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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.

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.

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.

Abstract-Formal concept analysis (FCA) provides a theoretical framework for learning hierarchies of knowledge clusters. This paper is devoted to the study of uncertainty in FCA. We introduce the notions of uncertain concept and its accuracy degree in FCA, and present approaches to characterizing accuracy degree of uncertain concepts from approximation operators and covering rough set points of views.

Abstract. This note makes a comparative study of multigranulation rough set model and generalized rough set model. It is pointed out that the pessimistic multigranulation rough set model (PMGRS) is a kind of generalized rough set model, it is induced by a reflexive and symmetric relation on the universe. On the contrary, the optimistic multigranulation rough set model (OMGRS) is not a generalized rough set model. In other words, OMGRS can not be induced by a binary relation in general. Furthermore, some mistakes in the existing papers are pointed out. Pessimistic multigranulation rough setsRough set theory, proposed by Pawlak [1], is a well-established mechanism for dealing with vagueness and uncertainty in data analysis. Rough set model is constructed on the basis of an approximation space ( , ) U R , where U is a non-empty set of objects (also called the universe of discourse) and R is an equivalence relation imposed upon U . An arbitrary subset of the universe (or target concept) is approximated by a pair of lower and upper approximations constructed by the equivalence classes associated with the equivalence relation R . The concepts of upper and lower approximations in rough set theory allow us to discover the knowledge hidden in information systems and express it in the form of decision rules.In Pawlaks rough set model, equivalence relation is a key and primitive notion. The equivalence classes are building blocks for constructing the lower and upper approximations. This equivalence relation, however, seems to be a very stringent condition that may limit the application domain of the rough set model. To solve this problem, Pawlak's rough set model has been generalized to arbitrary binary relation based rough set model, covering based rough set model, fuzzy rough set model, etc, to meet the needs of some real application problems. Yao [2] proposed generalized rough set model and investigated the constructive and algebraic approaches in the study of rough sets. In the constructive approach, one starts from a binary relation on the universe and defines a pair of lower and upper approximation operators using the binary relation. In the algebraic approach, one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators. The axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators.Definition 1 [1] Let U be a finite universe and R an equivalence relation on U . The pair ( , ) U R is referred to as a Pawlak approximation space. For any X U ⊆ , the lower approximation

Abstract-Rough set under incomplete information has been extensively studied. Based on valued tolerance relation for incomplete information system, several approaches were presented to dealing with the attribute reductions and rule extraction. We point out some drawbacks in the existing papers for valued tolerance relation based rough approximations and propose a new kind of rough approximation operators which is a generalization of Pawlak approximation operators for complete information system. Some basic properties of the approximation operators are investigated.