The crisis early warning of the quality of supply chain based on rough set & feature weighted support vector machine

A Rough Set&Feature Weighted Support Vector Machine(RS-FWSVM) model is proposed for the quality of supply chain crisis early-warning,which aims at some problems of the quality of supply chain. This model combines the advantages of the RS and FWSVM,which can get classification per-formances by changing the weights of different linear functions in the feature space. Application process of this model to the crisis early warning of SCQ is researched, which can help enable chain enterprises to identify crises in the process of operations and to predict possible crises.


Introduction
The complicated structure and the global extension of the supply chain have exacerbated the chain instability, not only the supply chain faces more and more risks, but also the supply chain crisis break out repeatedly.All above make the the quality of supply chain crisis early-warning management become an extremely important subject.So enterprises must realize that it is very important to adopt the early-warning management of the crisis of the quality of supply chain,do a good job of warning and preventing the crisis in advance, and then take effective measures to avoid that.
In 1993, Japan's famous supplier of semiconductor materials Sumitomo Chemical plant got exploded, which posed a serious threat to the global supply [1].The international financial crisis caused by the U.S.subprime crisis in 2009 putted great pressure on enterprises of our country.In 2015, the explosions at Tianjin Port brought the huge impact on global supply chain, which leaded to the electronics industry supply disruptions.
Frequent crisis shows to enterprises that the quality of supply chain crisis is needed.The quality of supply chain crisis early-warning is one of the important components of supply chain management.
The capability of fault-tolerance and generalization of RS is poor and it can deal only with quantized data .But this is an advantage of SVM.However, SVM can not single out redundant knowledge, which is the advantage of RS.So the RS-SVM model is proposed with both advantages and disadvantages of RS and SVM by some scholars.
Y. L.Wuġ [4], et.al. built logistics risk evaluation model based on RS and SVM.They carried on application study combining with examples by identifying and classifying the risk information set.X.L.Zhangġ [5], et.al. proposed a partner selection model based on RS and SVM.The core point of this model was using rough sets theory to pick out the important attributes, and then SVM was used for customer classification.This method that didn't affect classification performance can reduce the data dimensions and the complexity in classification process.J.F.Wangġ [6], et.al. presented a evaluation model of RS and SVM.They concluded that the accuracy of RS and SVM model in this article would be improved from 98.6% to 100% by comparison with applying the SVM directlyˊ The literatures mentioned above use RS to find out the features of reduced sets by retaining the core attributes to improve the ability of classification of SVM.But the influence of the importance of attributes on the classification failed to be taken into account.But in many cases, features that are not completely relative or even complete-ly irrelative to the problem in the used data, it may affect the classification performances of SVMġ [7].
In order to solve this problem, the Rough Set--Feature Weighted Support Vector Machine (RS-FWSVM)model is put forward So, it is required to impose different weights to different features.
Let S is the information system of RS,and S =(U, A, V, F), , the information quantity [8] of P is Theġ X indicates the base of X, U X i is the probability of the equivalence class X i in U.
The importance of attribute a(a ⊆ A) in A is The SVM that bases on feature weighted kernel function is called FW-SVMġ [8].Feature weighted kernel function P K is defined as ( ) ( ) The P=diag˄W 1 , W 2 , …, W n ˅is the matrix of a linear transformation, also known as feature weighted matrix.Then FWSVM classification model is ( )  The application process of RS-FWSVM in crisis early warning of the quality of supply chain is shown in Fig. 1.Firstly, designing questionnaire according to the index system for the crisis early warning of the quality of supply chain and collecting the data.Secondly, determining the weight of indicators using with the rough set theory and the computation formula of the importance of attribute,and As long as relevant data of the supply chain to be assessed are collected, the crises level of it can be known with the model.If the output is safety, the system will keep monitoring the quality of supply chain, whereas an alarm is raised.Risky supply chain must take action.

The Incentives of the crisis of the quality of supply chain and the evaluation index analysis
The incentives of the crises of the quality of supply chain are the most di-rect reason for supply chain crises.From the source of the crises,which can be grouped into external and internal incentives (Figure 2).
According to the incentives for the crises, relevant references and the investigation in the enterprises ,a set of original evaluation index system C={a 1 ˈa 2 ˈĂˈa m }is designed.

Data collection
This investigation altogether provides questionnaire 110, the actual recovery of 86 copies, of which 84 valid questionnaires, for an effective questionnaire returns-ratio is 76.4%.Data from the questionnaires is collected and analyzed.

Weight determination with rough set theory
Taking data collected in 84 questionnaires as sample, the weights of indicators of the crises of the quality of supply chain is determined by equation 2(see Table 1).

The construction of the crisis early warning of the quality of supply chain based on RS-FWSVM model
A method of multi-class classification based on FWSVM is put forward.Then FWSVM classifiers are used to conduct classification on crisis level of the quality of supply chain.Where I means safety, ɛ means mildly early-warning, III means moderately early-warning and IV means heavy earlywarning.First, Classifier 1 can divide the data into two groups: I IIand III IV, then Classifier 2 sets III and IV apart from each other, at last, Classifier 2 sets I and II apart from each other(see Fig. 3).The LIBSVM software is also used to classify the samples.The information about the FWSVM1and SVM1, as shown in Fig. 4 and Fig. 5.

Figure.4
The parameter information about FWSVM1and SVM1

Figure.5 The prediction of FWSVM1
Similarly, additional information about FWSVM and SVM can be calculated.The predict results suggest that the generalization ability of FWSV is superior to C-SVM.It's forecast accuracy is more accurate and than C-SVM,and the number of support vectors is decreased.This could mean that,by compressing geometric space,it has the performance of distinguishing attribute weight,which can improve it's classification capacity.

An application example on the crisis early warning of the quality of supply chain based on RS-FWSVM
An automobile industry supply chain ,where is marked as A ,and a textile business supply chain, where is marked as B,are selected to make some empirical analysis.Through investigation and researchnand according to RS-FWSVM model , then the crisis levelof the quality of supply chain is determined.
Data and information is obtained through conducting a number of high-level interviews with A and B. The final data of evaluating indexes as shown in table 3. Inputting the data from A and B into FWSVM1 classifier, the output is -1 and 1 respectively, indicating that the crisis level of A is safety or mildly early-warning and B is moderately earlywarning or heavy early-warning.When the data from A fed into the FWSVM3 classifier, the result is 1, so the quality of A's supply chain in the mild warning state.Then inputting the data from B into FWSVM2 classifier, the output is -1, so company B is moderately early-warning.The management personnel of the company A and B confirms that the results are consistent with actual situation , that the method and model has a certain practicality and feasibility.
According to the former research on preventing and controlling the crisis of the quality of the supply chain, A should adopt measures to focus in the incentives, paying close attention to deviate from normal levels of early warning indicators.B should take measure to monitor and prevent crisis, to monitor crisis incentives, and take corresponding measures to reduce crisis level of the quality of the supply chain.
Although the crisis level of the quality of the supply chain of B company is not high, can not rule out the individual indicators in a high position, such as the timely information transfer rate among node enterprises, not strictly inventory control, order disposal failure, training expenditures ratio and other indicators.They should be promptly and efficiently controlled by the preventive measures.Otherwise, it will lead to supply risks and damages the quality of the supply chain.Which will bring a huge economic loss to these supply chain enterprises.B company can establish an information sharing platform with suppliers to strengthen the communication among supply chain members, and heighten operation efficiency.
At the same time, supply chain enterprises can establish the information system to record the root cause of the crisis and propose solutions.We can effectively avoid the occurrence of the supply chain quality crisis by settitng up the mechanism of preventing, pre-alarming pre-controlling of crisis.The crisis can't be avoided but can be controlled.Effective crisis prevention can reduce the possible risks.Positive crisis reaction can minimize the loss the crisis may cause.

Conclusion
RS-FWSVM model is put forward based on the analysis of the advantages and disadvantages of the RS and SVM, and the application flow of this model in the crisis early warning of the quality of the supply chain is studied.The reduced index system of the quality of the supply chain and index weights are obtained based on the rough set,Which simplifying the sample space under the condition of good recognition capability of samples.The improved method takes into account the differences resulting

3Figure 1 .Figure 2 .
Figure 1.The application process of the crises early warning of the quality of supply chain

Figure 3 .
Figure 3. the multi-class classification based on FWSVM.

TABLE 1 .
the weights and means of indicators of the crises of the quality of supply chain

Table 2 .
Table 2 is a comparison table of FWSVM and SVM.Comparison table of FWSVM and SVM.

Table 3 .
The evaluation data of the quality of supply chain