Information fusion under extremely uncertain environments is an important issue in pattern classification and decision-making problems. The Dempster-Shafer evidence theory (D-S theory) is more and more extensively applied in dealing with uncertain information. However, the results contrary to common sense are often obtained when combining different evidence using Dempster's combination rule. How to measure the difference between different evidence is still an open issue. In this paper, a new divergence is proposed based on the Kullback-Leibler divergence to measure the difference between different basic probability assignments (BPAs). Numerical examples are used to illustrate the computational process of the proposed divergence. Then, the similarity for different BPAs is also defined based on the proposed divergence. The basic knowledge about pattern recognition is introduced, and a new classification algorithm is presented using the proposed divergence and similarity under extremely uncertain environments. The effectiveness of the classification algorithm is illustrated by a small example handling robot sensing. The proposed method is motivated by the urgent need to develop intelligent systems, such as sensor-based data fusion manipulators, which are required to work in complicated, extremely uncertain environments. Sensory data satisfy the conditions (1) fragmentary and (2) collected from multiple levels of resolution.
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