The multiobjective Quadratic Assignment Problem (mQAP) is considered as one of the hardest optimization problems but with many real-world applications. Since it may not be possible to simply weight the importance of each flow for the mQAP, it is best to use Pareto optimization to obtain the Pareto front or an approximation of it. Although Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems, research on mQAP has not much been investigated. This paper introduces a fuzzy particle swarm algorithm to handle the Multiobjective Quadratic Assignment Problem (mQAP). In the fuzzy scheme, the representations of the position and velocity of the particles in the conventional PSO is extended from the real vectors to fuzzy matrices. A new mapping is introduced between the particles in the swarm and the problem space in an efficient way. We evaluated the performance of the proposed approach. Empirical results illustrate that the approach can be applied for solving mQAP's very effectively.