Big graph data is different from traditional data and they usually contain complex relationships and multiple attributes. With the help of graph pattern matching, a pattern graph can be designed, satisfying special personal requirements and locate the subgraphs which match the required pattern. Then, how to locate a graph pattern with better attribute values in the big graph effectively and efficiently becomes a key problem to analyze and deal with big graph data, especially for a specific domain. This article introduces fuzziness into graph pattern matching. Then, a genetic algorithm, specifically an NSGA-II algorithm, and a particle swarm optimization algorithm are adopted for multi-fuzzy-objective optimization. Experimental results show that the proposed approaches outperform the existing approaches effectively.