Formalization of rough sets is a key issue in rough set theory. When rough sets are formalized by propositional logic, predicate logic, or modal propositional logic, it easily suffers from some problems. For instance, an incomplete system is obtained. The concepts of “ p r e c i s e” or “ r o u g h” of rough sets cannot be described. To tackle these issues, a new noncontingency axiomatic system is proposed for formalizing rough sets in this paper. First, a new concise accessibility relation is defined for the axiomatic system; then, two simpler axiom schemas of the axiomatic system are designed to replace the axiom schema K. This is helpful to prove the soundness and completeness theorems for the axiomatic system. Finally, rough sets can be perfectly formalized by our proposed axiomatic system. Theoretical analysis proves that a complete formal system is achieved. In addition, the concepts of “ p r e c i s e” or “ r o u g h” of rough sets can be described without the help of semantics functions of metalanguage.

Many-objective evolutionary algorithms (MaOEAs) are widely used to solve many-objective optimization problems. As the number of objectives increases, it is difficult to achieve a balance between the population diversity and the convergence. Additionally, the selection pressure decreases rapidly. To tackle these issues, this paper proposes a two-stage many-objective evolutionary algorithm with dynamic generalized Pareto dominance (called TS-DGPD). First, a two-stage method is utilized for environmental selection. The first stage employs the cosine distance to accelerate the convergence. The second stage uses L p ${L}_{p}$ -norm maintain the population diversity. Moreover, a dynamic generalized Pareto dominance (DGPD) is used to increase the selection pressure of the population. To evaluate the performance of TS-DGPD, we compare it with several other MaOEAs on two benchmark sets with 3, 5, 8, 10, 15, and 20 objectives. Experimental results show that TS-DGPO performs satisfactorily on convergence and diversity.

Firefly algorithm (FA) is a popular swarm intelligence optimization algorithm. Though FA was employed to solve various optimization problems, it still has some deficiencies, such as high complexity, slow convergence rate, and low precision of solutions. To tackle these issues, this paper proposes an efficient FA based on modified search strategy and neighborhood attraction (namely MSSNaFA). In MSSNaFA, there are four main modifications. First, a novel search strategy based on dimension differences is designed. The attractiveness in the original FA is related to the Euclidean distance, while our new method uses the differences of each dimension for two fireflies to compute the attractiveness. Then, a modified neighborhood attraction mechanism is utilized to reduce the computational complexity. When the current solution is selected, it will move to the global best solution based on the new movement strategy. Third, for each firefly, three neighborhood search operations are carried out based on a preset probability. Lastly, the step factor is adaptively adjusted in the search process. Performance validation between MSSNaFA and four other FA variants show the effectiveness of our approach.

With the rapid growing of data on Web, we are facing three serious problems. Firstly, there are a huge number of data resources which are heterogeneous and dynamic.Secondly, most of data on Web are unstructured. Thirdly, there are various kinds of Web users who have different interests and requirements. In this paper, we proposed a new system architecture for unstructured data management on Web to solve these problems by integrating data spaces, database and meta search engine. The system architecture consists of three layers for data gathering on demand, dynamic management and personalized service, respectively. Data servicing layer allows Web users to create data spaces with advanced functions to manipulate and access Web data, eg, cross media query and automatic recommendation. Data managing layer models both Web data and their semantic relationships using our object deputy database named as TOTEM; it also supports schema evolution and dynamic classification. Data gathering layer extracts user's interest from his or her data space; gathers the related data on Web and further analyzes their semantic relationships. Finally, we implemented a prototype system Tmusic based on this new system architecture to show its availability.