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Both fuzzy processing time and fuzzy due date are considered following a study of the fuzzy job shop scheduling problem, in order to achieve the object of minimum fuzzy completed time and maximum average degree of satisfaction. Fuzzy processing time is expressed with the triangle fuzzy variable, and fuzzy due date is expressed with the trapezoid fuzzy variable. The optimization genetic algorithm is proposed to solve the optimal scheduling sequence. Researches are made in coding, decoding, crossover and mutation etc. Finally, the experimental results and conclusion are given.