Rough set theory is a tool for dealing with uncertainty problems. How to measure the uncertainty of a knowledge is an important issue in the theory. However, the existing uncertainty measures may not accurately reflect the uncertainty degree. This study analyzes the causes of it and explores a reasonable solution to it. Firstly, the existing accuracy models only focuses on some factors related to the target set while neglecting its own important influence on the model. Secondly, since no one gives a clear definition of knowledge uncertainty in approximation space, it is difficult to evaluate the accuracy and rationality of a knowledge uncertainty measure. Thirdly, most uncertain measures of knowledge are constructed based on the structure of knowledge itself, while neglecting other factors in the approximation model. In view of these, we first propose a new accuracy model which fully considers the important role of the target set itself. Second, two definitions of accuracy measure of knowledge are proposed to explain what the uncertainty of a knowledge is. And then, two uncertainty measures of knowledge are proposed and a method for quickly calculating them is designed. At last, an uncertain entropy is constructed for more conveniently calculating of knowledge uncertainty.

Steganalysis attack is to statistically estimate the embedded watermark in the watermarked multimedia, and the estimated watermark may be destroyed by the attacker. The existing methods of false negative probability, however, do not consider the influence of steganalysis attack. This paper proposed the game theory based false negative probability to estimate the impacts of steganalysis attack, as well as unintentional attack. Specifically, game theory was used to model the collision between the embedment and steganalysis attack, and derive the optimal building/embedding/attacking strategy. Such optimal playing strategies devote to calculating the attacker destructed watermark, used for calculation of the game theory based false negative probability. The experimental results show that watermark detection reliability measured using our proposed method, in comparison, can better reflect the real scenario in which the embedded watermark undergoes unintentional attack and the attacker using steganalysis attack. This paper provides a foundation for investigating countermeasures of digital watermarking community against steganalysis attack.

Attribute reduction is a popular topic in research on rough sets. In the classical model, much progress has been made in the study of the attribute reduction of indiscernibility and discernibility relations. To enhance the fault tolerance of the model, concepts of both indiscernibility and discernibility relations involving uncertain or imprecise information are proposed in this paper. The attribute reductions of the relative -indiscernibility relation and relative -discernibility relation and their algorithms are proposed. When the precision satisfies certain conditions, the reduction of two relation concepts can be converted into a positive region reduction. Therefore, the discernibility matrix is used to construct the reductions of the two relation concepts and the positive region. Furthermore, the corresponding algorithm of the relative -indiscernibility (discernibility) relation reduction can be optimized when the precision is greater than 0.5, and this is used to develop an optimization algorithm that constructs the discernibility matrix more efficiently. Experiments show the feasibility of the two relation reduction algorithms. More importantly, the reduction algorithms of the two relations and the optimization algorithm are compared to demonstrate the feasibility of the optimization algorithm proposed in this paper.

Variable precision reduction (VPR) and positive region reduction (PRR) are common definitions in attribute reduction. The compacted decision table is an extension of a decision table. In this paper, we propose another extension, called the weighted decision table. In both types of decision tables, VPR is defined, and the corresponding discernibility matrices for the PRR are proposed. Then, algorithms for obtaining the PRR from the discernibility matrices are presented. In both types of decision tables, the relationship between VPR and PRR is established by comparing the corresponding discernibility matrices. If the precision of the VPR meets the given conditions, then the PRR algorithms can be used to obtain the results after modifying some decision values in the decision tables. An analysis of the modification process of the decision values and the compression process of decision tables is used to propose a new algorithm for VPR in decision tables that ensures credibility. The effectiveness of the proposed algorithm was evaluated by an experimental comparison with existing VPR algorithms.

Attribute reduction comes from machine learning and is an important component of rough set theory. Research on attribute reduction has produced many important achievements. The aim of attribute reduction is to reduce the complexity of data while retaining its original characteristics to the greatest extent. The concept of attribute reduction is of great significance in machine learning research. In previous studies, a variety of attribute reduction definitions have been proposed according to different rules. Based on the binary relations among objects and local decision rules, this paper describes a local indiscernibility relation reduction for information tables. The discernibility matrix for the proposed reduction is established, and examples for single- and multi-decision classes are presented to illustrate that the proposed local indiscernibility relation reduction can be applied to decision tables. According to the reduction concept developed in this paper, and considering a heuristic algorithm for calculating the significance of attributes and a binary integer programming algorithm based on the discernibility matrix, three reduction algorithms are proposed. Experiments are conducted using four classifiers and a number of publicly available datasets. A comparison of the experimental results presented in this paper demonstrates the feasibility of the proposed algorithms.

In the era of big data, the features of online public opinion give some serious challenges for existing data analysis methods and it's necessary to give a review on the status and development trend of it. By means of CNKI, this paper collects published papers which involved in online public opinion research in big data Environment from 2010 to 2017.Using bibliometrics analysis and CiteSpace5.0 visualization application software, we get the hot spot and important frontier trend of online public opinion research in big data environment, on this basis, give a review on this research field. Some existing problems are analyzed and the future research direction of this filed are looked ahead. We hope this work can provide references for future related research and innovation.