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The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to build the model with a trapezoidal possibility degree function.

Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.

The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.

In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.

Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of “power shortage” in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.

A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.

Grey set is the important foundation of the grey mathematics and grey system theory, and the possibility function is the way of expressing grey set. This paper aims to establish the method of determining the possibility function of grey set and discusses its extended applications.

First, the grey kernel and the grey support set of grey set are defined, and the properties of grey kernel are analyzed. Second, according to the decomposition theorem of grey set, a method of determining the possibility function of grey set is put forward in this paper, which is called the method of increasing information and taking maximum and minimum (IITMM), and then it is further simplified as the method of increasing information and taking maximum (IITM), and an simple example is given to illustrate the calculation procedure. Finally, the grey information cluster method (GICM) based on IITM is proposed and applied to the ecological and geographical environment analysis of pine caterpillar.

The results show that the grey kernel of grey set still has grey uncertainty; the method of IITM has simple calculation and strict mathematical basis, and it can synthesize the information of the research object and accords with the principle of using minimum information; the GICM and the fuzzy cluster method have the same classification effect.

The researches show that method of IITM can be used not only to determine the possibility function of the grey set effectively, but also be used for the evaluation and cluster analysis of connotative objects. The classification result of the GICM presented in this paper is more precise than that of the fuzzy cluster method.

The paper succeeds in realizing both the IITM method for determining the possibility function of grey set and the GICM based on IITM for the connotative objects.

The purpose of this paper is to establish a grey cloud incidence clustering model to assess the drought disaster degree under 15 indexes in 18 cities of Henan province.

The grey incidence degree between each index and ideal index is used to determine the index weight and combined with the subjective weight, the comprehensive weight is given; the traditional possibility function is transformed into grey cloud possibility function by using the principle of maximum deviation and maximum entropy, which fully reflects the coexistence of multiple decision-making conclusions and constructs the grey cloud incidence clustering model.

The drought disaster degree of Henan province is divided into four grades under the selected 15 indexes. The drought grades show obvious regional differences. The risk levels of the east and southwest are higher, and the risk levels of the north and southeast are lower. This result is consistent with the study of drought disaster grades in Henan province, which shows the practicability and usefulness of the model.

It provides an effective method for the assessment of drought disaster grade and the basis for formulating disaster prevention and mitigation plan.

By studying the method of multiattribute and multistage decision-making with interval grey number information. The objective weight model of index value is designed, and the subjective weight is given by experts. On the basis of the two, the comprehensive weight of subjective and objective combination is proposed, which effectively weakens the randomness of subjective weight and reasonably reflects the practicality of index decision-making. The time weight reflects the dynamic of the index. The traditional possibility function is transformed into the grey cloud possibility function, which effectively takes advantage of the grey cloud model in dealing with the coexistence of fuzzy information, grey information and random information. Thus, the conflict between the decision-making results and the objective reality is effectively solved. The interval grey number can make full use of the effective information and improve the accuracy of the actual information.

The purpose of this paper is to establish a two-stage grey cloud clustering model under the panel data for the multi-attribute clustering problem with three-parameter interval grey number to evaluation of agricultural drought resistance grade of 18 cities in Henan Province.

The clustering process is divided into two stages. In the first stage: Combining variance and time degree, the time weight optimization model is established. Applying the prospect theory, the index weight optimization model is established. Then, with the help of grey possibility function, the first stage of grey cloud clustering evaluation is carried out. In the second stage: the weight vector group of kernel clustering is constructed, and the grey class of the object is determined. A two-stage grey cloud clustering model under the panel data for the multi-attribute clustering problem is proposed.

This paper indicates that 18 cities in Henan Province are divided into four categories. The drought capacity in Henan province is high in the east and low in the west, high in the south and low in the north and the central region is relatively stable. The drought is greatly affected by natural factors. And the rationality and validity of this model is illustrated by comparing with other methods.

This paper provides a practical method for drought resistance assessment, and provides theoretical support for farmers to grasp the drought information timely and improve the drought resistance ability.

The model in this paper solves the situation of ambiguity and randomness to some extent with the help of grey cloud possibility function. Moreover, the time weight of time degree and variance are used to reduce the volatility and the degree of subjective empowerment. Considering the risk attitude of the decision makers, the prospect theory is applied to make the index weight more objective. The rationality and validity of the model are illustrated by taking 18 cities in Henan Province as examples.

The article proposes a new method of strategic analysis. The method was called the grey portfolio analysis method. The presented method is complementary to the popular BCG matrix. The use of the grey portfolio analysis method enables to make a dynamic portfolio analysis for data with a high level of uncertainty.

First, the article presents current problems related to the application of portfolio methods in strategic management, in particular with reference to the BCG matrix. Second, the basics of grey numbers, operations with them and the way of acting in the grey portfolio analysis method are presented. Finally, the developed method is presented in a case study concerning an IT enterprise, whose portfolio includes cloud computing services.

In the article, a new method of a strategic analysis based on the BCG matrix was presented. It combines grey methodologies of decision making with a grey prognostic model in the context of a strategic analysis. Due to this fact, a dynamic approach to the issues of portfolio methods is possible.

The article fits the current need related to the development of new expert systems supporting strategic management in enterprises.

An introduced method is new and innovative in the area of portfolio methods. Its originality results from the fact that it eliminates a static nature of the BCG matrix through the use of grey prognostic models. What is more, when grey numbers are used, a problem of uncertainty of information, which appears, is solved at a methodological level.

Personnel selection is an important process in management due to the high cost of unfavorable employee procurement. The multi criteria nature and the presence of both qualitative and quantitative factors make it considerably more complex. The purpose of this paper is to propose a grey theory‐based hybrid approach to solve personnel selection problems in uncertain environments.

The work procedure is as follows: first, grey analytic network process (GANP) is applied to calculate selection criteria weights and then candidates are ranked by using grey possibility degrees. Finally, an example of a selection problem of sniper for a military unit was used to illustrate the proposed approach.

The analyses of the results show that grey theory‐based methods have enormous chance of success for personnel selection problems in uncertain situations.

Although there are some applications for personnel selection problems that used grey system theory in the literature, the combination of GANP and grey possibility degrees is used for personnel selection problem in this study.

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 establish a two-stage grey cloud clustering model to assess the drought risk level of 18 prefecture-level cities in Henan Province.

The clustering process is divided into two stages. In the first stage, grey cloud clustering coefficient vectors are obtained by grey cloud clustering. In the second stage, with the help of the weight kernel clustering function, the general representation of the weight vector group of kernel clustering is given. And a new coefficient vector of kernel clustering that integrates the support factors of the adjacent components was obtained in this stage. The entropy resolution coefficient of grey cloud clustering coefficient vector is set as the demarcation line of the two stages, and a two-stage grey cloud clustering model, which combines grey and randomness, is proposed.

This paper demonstrates that 18 cities in Henan Province are divided into five categories, which are in accordance with five drought hazard levels. And the rationality and validity of this model is illustrated by comparing with other methods.

This paper provides a practical and effective new method for drought risk assessment and, then, provides theoretical support for the government and production departments to master drought information and formulate disaster prevention and mitigation measures.

The model in this paper not only solves the problem that the result and the rule of individual subjective judgment are always inconsistent owing to not fully considering the randomness of the possibility function, but also solves the problem that it’s difficult to ascertain the attribution of decision objects, when several components of grey clustering coefficient vector tend to be balanced. It provides a new idea for the development of the grey clustering model. The rationality and validity of the model are illustrated by taking 18 cities in Henan Province as examples.

In the current customer-driven market, the manufacturers have to be highly responsive and flexible to deliver a variety of products. Hence, to meet this dynamic and uncertain market changes, the production system, which enables the manufacturing of such variety of products should be able to meet such diverse, dynamic changes. Hence, selecting a suitable manufacturing system is a key strategic decision for today's manufacturing organization, which needs to survive in these uncertain market conditions. Hence, the purpose of this paper is to present a decision-making model for selecting the best manufacturing system and also discuss the criteria on the basis of which the management can select the same.

A case of small- and medium-sized company is presented, in which the management is deciding to establish a most suitable manufacturing system. To supplement this, a suitable multi-criteria decision-making model (MCDM), the grey approach is used to analyze manufacturing system alternatives based on various decision criteria to arrive a comparative ranking.

An extensive analysis of grey-based decision-making model described grey decision matrix, grey normalized decision matrix, grey weighted normalized decision matrix and grey possibility degrees for three alternatives revealed that lean manufacturing systems was found to be the most suitable manufacturing system among three alternatives for a given case.

The same study can be extended by including sub-criteria with main criteria for selection of manufacturing system by utilizing two MCDM techniques such as AHP or ANP with Grey approach.

The Grey approach has been discussed in a detailed way and it will be useful for the managers to use this approach as a tool for solving similar type of decision-making problems in their organizations in the future.

Although, the problem of selecting a suitable manufacturing system is often addressed both in practice and research, very few reports are available in the literature of Grey-based decision models that demonstrated its application for selecting a suitable manufacturing systems.

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.