For a multi-objective optimal design problem

usually some effective solutions can be obtained by the conventional methods.To find out the most effective solution from the effective solutions

the fuzzy closeness degree method is introduced into the multi-objective optimal design.Taking the minimization of the tooth crown of a worm wheel

the maximization of transmission efficiency and the minimization of the distance from the center as objectives

the mathematical model for the multi-objective optimal design of worm transmission is established on the condition that the worm wheel and the worm transmission meet the requirements for load

strength and others.The improved genetic algorithm is utilized to seek the ideal solution and some effective solutions of the multi-objective optimal design of worm transmission.The normal fuzzy distribution is used to convert the ideal solution and some effective solutions into fuzzy subsets over the space of objective function values.The fuzzy closeness degree method is used to order the efficient solutions according to the performance and determine the optimal solution

the best effective solution which is closest to the ideal one from the effective solutions.The process and result verify the validity and feasibility of the method presented.