INTRODUCTION
As an important part of modern decision making science, the multiattribute decision making is mainly used to solve the problem of limited plan decision making under the condition of multiple attributes and its theories and methods are widely applied in social, economic, military and management fields (Mundaca and Neij, 2009; Willems, 2009). Deng Julong, the theoretical founder of grey system first proposed the concept of grey target and deeply researched the grey target theory and a lot of experts and scholars also have engaged in the research on grey target decision making. With the increasing complication of the decision making problems, the uncertainty in problem evaluation also has been increasing and the multiattribute decision making research on the uncertain decision making background (like interval grey number) is becoming a hot research topic. For example, Ho et al. (2010) proposed the literature of the multicriteria decision making approaches for supplier evaluation and selection. Wu et al. (2005) presented an alternative evaluation procedure to help retailers, especially hyper marketers, make a location decision by using the grey multiobjective decision method. Eshlaghy and Razi (2015) presented an integrated framework for project selection and project management approach using greybased kmeans and genetic algorithms. The proposed approach of this study first cluster different projects based on kmeans algorithm and then ranks R and D projects by grey relational analysis model. Wang et al. (2009) considered the influence of correlation between indicators, different dimension and importance difference on decision making effect, employed weighted Mahalanobis distance to improve the traditional grey target decision making method, thus avoiding the influence of correlation between decision making indicators, different dimension and importance difference on the decision making effect. Liang et al. (2012) aimed at the uncertainty and multiple time point of multiattribute decision making, proposed the multitime point multiattribute grey decision making model based on interval number. Luo and Wang (2012) based on the grey system theory and methods, the greytarget decisionmaking problem is discussed, in which the attribute values are grey numbers and the maximum probability of the value of grey number is known. Liu et al. (2013a) proposed a novel multiattribute grey target decision model and demonstrated with a practical case study. Dai and Li (2014) aimed at the fact that the class 1 attribute values, attribute weight and decision maker weight are all the group decision making problem of interval grey number, introduced the concept of positive and negative clouts and group deviation approaching degree and proposed the group decision making method of grey multiattribute deviation approaching degree. Jianyou and Hua (2006) constructed a bonus and forfeit operator which can amplify the indicator difference in case of indicator nondimensionalization changing and established the weighted grey target decision making model on this basis. Yan and Liu (2014) considered the influence of decision maker’s expectancy grey target on the group decision making, proposed a group grey target decision making method based on the prospect theory. In this method, the expectancy grey target used as the reference point to define the prospect value function and the linear transformation operator of bonus and forfeit is used for normalized treatment of prospect value, which can fully reflect whether the evaluation value hits the target. The above researches provide some thoughts to decision the grey target decision making problem but it can also found that there are fewer researchers on the grey target decision making in which the decision making information is of interval grey number form and the attribute weight is uncertain, as such, a corresponding grey target decision making model is proposed in this study to meet the demand of such decision making.
There are n decision making plans in many attribute decision making problems, which form a decision making plan set A = {A_{1}, A_{2},..., A_{n}} and m evaluation indicators (attributes) which form an attribute set C = {C_{1}, C_{2},...,C_{m}}. The decision making information is not a specific accurate number but an interval grey number, the attribute value of plan A_{i} to attribute C_{j} is where, , i = 1, 2,..., n; j=1,2,…, m then the effect sample matrix X of plan set A to attribute set C is:
The matrix above can be converted into:
MATERIALS AND METHODS
Preliminaries
Grey target decision making: In 1982, the Chinese scholar Deng Julong established the grey system theory. Later, this theory was widely applied and generated a series of grey decision making methods, such as grey target decision making. Grey target decision making is the application and reflection of nonuniqueness principle in grey system theory in the decision making theory and its basic idea is to find out the standard indicator sequence most approach to the target value in a group of indicator sequences consisting of decision target and it is called the clout of grey target. The indicator sequence constituted by other decision making targets form a grey target jointly with the clout and the grey correlation between them and the clout is called approaching degree (Deng, 2002). The evaluation and ranking of the decision making target are mainly based on the size of approaching degree.
Distance of interval grey number: In the grey system theory, the number of which only the approximate range is known but the accurate value is known is called grey number and grey number is the basic unit of the grey system. The grey number with both lower bound and upper bound is called grey number, recorded as .
Definition 1: Let that there are two interval grey numbers and , k is a positive real number, then the operation rule is (Zeng et al., 2013):
Definition 2: Let that there are two interval grey numbers and , then the distance between the interval grey numbers a⊗ and b⊗ is (Song et al., 2010):
Multiattribute grey targe decision making model
Establishment of multiattribute grey target decision making model
Normalized treatment of decisionmaking matrix: As each attribute value in the decision making matrix has different weighing criteria and measuring units, for convenience of unified treatment, it is possible to generate the bonus and forfeit [1, 1] linear transformation operator for dimensionless treatment of attribute with Vague set and set pair analysis theory and by reference to the idea of bonus and forfeit, so as to obtain a normalized decision making matrix.
Let:
i = 1, 2,..., n; j = 1, 2, ...,m 
(2) 
If it is efficiency attribute, then:
If it is cost efficiency, then:
The converted matrix is:
In this way, the obtained might be less than 1 and might be more than 1. Therefore, the following conversion matrix can be used for normalize treatment of matrix D, so as to obtain the normalized decision making matrix:
Where:
The conversion above is called the linear transformation operator of the interval number [1, 1] (Liu et al., 2013b).
In this way, and each attribute can be subject to the above transformation to obtain the consistency effect measure matrix of plan A_{i} to the effect sample value of attribute C_{j}:
Grey target decision making of positive and negative clouts
Definition 3:
j = 1, 2, ...,m and the corresponding decision value is recorded as and:
is called the optimal effect vector of the grey target decision making, called the positive clout of the interval number.
Definition 4:
j = 1, 2,...m and the corresponding decision making value is recorded as and:
is called the worst effect vector of grey target decision making, called the negative clout of the interval number.
Wherein, the attribute weight is w = (w_{1}, w_{2},...,w_{m}) and
Definition 5:
is called the positive offtarget distance of effect vector z_{i}.
is called the negative offtarget distance of effect vector z_{i}.
Definition 6:
is called the spacing of positive and negative clouts.
As defined in literature (Luo, 2013), the distances ε_{i}^{+}, ε_{i}‾, ε_{i}^{0} fall on the same straight line or form a triangle. Therefore, it is possible to obtain the optimal decision making of the event by using size of projection of the positive offtarget distance on the connection between the positive and negative clouts, i.e., the larger the projection is, the more excellent the corresponding decision making will be. Let that the included angle between the positive offtarget distance and positive and negative connection is θ, according to the cosine law:
Both the positive offtarget distance ε_{i}^{+} and negative offtarget distance ε_{i}‾ are vectors, in consideration of the projection of offtarget distance on the connection between positive and negative clouts, the comprehensive offtarget distance ε_{i} is:
The comprehensive offtarget distance comprehensively considers the positive and negative clouts, the offtarget distance is used as a vector, so that the decisionmaking information is more scientific and reasonable.
Determination of attribute weight: If the attribute weight sequence w = w_{1}, w_{2},...,w_{m} is unknown, the sequence is grey connotation sequence and the grey entropy can be defined:
According to the principle of maximum entropy, it is required to adjust w_{j} (j = 1, 2, ..., m) to reduce the uncertainty of w = w_{1}, w_{2},...,w_{m}, i.e., to promote the maximization of H⊗(w). At the same time, the weight w_{j} (j = 1, 2, ..., m) is adjusted to minimize the overall comprehensive offtarget distance and in this way, the following multiobjective optimal model can be established:
To calculate the multiobjective optimal model, according to the fair competitiveness of each plan, the multiobjective optimal model above can be transformed into a singleobjective optimal model:
where, 0<μ<1. In consideration of the fair competitiveness of the optimal objective function, generally μ = 0.5. The model is calculated through Visual C++ programming and the attribute weight sequence w = (w_{1}, w_{2},..., w_{m}) is obtained. Finally, substituting it into formula 14, it is possible to get the comprehensive offtarget distance ε_{i}. The alternative plans are sequenced according to the size of ε_{i} value, the smaller ε_{i} is and the more excellent the corresponding plan will be.
Steps of multiattribute grey target decision making: As stated above, the specific steps of the interval number multiattribute grey target decision making based on positive and negative clouts are as follows:
Step 1: 
Construct the effect sample matrix according to the multiattribute decision making problem and [1, 1] interval number linear transformation operator is used to convert the effect sample matrix into a normalized decision making matrix 
Step 2: 
Use formulas 9 and 10 to respectively determine the positive and negative clouts of interval of grey target decision making 
Step 3: 
Use formulas 11 and 12 to respectively determine the positive and negative offtarget distances of the effect vector z_{i} and get the spacing of positive and negative targets according to formula 13 
Step 4: 
Through the singleobjective optimization model displayed in formula 17, apply software programming method to calculate this model and obtain the attribute weight sequence w = (w_{1}, w_{2},..., w_{m}) 
Step 5: 
Use formula 14 to determine the comprehensive offtarget distance ε_{i} and rank each alternative plan according to the size of ε_{i} value 
RESULTS AND DISCUSSION
Application example: A sophisticated product manufacturing enterprise decides to have technical transformation to the original leading products, now there are 4 transformation plan (A_{1}, A_{2}, A_{3}, A_{4}), with 4 major assessment attributes, cost C_{1}, reliability C_{2}, product life C_{3} and risk loss value C_{4}, where C_{1} and C_{4} belong to cost attributes, C_{2} and C_{3} belongs to efficiency attribute. The decision maker gives the criteria weight space of incompletely certain information form: 0.2≤w_{1}≤0.4, 0.25≤w_{2}≤0.3, 0.15≤w_{3} ≤0.25, 0.3≤w_{4}≤0.4 and
The optimal transformation plan is determined.
Upon investigation statistics, the relevant parameter assessment of this enterprise in a year is obtained and the data obtained are as shown in Table 1 after sorting.
According to the [1, 1] interval number linear transformation operator, the interval number effect sample matrix is converted into the dimensionless decision making matrix i.e., the normalized decision making matrix, as shown in Table 2.
Respectively calculate the interval number positive and negative clouts of grey target decision making with formulas 9 and 10:
Determine the positive and negative offtarget distances of the effect vector z_{i} with formulas 11 and 12.
The positive offtarget distance is:
Table 1:  Interval number effect sample matrix 

Table 2:  Normalized decision making matrix 

The negative offtarget distance is:
The spacing between positive and negative clouts is:
Through the singleobjective optimization model determined in formula 17, apply the software programming to calculate this model and get the attribute weight.
Use formula 14 to determine the comprehensive offtarget distance ε_{i} and rank each alternative plan according to the ε_{i} value.
In this way, ε_{1}<ε_{2}<ε_{3}<ε_{4}, so the ranking result of each plan is ε_{1},≻ε_{2}≻ε_{3}≻ε_{4}. Upon calculation and analysis, this result is consistent with the conclusion in literature (Liu et al., 2013a) proving that this method is feasible and effective.
CONCLUSION
The grey target decision making is one of the important methods to solve the multiattribute decision making problem. Aimed at the complexity and uncertainty of the actual decision making environment, an interval number multiattribute grey target decision making method based on positive and negative clouts is proposed in this study. In this method, the interval number linear transformation operator is used for normalized treatment of multiattribute grey target decision making value and the concepts of positive and negative clouts and positive and negative offtarget distances of grey target decision making are introduced and on this basis, in combination with the spatial analysis, the calculation method of the comprehensive offtarget distance is proposed; at the same time, each plan is ranked according to the comprehensive offtarget distance. A practical decision making method is proposed to solve the grey target decision making problem in which the decision making information is an interval grey number and the feasibility and effectiveness of the model constructed are verified through example analysis.
ACKNOWLEDGMENTS
This study was supported by the Scientific Research Fund of Hunan Provincial Education Department (No. 14C0184) by the Hunan Province Philosophy and Social Science Foundation (No. 14YBA065). Supported by the construct program of the key discipline in Hunan province.