STUDY AND APPLICATION OF GREY ENTROPY WEIGHT DECISION MAKING IN RISK MANAGEMENT

In traditional risk evaluation, the weight of a risk index is given in advance, so it lacks objectivity. Using weights and properties generated by entropy concepts, including the idea of information entropy, the comprehensive weight, which can be combined with entropy weight, is calculated. A grey evaluation model of a project risk evaluation index based on comprehensive entropy weight is built. Further, we present empirical research on a real project, which indicates that this approach calculates easily, gives weight scientifically, and provides evaluation accurately


INTRODUCTION
Risk is a kind of measurement that measures the probability that the project objectives can not be achieved within the limit of the specified cost, progress, and technology.It means both the probability that specific targets can not be achieved and the consequences of this kind of failure (Song, Ran, &Li, 2003).Project risks include those technologies based on, planning, security, costs, and progress.Because of the complexity of these risks, procedures, methods, and techniques for risk management tend to be complex and run through the whole process of the project.Risk assessment is a very important part of project risk management.It studies the development process and the key risk areas and then identifies and records the related risks.Once the information above is obtained, we are able to rate these risk incidents by project criteria, in other words, to make an overall assessment.Risk assessment is a complex issue, because a project itself has great uncertainty and often lacks historical data and comparison with similar objects.Many factors can not be quantitatively evaluated objectively but can only be qualitative assessed.Delphi methods are often used, leading to poor objectivity and inaccurate risk assessment index weights.Risk factors for the entire project tend to be in a "some are known, and some are unknown" state, meaning grey.In the 1990s, the concept of grey-associated entropy was discovered by Zhang Qishan.Some scholars have conducted indepth research of it in theory and applied it to various areas (Zhang, Guo, & Deng, 1996;Zhang, 2002;Luo & Liu, 2004;Li, 2005;Guo, 2005;Xie & Zhong, 2002).In this paper, we use the concept of information entropy and the decision-making method of the grey system; the grey entropy weight method for risk assessment is proposed, and a grey entropy weight model for risk assessment, which has a broad adaptability, is built (Cai, Wang, & Li, 2003).

THE ENTROPIES AND ENTROPY WEIGHTS OF RISK INDICATORS
The concept of entropy originated in thermodynamics.It describes the irreversible phenomenon of the movement of particles, such as molecules, atoms, or ions.Shannon later introduced it into information theory, and now it is widely used in engineering technology, socio-economics, and other fields.According to the basic principles of information theory, information is a measure of the degree of system order, while entropy is a measure of the degree of disorder.They have equal absolute value but opposite signs (Qiu, 2002;Mao, 2004).In this paper, an entropy method is used in the assessment and sorting of risk indicators, and the information contained in properties of indicators is fully used.For an index x j , its information entropy E j is as follows.
Data Science Journal, Volume 7, 4 November 2008 where k = 1/lnn and p is the probability mass function.
The assumption is made that when p ij = 0, p ij ln p ij For some index property j, if different evaluation factors are very close in this property value, according to (1), we can know that the larger the entropy of j, the less obvious the role of j.If different evaluation factors are the same for this property value, the entropy value will reach the maximum value of 1, which means the indicator j is of no importance in the comparison of plans.Therefore, the larger the difference among these indicator property values, the more information that is provided, and the more important the indicator is.

Definition 1
The entropy weight of the indicator j . (2) Obviously, j ω meets 0 According to (2), the smaller the indicator entropy, the larger the variation of the indicator value is, the more information is provided, and the bigger the role it plays in a comprehensive evaluation, and the larger its weight is.On the contrary, the larger the indicator entropy, the smaller the variation of the indicator value is, and the less information is provided, consequently the smaller the role it plays in the comprehensive evaluation, and the smaller its weight is.In extreme situations, if the entropy of one indicator is the maximum, E max ' j w = 1, it means that for each object, the values of the indicator will be same, so the indicator is no use for the evaluation and can be removed completely.

The comprehensive entropy of the indicator
Weight is the measure of the importance of goals (indicators), which is method of measuring the importance of goals.This concept of weight includes and reflects the following three factors: (1) the importance policy makers place on the goal; (2) the variation of the goal property values; and (3) the reliability of property values (Yue & Zhang, 2004).
Entropy measures the amount of useful information in available data.Evaluation of entropy indicators and entropy weights show the amount of useful information and extent of differences in property values.If policy-makers have given an indicator j a priori weight (or given by industry experts based on experience) to show the extent importance they lay on the goals, we can combine the priori weight with the entropy weight to get the comprehensive posterior weight, as follows.( ) means the property values of i x .When the objective function is ( )  , the property value of each project can be listed as attribute value tables or attribute matrices . To give the actual value of the property in evaluating a project, we need the normalization of property value table above.Then we get: Data Science Journal, Volume 7, 4 November 2008

THE GREY EVALUATION BASED ON THE GREY ENTROPY
Definition 2 Suppose the number of cluster objects is n, the cluster indicators m, and different grey classes s.
For indicator j V , the total evaluation coefficient for each grey class j X meets the criteria that .
(2) The grey evaluation weight vector and matrix are calculated.For the grey evaluation weight of the evaluation indicator j V in grey class k for all evaluators, the evaluation matrix of indicator for each grey class is 1 2 ( , , , ) .
(3) The grey evaluation matrix of all indicators is evaluated.The matrix is evaluated by the following: (4) The risk evaluation index V is comprehensively evaluated.The index is calculated by: (5) The risk evaluation index V is evaluated by the grey method.The index is evaluated by: Data Science Journal, Volume 7, 4 November 2008

CASE STUDY
The hierarchical structure of risk assessment and the structure of risk indicators are shown in Figure 5. Project risk indicators on the first levels cover technical, financial, planning, security, and market risks.

The comprehensive evaluation of technical risk entropy weight
Suppose a technical risk observation matrix is as follows.
According to the normalization matrix above, using formulas (1), (2), and (3), we can calculate the entropy and its weight for each indicator for technical risks.In Table 1 we add prior weights of importance that policy makes place on the goals in column 4 and then use the formula (4) to calculate the comprehensive entropy.7 7 9 7 7 3 7 5 7 7 7 3 7 5 7 7 7 3 7 5 7 7 5 3 7 5 5 5 5 3 5 3 5 5 5 3 5 3 3 5 5 1 5 3 3 5 5 1 The risk indicators have five grey classes: A, B, C, D, and E. The whitenization weight functions given by the experts, taking into account that every indicator is normalized and the whitenization weight functions are only different in levels, meaning that they are the same in other property values, which simplifies the problem, are as follows: 1 [0,9, , ] Applying steps (1) and ( 2), we get r 1 = (0.2614, 0.3764, 0.3011, 0.0612, 0.0000) Similarly, we get r 2 , r 3 , r 4 , r 5 , and r 6 .Applying step (3), we get Step (4) gives the comprehensive evaluation of the technical risk as: We determine that k = 2 and conclude the technical risks have a higher value, that is, B-class.Similarly we can do a comprehensive evaluation of other risks, as shown in Table 2.
From the calculation above, we know that among the project risk evaluation indicators on level one, the plan risks are the highest both for the impact and on the risk levels.Because the plan risks result from improper decisions made by people, they bring to the project both the greatest risk and risk on the highest level.The impact of the project risk levels rank as follows.

Plan risks > Technical risks > Financial risks > Market risks > Security risks
The levels of risk rank as follows.
So formula (3) can calculate the comprehensive weight of an indicator, and formula (2) shows how to obtain j ω .It contains and reflects the three factors that should be reflected by weight in a comprehensive and reasonable way.According to the indicator property value table ' ( )ij n m D z × =and formula (3), we obtain the comprehensive weight of each indicator j w .The comprehensive entropy weight matrix for each indicator is as follows.Supposing there is a multi-attribute decision-making problem MA(m, n), 1, 2,

Definition 3
According to the indicator j value of n objects, these objects are divided into grey clusters s which are called indicator subclasses j.The whitenization weight function of indicator j subclass k is recorded as k j f (•) Definition 4 The whitenization weight function k j f of indicator j subclass k shown in Figure 1 is the typical whitenization weight function.(1), (

Figure 2 .
Figure 1.The typical whitenization weight function

Figure 3 .
Figure 3.The moderate measure whitenization weight function

Figure 4 .
Figure 4.The upper measure whitenization weight function

Figure 5 .
Figure 5.The architecture of risk indicators in one project Taking technical risks as an example, the factors impacting technical risks are uncertainty of the outcome of research and development v 1 , the possibility that the technology cannot meet the requirements v 2 , the possibility that production conditions cannot meet the requirements v 3 , the uncertainty of the life of the technology v 4 , the uncertainty of of technological change happening v 5 , and the uncertainty involved in the circumstances of the application v 6 .
Table1.Entropy, entropy weight and comprehensive entropy weight of risk index

Table 2 .
Results of the evaluation of risk indices