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This paper puts forward a grey situation group decision-making method on the basis of prospect theory, in view of the grey situation group decision-making problems that decisions are often made by multiple decision experts and those experts have risk preferences. The method takes the positive and negative ideal situation distance as reference points, defines positive and negative prospect value function, and introduces decision experts’ risk preference into grey situation decision-making to make the final decision be more in line with decision experts’ psychological behavior. Based on TOPSIS method, this paper determines the weight of each decision expert, sets up comprehensive prospect value matrix for decision experts’ evaluation, and finally determines the optimal situation. At last, this paper verifies the effectiveness and feasibility of the method by means of a specific example.

Grey situation decision is a method to choose the decision with optimal effect from multiple decisions and objectives, with the prerequisite that decision information should have grey elements [

In the aspect of improvement for grey situation model, [

In recent years, the grey situation model has made a lot of achievements in application field too. Reference [

Throughout relevant researches on grey situation decision-making, it is found that the situation that multiple decision experts participate in decision-making and those decision experts have risk preference is rarely considered. However, in practical decision-making process, especially in the case that the scheme set has numerous qualitative indexes, multiple decision experts should participate in decision-making and inevitably their subjective preference will influence the final decision results. Therefore, this paper makes use of prospect theory [

In a grey situation group decision-making problem, the event set is denoted as

The effect sample value matrix of the

Given the corresponding value of

Given the corresponding value of

Given the value measure of the

Assuming that the effect measure of the situation

However, the situation distance of alternatives cannot be worse than that of negative ideal scheme. That is to say, if the situation distance of negative ideal is taken as reference point, its value function will become

If the situation distance of positive ideal is taken as reference point, the situation distance of alternatives will be worse than that of positive ideal scheme. At this time, psychological perception of decision expert is risks. The value function is

However, the situation distance of alternatives cannot be superior to that of positive ideal scheme. That is to say, if the situation distance of positive ideal is taken as reference point, its value function will become

Assuming that the effect measure of the situation

However, the situation distance of alternatives cannot be superior to that of positive ideal scheme. That is to say, if the situation distance of positive ideal is taken as reference point, its value function will become

If the situation distance of negative ideal is taken as reference point, the situation distance of alternatives will be worse than that of positive ideal scheme. At this time, psychological perception of decision expert is risks. The value function is

However, the situation distance of alternatives cannot be worse than that of negative ideal scheme. That is to say, if the situation distance of negative ideal is taken as reference point, its value function will become

No matter in the case of efficiency index or cost index, both

No matter in the case of efficiency index or cost index, the prospect value by taking positive and negative ideal situation distance as different reference points is positive value of gains and negative value of risks in decision experts’ psychological perception. In order to eliminate the influences of dimension to calculation results, the prospect value gotten from positive and negative ideal situation as different reference points is normalized as follows:

Normalized prospect value

Consider the following

According to the value function given by [

Therefore, the comprehensive prospect based on positive and negative ideal situation distance as two reference points is the sum of positive prospect value taking negative ideal situation distance as reference point and negative prospect value taking positive ideal situation distance as reference point.

According to [

Assume that

Assume that

Given

In order to avoid one-sidedness of evaluation results, make full use of decision information and keep the consistency of decision results; the greatest weight is given to the decision expert whose matrix is closest with the optimal prospect value and is the most far away from the worst prospect value matrix, and vice versa. This paper takes the optimal prospect value matrix as the optimal situation and the worst prospect value matrix as the worst situation and calculates the prospect value close degree of decision experts’ situation according to traditional TOPSIS concept, and in view of the distance between prospect value matrix of multiple decision experts and the optimal and the worst prospect value matrix. Consider

Then, the weight of the

And then, the comprehensive prospect value matrix based on the weight vector of decision experts is

Given the comprehensive prospect value matrix

To sum up, the procedure of grey situation group decision-making method based on prospect theory is as follows.

According to the event set

Determine the decision objective and give corresponding effect sample matrix of multiple decision experts for objective

In light of Definitions

Give target weight vectors of the situation given by each decision expert, plug those target weight vectors into formula (

According to Definition

According to formulas (

A new round of aid program for Xinjiang is an important decision and strategic deployment made by the Party Central Committee and the State Council to promote Xinjiang’s development and maintain Xinjiang’s social stability, requiring that 19 provinces and cities in the mid-east region aid Xinjiang’s development. Since March 2010, new industry production lines in Xinjiang are increasing day by day. Suppose that there are 3 production lines in an industry area, 4 suppliers are shortlisted in selecting suppliers, and there are 3 experts in decision-making expert group.

Choose suppliers’ choices in 3 production lines as the events, and the event set is

Determine decision-making objective. After several rounds of specialist researches, take quality, design, and price as decision-making objectives, where quality and design are qualitative index. Decision experts make assessment by means of expert scoring method. The higher the score is, the more uncertain the index is. Decision experts give scores between 0 and 10. Price is cost index; the lower the data which the suppliers provided, the better the decision. Effect sample value matrix given by multiple experts with regard to the quality and design of decision-making objectives is as follows:

The decision objective target is an effect sample value matrix of suppliers’ offers. Because this is not assessed by decision experts, the sample value matrix of target effect is the same. Consider

Calculate the distances of the positive and the negative ideal situation according to Definitions

Other normalized positive and negative prospect value matrixes can be gotten in the same way.

The weight vectors of situation given by multiple experts are

Determine the optimal and the worst prospect value matrix based on decision experts’ judgment according to Definition

Calculate the weight of experts’ strategy according to formulas (

According to comprehensive prospect value matrix, choosing supplier 2 is the optimal strategy for production line 1; choosing supplier 2 is the optimal strategy for supplier 2; choosing supplier 3 is the optimal strategy for supplier 3; providing production line 1 is the most appropriate for supplier 1; providing production line 1 is the most appropriate for supplier 2; providing production line 3 is the most appropriate for supplier 3; and providing production line 1 is the most appropriate for supplier 4. In a word, the optimal situation is

According to the methods used to calculate grey situation in group decision-making in [

The comprehensive effect sample value matrix of situation based on normative approaches given by [

According to the effect sample value matrix without the decision makers’ behavioral preference, the optimal situation is

From the example analysis and comparison, the method studies the group decision problem with a view to decision experts’ risk attitude and effect sample value, considers decision experts’ decision-making psychology, takes reference points as the positive and the negative ideal situation group distances, gets comprehensive prospect value matrix under multiple experts’ evaluation, plugs the decision experts’ risk preference into grey situation group decision, and makes sure that the final decision conforms to the psychology behavior of decision experts. Meanwhile, determine multiple decision experts’ weight based on TOPSIS method by considering the close degree between expert’s individual evaluation and overall assessment. Compared with the former subjective value methods, this method is more objective and is almost not relying on subjective experience and judgment.

This paper puts forward a grey situation group decision-making method based on the prospect theory, aiming at solving such problem that the grey situation group decision model does not consider the decision experts’ risk preference. According to various types of effect sample value, different prospect value functions are constructed, the value functions for two reference points are integrated, strengths and weaknesses are measured by means of prospect value, and the prospect value is normalized to

The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work, and there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in, or the review of, the paper.

This paper is sponsored by the National Natural Science Foundation of China (no. 71363046, no. 71271226, no. 71301064); the Humanistic and Social Science Foundation of Ministry of Education of China (no. 10YJA790174); the Humanistic and Social Science Youth Foundation of Ministry of Education of China (no. 13YJC790198).