Fuzzy Relational Clustering Based on Knowledge Mesh and its Application

A selection method of knowledge meshes based on fuzzy relational clustering is proposed. Considering the perfection degree, the matching degree among knowledge meshes and the level frame of knowledge mesh, the similarity function is defined. Its properties are proved. The similarity values between knowledge meshes are regarded as clustering data. The fuzzy relational matrix is constructed and decomposed. The knowledge meshes with high membership in each class are regarded as referenced knowledge meshes. Or the knowledge meshes in the class are further chosen according to user’s needs. Finally the example shows that the method is effective.


Introduction
Knowledgeable manufacturing [1] transform all types of advanced manufacturing modes into corresponding knowledge meshes (KMs) [2] and included them in knowledgeable manufacturing system (KMS), which selects and uses the most appropriate combination of the modes or the best one when necessary. KMS is characterized with self-adaption, self-learning, self-evolution, self-reconfiguration, self-training and self-maintenance, which are named 'six-self-characteristic'. The selection of KM is the first facing problem in the application of most KMS's six-self-characteristic technologies. With the consummate of six-self-characteristic technologies, more and more KMs, which must exist the same or similar parts among these KMs, are stored in KM base. When user search KM in KM base, it is sometimes difficult to choice, especially for the low-quality user who can not clearly describe specific needs. If system can automatically give some representative referenced KMs, it can help user clear needs and quickly find the required KM.
Clustering is an important tool for data analysis, unsupervised learning, data graining and information compression. The fuzzy clustering, such as fuzzy c-means clustering(FCM) [3] , supervised fuzzy clustering(SFC) [4] , fuzzy relational clustering(FRC) [5] , fuzzy kernel clustering with outliers(FKCO) [6] , allow partial membership by fuzzy concept and make the result of clustering more conform practical situation. But it isn't reported about using clustering to solve the selection of KMs in KMS. Some literatures have the similar ideas. Shen and Chen [7] discovery the generic model by fuzzy clustering in the level of particular reference model for knowledge management in enterprise modeling. Then constructing the corresponding relationship between the new model object and generic model, and predicting the new mode, solve the retrieval problem. But the clustering objects are reference process models and the clustering data gave by domain experts are the results of comparing each model, which entirely depend on experts' experience. But each KM represents a real manufacturing system which contains a lot of data and the inherent information. It is different from the previous clustering objects. In addition, the clustering methods through comparing the relational degree between the classification samples and standard samples aren't suitable for the clustering of KMs, because the corresponding feature space is difficult to build, and the high-dimensional number and the limited sample set make it difficult to describe the construction of data.
This paper proposes a selection method of KMs based on fuzzy relational clustering whose clustering data are the similarity degree. Construct the sample-class relation by decomposing fuzzy relation. The KMs having high membership in each class have reference value. The comparison of them and target KM narrow the scope of user's choice. User only select the KMs in certain class. . It is remarkable that definition 1 reflect the quantity of similarity in KM's function. When user needs certain functions, the KM satisfying user's needs is more than just having those functions in practical situation. User may hope to improve functions to meet the further development. Or user only needs the basic functions to save the cost. In addition, we also know that the representation of KP is the same but the corresponding contents in practical system may vary a little. This kind of difference between KMs is taken as the perfection degree of KM for comparison of their "quality". Using a fuzzy set for the definition is a more practical choice. And the perfection degree of father KP's function is gotten by child KP's. p , the more perfect its function. According to definition 2, there is one-to-one correspondence between each KM and its fuzzy set µ . It is assumed that each KM corresponds to one fuzzy vector µ , . Definition 1 and definition 2 reflect the similariy from two aspects of functional quality and quantity. Though the matching degree and perfection degree of two KM are completely the same, their corresponding structures of KM may differ. The level number of KP can reflect the KM's structure. Introduce it into the definition of KM's similarity. So taking quality, quantity and structure into account, the similarity degree is defined. (1) is the level number and functional perfection degree of the KPs relating to those functions. } , min{ It is need to explain that the level number is increased from the root KP, i.e. the level number of father KP is less than that of child KP. If the KP having the same function as KP . When KM V and W have the identical function, and the functional perfection degree and level number of KP corresponding with those functions are also the same, 1 ) , . When KMV andW don't have any same function, 0 ) ,

Selection method of KMs
Each KM in KM base is affiliated with a class by the above method and maximum membership principle. The KMs having the highest membership in class are regarded as referenced KM for user. But these KMs having the highest membership, which can reduce the range of choice, is not necessarily the best choice for the high-quality user. Suppose that the target KM W satisfy user's needs. Modify formula (1) and get formula (2)  Simplify the calculation process of fuzzy relational matrix because of the lack of space. Transform all KMs into KMs having the same LKPs by regarding the lacking LKPs as KPs of zero perfection degree. Then make some simplifications and assumptions for formula (1). Let . If user is the high-quality user, his target KM is W , whose level number is the same as that of existing KMs' LKP. Then formula (2)    . So 6 W is the best selection for user.

Conclusion
With the promotion of KMS technologies, the selection of KM must be faced for user. How to select some representative referenced KMs for user by the convenient and quick way, some try are made in this paper. Forming a reasonable similarity model is the precondition of clustering for KMs. The similarity model from the quality, quantity and structure aspects can completely reflect on the similarity among KMs. It makes the original clustering space convert to that constituted by similarity. It overcomes the sparse distribution of high-dimensional sample sets. The KMs having high membership help user narrow the choice scope. It makes the relations of KMs more clear. It also helps user clear needs and make the right choice.   The