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In this paper, decision making problems arising from optimal operation planning for hot parts scheduling of gas turbines of thermal power plants are formulated as multiobjective 0-1 integer programming problems. By considering the imprecise or fuzzy nature of human judgments, the fuzzy goals of the decision maker (DM) for each of the objective functions are introduced. Then approximate solutions for the formulated problems are derived through the genetic algorithms for solving general combinatorial optimization problems. In order to decrease the difficulties for the determination of not only appropriate parameter values in the genetic algorithms but also membership functions representing the fuzzy goals of the DM, simple genetic algorithms are revised and auto-tuning method of the membership functions are proposed. On the basis of the proposed methods, an interactive decision support system is developed on the workstation and the feasibility and efficiency of both the proposed methods and the corresponding decision support system are demonstrated via numerical examples.