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Interval-valued information systems are generalized models of single-valued information systems. However, there are few studies on incomplete interval-valued data, which exist in many practical issues. In this paper, we propose a dominance relation for incomplete interval-valued information systems. Based on the dominance relation, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation, knowledge granularity measure are introduced into incomplete interval-valued information systems, some important properties are discussed, and the relationships among those concepts are studied. Experimental results show that the proposed measures are helpful for evaluating the discernibility ability of knowledge in incomplete interval-valued information systems.

Artificial Bee Colony (ABC) algorithm, which simulates the intelligent foraging behavior of a honey bee swarm, is one of optimization algorithms introduced recently. The performance of the ABC algorithm has been proved to be very effective in many researches. In this paper, ABC algorithm combined with kernel strategy is proposed for clustering semi-supervised information. The proposed clustering strategy can make use of more background knowledge than traditional clustering methods and deal with non-square clusters with arbitrary shape. Several datasets including 2D display data and UCI datasets are used to test the performance of the proposed algorithm and the experiment results indicate that the constructed algorithm is effective.