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(C). Generally there is not only a reduction. The intersection between reductions is called “core”, and marks as Ccore (C). 3. Case retrieval Case retrieval based on problems description is to find out the most similar case for the currently conformable problems from case database by using corresponding case information. It is regarded as the reference case of meeting design requirement [4]. The retrieval is the process of searching and matching model is shown in Figure 1. Figure 1 Case Retrieval and Matching Model 3.1. Stamping die case representation Die design case representation is the foundation of the whole scheme design. Its aim is to record the existent successful design cases and make it to be a kind of data structure which can be recognized and used by computer. A die design case expresses a series of the complicated content, which could include product function, structure and other products attributes information, materials, process information and also design specification, design experience and other inductive knowledge, as well as design procedural knowledge. For this kind of complicated structure, design cases mostly include following 3 strategies at present [5]: (1) Hierarchical representation A design case can be decomposed into different levels to express. It is a strategy of CBR design type, which is used frequently. (2) Co-representation in different points A product’s design can not only co-express in different points but also map multiple design case. (3) Taking multimedia technology Multimedia technology makes a case which includes possibly different data record formats.
Consequently, it makes a design case which includes different points and types information at same time. The idiographic methods which are adopted by design case mainly cover frame, semantic network, and object oriented representation, etc [6]. Frame and object oriented methods reflect hierarchical description of knowledge in a certain degree. They are suitable for hierarchical design case representation relatively. The class of object oriented representation succeeds to present hierarchical relation from general to specific one. The attribute definition in class presents the relationship between objects and attributes, but it cannot illuminate the relationship between whole and part. This paper adopts a hierarchical object oriented method to express design case. 3.2. Case retrieval strategy based on rough set theory Die deign includes abundant information. Because of the vast and complex database, there need adopt a certain retrieval strategy to organize and manage case database orderly. Common case retrieval methods mainly contain the nearest neighbor strategy, the inductive reasoning strategy, the knowledge index strategy, and the template retrieval strategy. But the information of every design has not the same influence for case attributes. Thus we only consider those key characteristic attributes which are helpful for distinguishing cases. This paper adopts two-level case retrieval strategy [7]. The first level takes the inductive reasoning strategy, and takes advantage of rough set theory to analyze and process case base. There will take a discrete method based on classification clustering method and decision attribute support degree which deals with quantitative problems in attribute table, confirms the important degree of each characteristic attribute, and extracts key feather attributes of case to establish retrieval. The second level takes the nearest neighbor strategy [8], and searches out the proximate case of design problems. (1) Decision table and decision attribute In rough set theory, decision table is a special and important knowledge representation system. Most decision problems could be represented by decision table. Decision table is also a kind of classification, whose decision attribute is equal to the class attribute of classification. What deals with decision table is mainly reducing and minimizing. Reduction contains attribute set reduction, attribute value reduction and redundant rules deletion. Firstly, die case information is represented as attribute decision table. Let knowledge representation system of rough set theory be S=（U，A）. U is a nonempty finite set of objects included all cases in case base. A is a nonempty finite set of attributes included condition attribute set C and decision attribute set D, C∪D=A,C∩D= . A certain attribute a∈A in C, Va is the range of attribute a. Attributes of die case usually include qualitative and quantitative attributes, but rough set theory cannot directly process quantitative attribute [9]. So quantitative problems must be discretized firstly, and then they will become qualitative problems. We can use rough set theory to process them at this moment. (2) Discretization The key of discretization is to pide attribute range into appropriate discrete area. Values in decision table must be represented by discrete data when decision tableis processed by rough set theory. If the range of some condition attributes or decision attributes are continuous values (e.g. floating point numbers), they must be discretized before processing. Some discrete data also need to be integrated (abstracted) into higher abstract level discrete values. According to the characteristics of rough set theory, this paper adopts an attribute discretization algorithm. This algorithm will be mainly pided into two steps to process the quantitative attribute in decision table [10]: ① Adopt the hierarchical clustering to confirm respectively discrete ranges of quantitative attributes; ② Adopt the maximum support degree of the discretized decision table. The discrete ranges of the quantitative attributes are selected to keep relatively strong classification ability. Attribute discretization algorithm processes respectively the decision table because of the different effects of every condition attributes.
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