Ontology mapping is the key point to reach interoperability over ontologies. In semantic web environment, ontologies are usually distributed and heterogeneous and thus it is necessary to find the mapping between them before processing across them. Many efforts have been conducted to automate the discovery of ontology mapping. However, some problems are still evident. In this paper, ontology mapping is formalized as a problem of decision making. In this way, discovery of optimal mapping is cast as finding the decision with minimal risk. An approach called Risk Minimization based Ontology Mapping (RiMOM) is proposed, which automates the process of discoveries on 1: 1, n: 1, 1: null and null: 1 mappings. Based on the techniques of normalization and NLP, the problem of instance heterogeneity in ontology mapping is resolved to a certain extent. To deal with the problem of name conflict in mapping process, we use thesaurus and statistical technique. Experimental results indicate that the proposed method can significantly outperform the baseline methods, and also obtains improvement over the existing methods.