Ontology-based information retrieval is precise and effective but suffers from the problem of ontology heterogeneity. This paper focuses on the approximate information retrieval approach to solve the heterogeneity problem of both common ontologies as well as fuzzy ontologies on the semantic web. Approximate information retrieval needs to find approximations of concepts. However, current methods cannot find the best approximations of concepts for common ontologies, and there is still no published work for fuzzy ontologies. This paper firstly proposes a method of approximate information retrieval between common ontologies. It defines multielement least upper bounds and multielement greatest lower bounds, and then simplifies the multielement bounds to remove redundancy. It provides effective algorithms to find the simplified multielement bounds, and get the best approximations of concepts from the bounds. Then for the fuzzy ontologies, the paper defines cut concepts to transform fuzzy concepts into common concepts, and then applies the proposed method for approximate information retrieval between fuzzy ontologies. The improved algorithms for fuzzy ontologies are given to make the method more feasible and effective.