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The purpose of this paper is to study a novel grey possibility degree approach, which is combined with multi-attribute decision making (MADM) and applied MADM model for solving supplier selection problem under uncertainty information.

The supplier selection problem is a typical MADM problem, in which information of a series of indexes should be aggregated. However, it is relatively easy for decision makers to define information in uncertainty, sometimes as a grey number, rather than a precise number. By transforming linguistic scale of rating supplier selection attributes into interval grey numbers, a novel grey MADM method is developed. Steps of proposed model were provided, and a novel grey possibility degree approach was proposed. Finally, a numerical example of supplier selection is utilized to demonstrate the proposed approach.

The results show that the proposed approach could solve the uncertainty decision-making problem. A numerical example of supplier selection is utilized to demonstrate the proposed approach. The results show that the proposed method is useful to aggregate decision makers’ information so as to select the potential supplier.

The approach constructed in the paper can be used to solving uncertainty decision-making problems that the certain value of the decision information could not collect while the interval value set could be defined. Obviously it can be utilized for other MADM problem.

The paper succeeded in redefining interval grey number, constructing a novel interval grey number based MADM approach and providing the solution of the proposed approach. It is very useful to solving system forecasting problem and it contributed undoubtedly to improve grey decision-making models.

The purpose of this paper is to combine the interval grey number algorithm with a project scheduling model, so as to solve the interval grey number based project scheduling problem.

According to the grey system theory, if we could not clearly collect the right value of an activity while obtaining the upper and lower boundaries of the activity duration time, we can find activity duration time as interval grey number. This paper tries to combine interval grey number with project scheduling problem. The general definition of interval grey number was given. And then the linear operations of independent interval grey number and non-independent interval grey number were further defined. Interval grey number based project scheduling model and its algorithm were further proposed. Finally, a numerical case was adopted to test the effectiveness of the proposed method.

The results show that grey project scheduling and grey critical path method could be established under interval grey number measured activities.

Scheduling problem was widely used in project planning and control. This manuscript attempted to combine interval grey number with project scheduling so as to explain the flexible deadline in a special project. It is truly in accordance with the requirements for real applications.

This paper proposed linear operations of independent and non-independent interval grey numbers, and proposed a interval grey number based project scheduling model. Valuable contribution is to combine interval grey numbers with project scheduling and it is meaningful to make a useful strategy in a flexible condition of project scheduling.

The purpose of this paper is to propose the grey target decision method based on three-parameter interval grey number for dealing with multi-attribute decision-making problems under uncertain environment.

First, the kernel and ranking method of three-parameter interval grey number are defined, which is the basis of determining the positive and negative bull’s-eye. Next, a new distance measure of three-parameter interval grey number is defined in view of the importance of the “center of gravity” point. Furthermore, a new comprehensive bull’s-eye distance is proposed based on the kernel which integrates the distance between different attributes to the positive and negative bull’s-eye. Then attribute weights are obtained by comprehensive bull’s-eye distance minimum and grey entropy maximization.

The paper provides a grey target decision method based on three-parameter interval grey number and example analysis shows that the method proposed in this paper is more reasonable and effective.

If we have a better understanding of the distribution characteristics of three-parameter interval grey number, it is possible to have a more reasonable measure of the distance of three-parameter interval grey number.

The paper provides a grey target decision method, which can help decision maker deal with multi-attribute decision-making problems under uncertain environment.

This paper proposed the kernel and ranking method of three-parameter interval grey number, and defined a new distance measure of three-parameter interval grey number and proposed a new comprehensive bull’s-eye distance, Furthermore, this paper structured a grey target decision method based on three-parameter interval grey number.

Nowadays, evaluation objects are becoming more and more complicated. The interval grey numbers can be used to more accurately express the evaluation objects. However, the information distribution of interval grey numbers is not balanced. The purpose of this paper is to introduce the central-point triangular whitenization weight function to solve the clustering process of this kind of numbers.

A new expression of the central-point triangular whitenization weight function is presented in this paper, in terms of the grey cluster problem based on interval grey numbers. By establishing the integral mean value function on the set of interval grey numbers, the application range of grey clustering model is extended to the interval grey number category, and, in this way, the grey fixed weight cluster model based on interval grey numbers is obtained.

The model is verified by a case which reveals a high distinguishability, validity and practicability.

This model can be used in many fields, such as agriculture, economy, geology and medical science, and provides a feasible method for evaluation schemes in performance evaluation, scheme selection, risk evaluation and so on.

The central-point triangular whitenization weight function is introduced. The method reflects the thought “make full use of the information” in grey system theory and further enriches the system of grey clustering theory as well as expands the application scope of the grey clustering method.

As productions show characteristics of multi-varieties and small batch in a recent new product system, it is more difficult to acquire its failure rate data. With the help of expert experience information, the authors can get the interval estimation of failure rate data under different methods, so how to make the interval convergence with the new information is an important problem to be solved. The paper aims to discuss this issue.

In this paper, the concept of generalized standard grey number is used to characterize the multi-source heterogeneous uncertainty failure rate data into a unified framework. Then, the engineering construction method is used to calculate the average failure rate and build the grey exponential distribution reliability function, whose image is presented as the possible region of the two-curve envelope.

Further, according to the normal distribution assumption of the regional convergence based on the information supplement, the convergence problem of the reliability function is transformed into the convergence of the area of the curve envelope region, and construct the multi-objective programming model with the minimum envelope area and the lowest total cost of information acquisition, acquire the conclusion that the failure rate is equal to the nuclear of the average failure rate when the envelope region converges.

Through the case analysis of the equipment ejection system of the Harbinger system, five groups of results are obtained by Matlab simulation, which verify the rationality and feasibility of the model described in this paper.

The purpose of this paper is to redefine the concept of grey number with information background and to propose novel grey number algorithms.

As the basic element of a grey system, grey number is defined as a number of which the true value is unknown because of the limited information while the boundary or possible value set can be known. Grey number algorithms are key points for constructing grey system models and helping to calculate model results. The concept of grey number is redefined with information background in this paper. Novel grey number algorithms are defined considering all the different forms of grey number information background. Several illustrative examples are applied to state the process of the proposed algorithms.

The results show that the novel grey number algorithms can do the operations well no matter what the grey number's type. It is useful to create effective grey system models and to do system analysis, forecasting, decision making and control in grey systems.

The method exposed in the paper can be used to calculate different grey numbers and used in constructing new grey models.

The paper succeeds in defining new grey number algorithm. The concept and its remarks of grey number are discussed. The novel algorithm can be used in creating new grey models and solve the modelling parameters in of grey systems theory undoubtedly.

Ranking and comparing grey numbers represent a very important decision-making procedure in any given grey environment. The purpose of this paper is to study the existing approaches of ordering interval grey numbers in the context of decision making by surveying existing definitions.

Different methods developed for comparing grey numbers are presented along with their disadvantages and advantages in terms of comparison outcomes. Practical examples are employed to show the importance and necessity of using appropriate methods to compare grey numbers.

Most the available methods are not suitable for pointing out which number is larger when the nuclei of the grey numbers of concern are the same. Also, these available methods are also considered in terms of partial order and total order. Kernel and degree of greyness of grey numbers method is more advantageous than other methods and almost eliminates the shortcomings of other methods.

Different methods for ranking grey numbers are presented where each of them has disadvantages and advantages. By using different methods, grey interval numbers are compared and the results show that some methods cannot make grey number comparisons in some situations. The authors intend to find a method that can compare grey numbers in any situation. The findings of this research can prevent errors that may occur based on inaccurate comparisons of grey numbers in decision making. There are various research studies on the comparison of grey numbers, but there is no research on the comparison of these methods and their disadvantages, advantages or their total or partial order.

The purpose of this paper is to research attribute reduction and decision making by gray dual‐information, taking into account the attribute reduction of attribute decision unknown for the interval gray numbers.

The authors obtain the attribute weights considering the consistency of experts’ judgment matrixes and the decision matrixes with gray information. They propose some experts’ attribute reduction ideas based on interval gray numbers of rough set. With the help of experts’ decision information, they consider attribute uncertainty ratio and attribute value ratio to reduce attribute. Finally, a numerical example shows its feasibility.

Some experts’ attribute reduction ideas are proposed based on interval gray numbers of rough set. With the help of experts’ decision information, attribute uncertainty ratio and attribute value ratio to reduce attribute can be considered.

Attribute reduction is keeping classified information systems under the same conditions and deleting redundant and irrelevant or unimportant attributes in order to solve the problem of decision making. This paper considers the attribute reduction based on gray dual‐information.

A study is made of the payoff matrix which is made up of grey interval number because of asymmetry information, player's finite knowledge and bounded rationality and all sorts of stochastic and non‐stochastic factors.

On the base of concept of equipollent, superior and inferior potential degree, the paper designs determinant rules of interval grey number potential relations, opens out player's decision‐making laws in the conditions of finite knowledge and logos. And it designs the grey game decision‐making rules which player choices maximum potential degree of grey game value (the most favorableness situation) under the cases of that there are all likely to be minimum potential degree of grey game value (the most disadvantage situation), which is a reliable way for both sides to accept.

The paper recognizes and defines overrated and underrated risk of potential optimal pure strategy in the grey game, designs arithmetic for determining player's overrated and underrated risk under the situation of potential optimal pure strategy.

The presents system meets the requirement of judging pure strategy solutions in the grey potential situation.

This paper builds up the system of judgment for grey potential.

The purpose of this paper is to propose a multi-scale extended grey target decision method for dealing with multi-attribute decision-making problems with interval grey numbers whose value distribution information is asymmetrical.

First, the whitenization weight function (WWF) was adopted to show the value distribution information of interval grey numbers. The definitions of kernel, degree of greyness, relative kernel and whitenization standard deviation of interval grey numbers were given based on the WWF. Then, the relative kernel grey target and whitenization standard deviation grey target were constructed to take full advantage of the owned decision information. Finally, the relative bull’s-eye coefficient was proposed to rank the preference order of all alternatives.

The relative bull’s-eye coefficient reflects the influence of the decision information on decision results with respect to the mean level and value distribution of attribute values. Thus, the decision-maker could set the return and risk adjustment coefficient according to their preferences and select the optimal alternative with a high expected return and low risk.

The paper considers the valve distribution information of interval grey numbers, and a novel definition for kernels, degrees of greyness, relative kernels and whitenization standard deviations, which are given based on the WWF. The paper not only considers the influence of mean levels of decision information over decision results, but also takes the value distribution information into account.