附录附录1An Improved Rough Set Approach to Design of Gating Scheme for Injection MouldingF. Shi,1 Z. L. Lou,1 J. G. Lu2 and Y. Q. Zhang1 1Department of Plasticity Engineering, Shanghai Jiaotong University, P. R. China; and 2Center of CAD, Nanjing University of Chemical Technology, P. R. ChinaThe gate is one of the most important functional structures in an injection mould, as it has a direct influence on the quality of the injection products. The design of a gating scheme includes the selectionof the types of gate and calculation of the sizes and determination of the location, which depends heavily on prior experience and knowledge and involves a trial-and-error process. Due to the vagueness and uncertainty in the design of a gating scheme, classical rough set theory is not effective. In this paper, a fuzzy rough set model is proposed, which is not based on equivalent relationships but on fuzzy similarity relationships. An inductive learning algorithm based on the fuzzy rough set model (FRILA) is then presented. Compared to decision tree algorithms, the proposed algorithm can generate fewer classification rules; moreover, the generated rules are more concise. Finally, an intelligent prototype system for the design of a gating scheme based on an induced fuzzy knowledge base is developed. An illustrative example proves the effectiveness of the proposed method.Keywords: Fuzzy rough set; Gating scheme; Injection mold; Intelligent design; Knowledge acquisition1. Introduction The manufacturing industry for plastic products has been growing rapidly in recent years, and plastics are used widely to substitute for metals. The injection moulding process is the most popular moulding process for making thermoplastic parts. The feeding system, which is one of the important functional structures, comprises a sprue, a primary runner, a secondary runner and a gate. The molten plastic flows from the machine nozzle through the sprue and runner system and into the cavities through the gate. Acting as the connection between the runner and the cavity, the gate can influence directly the mould venting, the occurrence of jetting, the location of weld lines, and warpage, shrinkage and residual stresses. Hence, the gate design is important for assuring the quality of the mould.The design of a gate includes the selection of the type of gate, calculation of the size and determination of the location. And the design of a gate is based on the experience and knowledge of the designers. The determinations of the location and sizes are made based on a trial-and-error process. In recent years, a feature-modelling environment and intelligent technology have been introduced for gate design. Lee and Kim investigated gate locations using the evaluation criteria of warpage, weld lines and izod impact strength. A local search was used to determine the nodes of the location of the gate 1. Saxena and Irani proposed a frame for a non-manifoldtopology-based environment. A prototype system for gate location design was developed. The criteria for evaluation were based on geometry-related parameters 2. Lin selected the injection location and size of the gate as the major control parameters, and chose the product performance (deformation) as the optimising parameter. Combining the technologies of abductive networks and simulation annealing optimisation algorithms, the optimal model for the location and size of the gate was constructed 3,4. Zhou et al. established a rule set for determining the location of the gate based on analysis of the plastic parts. The location of the gate was determined through reasoning with rules 5. Pandelidis et al. developed a system which can optimise gate location based on the initial gating plans. The system used MOLDFLOW software for flow analysis, and controlled the temperature differential and the number of elements overpacked with an optimisation strategy 6.Deng used ID3 and its modified algorithms to generate the rule set for the selection of the gate types 7. However, there are many fuzzy or vague attributes in the selection of the types, such as the attribute of loss of pressure that has two fuzzy linguistic variables i.e. can be high and must be low. The ID3 algorithms cannot deal with fuzzy or “noise” information efficiently. It is also difficult to control the size of the decision tree extracted by the algorithms and sometimes very large trees are generated, making comprehensibility difficult 7,8.Rough set theory provides a new mathematical approach to vague and uncertain data analysis 9,10. This paper introduces the theory of rough sets for the design of a gating scheme. The selection of the type of gate is based on the theory of rough sets. Considering the limitations of rough sets, this paper proposes an improved approach based on rough set theory for the design of the gating scheme. The improved rough set approach to the scheme design will be given first. A fuzzy rough-set-base