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The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Based on the axiomatic definition of a grey number and its greyness degree in grey system theory, the whitenization mean, whitenization difference, whitenization covariance of sequences with interval grey numbers and their greyness degrees are defined in turn. In addition, the whitenization correlation coefficient and its greyness degree of sequences with interval grey numbers are also defined. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenization value and greyness degree of correlation coefficient to form of interval grey numbers are put forward further.

The whitenization value of correlation coefficient efficient of two arbitrary sequences with interval grey numbers have symmetry, with same greyness degree but without normalization in the interval [−1, 1]; the mean, difference, covariance and correlation coefficient defined in statistics are all the special cases of those in sequences with interval grey numbers.

Due to the complexity of operation of grey numbers, the reliability of correlation coefficient of interval numbers sequence is difficult to be tested by constructing statistics at present. The further research is needed.

The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.

On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.

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.

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.

This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according to the principle of grey numbers operation. The domain means the emerging background of interval grey numbers, it is vital for the operational mechanism of such interval grey numbers. However, the criteria of selection of domain always remain same that is not only for the calculated grey numbers but also for the resultant grey numbers, which can be assumed as unrealistic up to a certain extent.

The existence of interval grey number operation based on kernel and the degree of greyness containing two calculation aspects, which are kernel and the degree of greyness. For the degree of greyness, it includes concepts of domain and calculation of the domain. The concepts of a domain are defined. The enhanced algorithm is also comprised of four deductive theorems and eight rules that are linked to the properties of the enhanced algorithm of the interval grey numbers based on the kernel and the degree of greyness.

Aiming to improve the algorithm of the degree of greyness for interval grey numbers, based on the variation of domain in the operation process, the degree of greyness of the operation result is defined in this paper, and the specific expressions for algebraic operations are given, which is relevant to the kernel, the degree of greyness and the domain. Then, these expressions are used to the algorithm of interval grey numbers based on the kernel and the degree of greyness, improving the accuracy of the operation results.

The enhanced algorithm in this paper can effectively reduce the loss of information in the operation process, so as to avoid the situation where the decision values are the same and scientific decisions cannot be made during the grey evaluation and decision-making process.

The purpose of this paper is to establish the algorithm rules of the interval grey numbers and propose a new ranking method of the interval grey numbers.

The definitions of “kernels” based on lower measure, upper measure or moderate measure are given according to the properties of the interval grey number problems. By means of the measurement error, the concept of the absolute degree of greyness and the relative degree of greyness corresponding to different “kernel” are given, and different simplified forms of the interval grey numbers are put forward.

The definitions of “kernel” and the degree of greyness in this paper not only take the upper limit, lower limit and the coverage of the interval grey numbers into account, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse.

Though the method proposed in this paper has some deficiencies, such as the definition of relative degree of greyness is meaningless when the kernel of the interval grey number is 0, it provides a new idea for calculating and sorting the interval grey numbers and is conducive to the further development of the grey system theory.

The method proposed in this paper can not only distinguish interval grey numbers in different situations, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse. In this basis, the interval grey number algorithm is established and a new ranking method of interval grey numbers is given.

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.

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 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.

In multi-criteria decision-making with interval grey number information, decision makers usually take a risk to rank or choose some very similar alternatives. Additionally, when evaluating only one alternative, decision makers can only obtain a specific value using traditional decision-making methods and may find it hard to cluster the alternatives to the “correct class” because these methods lack predetermined reference points. To overcome this problem, this paper aims to propose a two-stage grey decision-making method.

First, a new type of clustering method for interval grey numbers is designed by proposing a new possibility function for grey numbers. Based on this clustering method, a new grey clustering evaluation model for interval grey numbers is proposed by which decision makers can obtain the grade rating information of each alternative. Then, according to the grey clustering evaluation model, a new two-stage decision-making method is introduced to solve the problem that some alternatives are very similar by designing a grey comprehensive decision coefficient of alternatives.

The authors propose a new grey clustering evaluation model to deal with interval grey numbers. They design a new model to obtain the membership degree for the interval grey numbers and then propose a new grey clustering evaluation model, which can evaluate only one alternative by predefined grey classes. Then, by the grey comprehensive decision coefficient, a two-stage grey evaluation decision-making method is put forward to solve the problem that some alternatives are very close and hard to be distinguished.

A new grey clustering evaluation model is proposed, which can evaluate only one alternative by predefined grey classes. A two-stage grey evaluation decision-making method is given to solve the problem that some alternatives are very close and hard to be distinguished.

The purpose of this paper is to propose a dynamic multi-attribute decision-making method based on the prospect theory for dealing with the dynamic multi-attribute decision-making problem with three-parameter interval grey number.

First, the kernel and comparison rule of three-parameter interval grey numbers are defined, which are the basis of collecting and sorting grey numbers. Next, the prospect value function is determined in view of the decision-making information with different time points as the reference points. Then, an optimal model for solving the attribute weight and time weight is constructed based on the grey entropy principle.

The paper provides a dynamic grey interrelation decision method based on the prospect theory with three-parameter interval grey number, and the example analysis shows that the method proposed in this paper has validity and rationality.

If we have a better understanding of the weights of different reference points, it is possible to receive a more reasonable expression for the comprehensive prospect utility value function.

The paper provides a grey interrelation decision method based on the prospect theory, which can help the decision maker deal with the dynamic multi-attribute decision-making problems under the uncertain environment.

The paper proposes the kernel and ranking method of three-parameter interval grey number, and uses different time points as the reference points to define the prospect value function. Furthermore, this paper structures a dynamic grey interrelation decision method with three-parameter interval grey number based on the prospect theory.