolation problem. Firstly, the multiplicity of the points is adjusted strategically. Secondly, bivariate Thiele-like rational interpolation continued fractions with parameters is developed. We also discuss the interpolant algorithm, theorem, and dual interpolation of the proposed interpolation method. Many interpolation functions can be gained through adjusting the parameter, which is flexible and convenient. We also demonstrate that the novel interpolation function can deal with the interpolation problems that inverse differences do not exist or that there are unattainable points appearing in classical Thiele-type continued fractions interpolation. Through the selection of proper parameters, the value of the interpolation function can be changed at any point in the interpolant region under unaltered interpolant data. Numerical examples are given to show that the developed methods achieve state-of-the-art performance.

Gas supply system risk assessment is a serious and important problem in cities. Existing methods tend to manually build mathematical models to predict risk value from single-modal information, i.e., pipeline parameters. In this paper, we attempt to consider this problem from a deep-learning perspective and define a novel task, Urban Gas Supply System Risk Assessment (GSS-RA). To drive deep-learning techniques into this task, we collect and build a domain-specific dataset GSS-20K containing multi-modal data. Accompanying the dataset, we design a new deep-learning framework named GSS-RiskAsser to learn risk prediction. In our method, we design a parallel-transformers Vision Embedding Transformer (VET) and Score Matrix Transformer (SMT) to process multi-modal information, and then propose a Multi-Modal Fusion (MMF) module to fuse the features with a cross-attention mechanism. Experiments show that GSS-RiskAsser could work well on GSS-RA task and facilitate practical applications. Our data and code will be made publicly available.

Fuzzy similarity ratio method is a widely used method of fuzzy decision-making, not only to classification, but also to sort. In this paper, we constructed a geochemical anomaly evaluation model using the Fuzzy similarity ratio method; we also program it with C# language and applied the model to practical work. Practice has proved that the fuzzy decision-making applies to the evaluation of geochemical anomalies can effectively improve the accuracy of the evaluation.