Inventory management is critical for many industries. A proper control of inventory can considerably enhance a company's profit margins. Determination of the Economic Order Quantities (EOQ) is important in order to achieve optimal operating conditions. There are various EOQ models which originate from the classical EOQ model in the literature. In reality, it is not easy to determine parameters of an EOQ model precisely. Fuzzy set theory gives an opportunity to represent the linguistic terms and vagueness in EOQ models. In the literature, various researchers solved different fuzzy versions of EOQ problem. In this study, a fully fuzzy constrained multi-item EOQ model is considered. The parameters of the problem are defined as triangular fuzzy numbers. The fuzzy constrained multi-item EOQ problem is tried to be solved directly by employing four different fuzzy ranking functions and Particle Swarm Optimization (PSO) algorithm. One of the primary objectives of this study is to show that fuzzy mathematical programming models can also be solved directly by employing fuzzy ranking functions and meta-heuristic algorithms. Results obtained from both approaches (direct approach and transformation approach) are also reported in the paper.