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In this paper, for multiobjective block angular 0-1 programming problems, fuzzy parameters are introduced into them to consider the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process. To begin with, multiobjective block angular 0-1 programming problems with fuzzy parameters and the concept of their solutions are defined. Then, in order to take advantage of the special structure of problems, an interactive method through a genetic algorithm with decomposition procedures is proposed and explained in detail. Finally, both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments.