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Due to the nondeterministic nature of the business environment of a manufacturing enterprise, it is more appropriate to describe the aggregated production planning by using a fuzzy mathematical programming model. In this paper, a genetics-based inexact approach is proposed to imitate the human decision procedure for production planning. Instead of locating one exact optimal solution, the proposed approach finds a family of inexact solutions within an acceptable level by adopting a mutation operator to move along a weighted gradient direction. Then, a decision maker can select a preferred solution by examining a convex combination of the solutions in the family via the human-computer interaction. Our computational experiments illustrate how the enterprise managers can be more satisfied by this new approach than others.