The rapid progress of the intermodal freight transportation in recent years has induced fierce competition among the adjacent hub ports for container transport. This brings increased attention to the evaluation of the port competitive ability. But it is not easy to evaluate the port competitive ability because this belongs to ill-defined system which is composed of ambiguous interacting attributes. Paying attention to this point, this paper deals the competitive ability of container port in Far-East Asia by fuzzy integral evaluation which is adequate to interacting ambiguous attribute problem. For this, the proposed fuzzy evaluation algorithm is applied to the real problem, based on the factors such as cargo volumes, costs, services, infrastructure and geographical sites These are extracted from the precedent study of port competitive ability, etc. The results show that the port evaluation factors come in following order ; services, costs, infrastructure, geographical sites and cargo volumes. There are some interactions(interaction coefficient, ${lambda}=-0.664$ between evaluation attributes. The port competitive ability comes in following order : Singapore, Hongkong, Kobe, Kaoshiung and Busan. According to the sensitivity analysis, the rank between Busan and Kaoshiung changes when ${lambda}=0.7$. From the analysis of the results, we confirmed that the proposed fuzzy evaluation algorithm is very effective in the complex-fuzzy problem which is composed of hierarchical structure with interacting attributes.