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In response to the multiscale shape of coal and gangue in actual production conditions, existing coal separation methods are inefficient in recognizing coal and gangue, causing environmental pollution and other problems. Combining image data preprocessing and deep learning techniques, this paper presents an improved EfficientNetV2 network for coal and gangue recognition. To expand the dataset and prevent network overfitting, a pipeline-based data enhancement method is used on small sample datasets to simulate coal and gangue production conditions under actual working conditions. This method involves modifying the attention mechanism module in the model, employing the CAM attention mechanism module, selecting the Hardswish activation function, and updating the block structure in the network. The parallel pooling layer introduced in the CAM module can minimize information loss and extract rich feature information compared with the single pooling layer of the SE module. The Hardswish activation function is characterized by excellent numerical stability and fast computation speed. It can effectively be deployed to solve complex computation and derivation problems, compensate for the limitations of the ReLu activation function, and improve the efficiency of neural network training. We increased the training speed of the network while maintaining the accuracy of the model by selecting optimized hyperparameters for the network structure. Finally, we applied the improved model to the problem of coal and gangue recognition. The experimental results showed that the improved EfficientNetV2 coal and gangue recognition method is easy to train, has fast convergence and training speeds, and thus achieves high recognition accuracy under insufficient dataset conditions. The accuracy of coal and gangue recognition increased by 3.98% compared with the original model, reaching 98.24%. Moreover, the training speed improved, and the inference time of the improved model decreased by 6.6 ms. The effectiveness of our proposed model improvements is confirmed by these observations.

The incremental updating of lower and upper approximations under the variation of information systems is an important issue in rough set theory. Many incremental updating approaches with respect to different kinds of indiscernibility relations have been proposed. The grade indiscernibility relation is a fuzzification of classical Pawlak's indiscernibility relation which can characterize the similarity between objects more precisely. Based on fuzzy rough set model, this paper discusses the approaches for dynamically acquiring of the upper and lower approximations with respect to the grade indiscernibility relation when adding and removing an attribute or an object, and changing the attribute value of the object, respectively. Since the approaches are used in succession, they make the approximations can be updated correctly and effectively when any kind of possible change in the information system. Finally, extensive experiments on data sets from University of California, Irvine (UCI) show that the incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method.

Abstract--This paper is devoted to the discussion of uncertainty measures of soft sets. We make an analysis of the existing works on soft set entropy and show their limitations. We propose a new axiomatic definition of soft set entropy. Furthermore, some distance based entropies for soft sets are presented.

The rough set theory, introduced by Pawlak in 1982, is a formal for dealing with the uncertainties. But it cannot directly deal with the uncertainties with order structure. The lattice theory, introduced by Peirce and Schr$\ddot{o}$der towards the end of the nineteenth century, is a mathematical tool with order structure, algebraic structure and topological structure. In this paper, the rough theory is applied to the lattice theory, and the concept of the rough lattice is presented in order that a tool is presented which can deal with the uncertainties with lattice structure. For this purpose, an equivalence relation on a lattice is defined and then the notions of rough lattice and lower and upper approximations are introduced and some related properties are investigated. At last, some related algebraic structures are studied.