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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 study the grey decision model and distance measuring method of general grey number.

First, intuitionistic grey number (IGN) set and an IGN are defined by grey number probability function. Second, each interval grey number in general grey number is represented by an IGN and converts the general grey number into an IGN set. Final, the operation of two general grey numbers is defined as the operation between IGN sets, and the distance measure of the general grey number is given.

Up to now, the method of measuring the distance and the grey decision model of general grey number is established. Thus, the difficult problem for set up decision mode of general grey number has been solved to a certain degree.

The method exposed in this paper can be used to integrate information form a different source. The method that a general grey number converted to a set of IGNs could be extended to the case of grey incidence analysis models, grey prediction models and grey clustering evaluation models, which includes general grey numbers, etc.

The concepts of IGN and IGN set are proposed for the first time in this paper; The operation of two general grey numbers can be defined as the operation between IGN sets. On this basis, the algorithm of IGN, the integration operator of IGN and the distance measure between IGN sets are given.

The purpose of this paper is to advance a novel grey variable dual precision rough set model for grey concept.

To obtain the approximation of a grey object, the authors first define the concepts of grey rough membership degree and grey degree of approximation on the basic thinking logic of variable precision rough set. Based on grey rough membership degree and grey degree of approximation, the authors proposed a grey variable dual precision rough set model. It uses a clear knowledge concept to approximate a grey concept, and the output result is also a clear concept.

The result demonstrates that the proposed model may be closer to the actual decision-making situation, can effectively improve the rationality and scientificity of the approximation and reduce the risk of decision-making. It can effectively achieve the whitenization of grey objects. The model can be degenerated to traditional variable precision rough fuzzy set model, variable precision rough set model and classic Pawlak rough set, when some specific conditions are met.

The method exposed in the paper can be used to solve multi-criteria decision problems with grey decision objects and provide a decision rule. It can also help us better realize knowledge discovery and attribute reduction. It can effectively achieve the whitenization of grey object.

This method proposed in this paper implements a rough approximation of grey decision object and obtains low-risk probabilistic decision rule. It can effectively achieve a certain degree of whitenization of some grey objects.

The purpose of this paper is to propose a framework for data analytics where everything is grey in nature and the associated uncertainty is considered as an essential part in data collection, profiling, imputation, analysis and decision making.

A comparative study is conducted between the available uncertainty models and the feasibility of grey systems is highlighted. Furthermore, a general framework for the integration of grey systems and grey sets into data analytics is proposed.

Grey systems and grey sets are useful not only for small data, but also big data as well. It is complementary to other models and can play a significant role in data analytics.

The proposed framework brings a radical change in data analytics. It may bring a fundamental change in our way to deal with uncertainties.

The proposed model has the potential to avoid the mistake from a misleading data imputation.

The proposed model takes the philosophy of grey systems in recognising the limitation of our knowledge which has significant implications in our way to deal with our social life and relations.

This is the first time that the whole data analytics is considered from the point of view of grey systems.

The purpose of this paper is to advance new rules about operations of grey sets based on grey numbers and greyness and investigate their capability in reducing uncertainty.

A grey set can have its characteristic function values restricted by grey numbers, and such a representation makes the operations of grey sets different from other sets. Based on the concept of whitenisation of grey sets, two extended operations of grey sets are defined and their properties are discussed.

The result demonstrates that the proposed meet operation can significantly reduce uncertainty in grey sets and that the novel rules about operation of grey sets can reduce uncertainty of the set significantly. The propagation of uncertainty under different operations is investigated.

The method exposed in the paper can be used to integrate information from different sources to reduce uncertainty in information.

The paper succeeds in constructing novel operation rules of grey sets. The capability of novel operation rules to reduce uncertainty is studied and it is a new development of grey systems theory.

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

From the grey hazy set, the paper re‐defines grey number and the operation of grey‐number element, then some properties are obtained. Based on them, the operation of grey‐matrix element is given. The general definition of grey function and its operation are also proposed.

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Grey mathematics may become a branch of mathematics to deal with proximate calculation.

The differences and relations between grey sets and rough sets are discussed. Based on the concept of a rough grey set, its entropy is studied. Moreover, the grey inference resulting from a rough grey set is pointed out. The relative propositions and theorems are obtained.

This paper aims to resolve the uncertain problem in suppliers selection chain management system through using the proposed multiple attribute decision‐making (MADM) approach.

The approach which combines grey system theory with rough set theory is proposed.

This proposed approach take advantage of mathematical analysis power of grey system theory and at the same time take advantage of data mining and knowledge discovery power of rough set theory. It will be suitable to decision making under a more uncertain environment.

Provides a viewpoint on the attribute values and attribute weights of rough set decision table for all alternatives are decided by grey number based on grey system theory. The best ideal supplier can be decided by grey relational analysis based on grey number.

Due to the limitation of acknowledgment, the complexity of software system and the interference of noises, this paper aims to solve the traditional problem: traditional software cost estimation methods face the challenge of poor and uncertain inputs.

Under such circumstances, different cost estimation methods vary greatly on estimation accuracy and effectiveness. Therefore, it is crucial to perform evaluation and selection on estimation methods against a poor information database. This paper presents a grey rough set model by introducing grey system theory into rough set based analysis, aiming for a better choice of software cost estimation method on accuracy and effectiveness.

The results are very encouraging in the sense of comparison among four machine learning techniques and thus indicate it an effective approach to evaluate software cost estimation method where insufficient information is provided.

Based on the grey rough set model, the decision targets can be classified approximately. Furthermore, the grey of information and the limitation of cognition can be overcome during the use of the grey rough interval correlation cluster method.

This paper proposed the grey rough set model combining grey system theory with rough set for software cost estimation method evaluation and selection.

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.