In this paper, we put forward a fast simplification method for the terrain model by integrating the discrete particle swarm optimization with the hierarchical structure. In this method, each particle is represented as a hierarchical structure and corresponds to a candidate solution of the simplified terrain model. In order to acquire an optimal simplified model, we proposed a new model error evaluation function based on the terrain features. Thereby the terrain model yielded by this method has high self-adaptability and optimal simplification ratio. Furthermore, the velocity of the particle is redefined as the probability of the model being simplified superiorly. Therefore, the particles can converge to the optimal simplified model rapidly. The experimental results performed on benchmark terrain data show that the efficiency and the precision of our algorithm are improved greatly and the detailed features in the simplified model are preserved, compared with the others common simplification method.

Model net proposed in this paper is a kind of directed graph used to represent and analyze the static structure of a modelbase. After the formal definition of the model net was given, a construction algorithm is introduced. Then, two simplification algorithms are put forward to show how this approach can reduce the computational complexity of model composition for a specific decision problem. In succession, a model composition algorithm is worked out based on the simplification algorithms. As a result, this algorithm is capable of finding out all the candidate composite models for a specific decision problem. Finally, several advantages of the model net are discussed briefly.

The purpose of this paper is to start a conceptual investigation of approximation rule based on VPRS as a result of the certainty degree of rules in complete information system that cannot exactly express the uncertainty of those in incomplete information system, and then an efficient approximation rule induction algorithm under the rough set framework is presented. Instead of focusing on the minimal rule set, this algorithm hierarchically extracts rules in multistages from data sets to suit changing environments in learning and classification. In addition, a heuristic strategy is employed in the algorithm to improve its performance and reduce the time consumed in inducing. Experiments are carried out, and the results show that the proposed algorithm is effective in inducing rules which can enhance their adaptive capacities.