In cloud computing, the most important challenge is to enforce proper utilization of physical resources. To accomplish the mentioned challenge, the cloud providers need to take care of optimal mapping of virtual machines to a set of physical machines. In this paper, the authors address the mapping problem as a multi-objective virtual machine placement problem (VMP) and propose to apply multi-objective fuzzy ant colony optimization (F-ACO) technique for optimal placing of virtual machines in the physical servers. VMP-F-ACO is a combination of fuzzy logic and ACO, where we use fuzzy transition probability rule to simulate the behaviour of the ants and the authors apply the same for virtual machine placement problem. The results of fuzzy ACO techniques are compared with five variants of classical ACO, three bin packing heuristics and two evolutionary algorithms. The results show that the fuzzy ACO techniques are better than the other optimization and heuristic techniques considered.