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The aggregation of information from a group of decision experts for developing collective opinion is the important question in practice. The purpose of this paper is to provide a group decision-making method via ordered weighted aggregation (OWA) operator and grey incidence analysis.

In this study, OWA operator provides aggregation of attribute values to form an overall decision for each decision expert, and grey incidence model provides aggregation of decision experts’ evaluations to form overall score for each alternative. The example illustrates the procedure and practicability of the proposed model.

A new thought for multiple attribute group decision-making problems is given. The proposed method produces an overall desirability score for each alternative.

This is to obtain a more comprehensive and realistic solution to the given group decision-making problem. The proposed analysis method of group decision-making problems reveals vitality of grey systems theory.

This paper combines OWA operator and grey incidence analysis to obtain a novel and effective method for group decision making. It is suitable for group decision-making problems in which the attribute weights are completely unknown, expert weights are completely unknown.

This paper aims to develop a grey decentralized bi-level multi-objective programming (MOP) model. A solution approach is also proposed for the given model. A production and transportation plan for a closed loop supply chain network under an uncertain environment and different scenarios is also developed.

In this paper, we combined grey linear programming (GLP) and fuzzy set theory to present a solution approach for the problem. The proposed model first solves the given problem using GLP. Membership functions for the decision variables under the control of the leader and for the goals are created. These membership functions are then used to generate the final solutions.

This paper provides insight for fomenting the decision-making process while providing a more flexible approach in uncertain logistics problems. The deviations of the final solution from the individual best solutions of the two levels are very little. These deviations can further be reduced by adjusting the tolerances associated with the decision variables under the control of the leader.

The proposed approach uses the concept of membership functions of linear form, and thus, requires less computational efforts while providing effective results. Most of the organizations exhibit decentralized decision-making under the presence of uncertainties. Therefore, the present study is helpful in dealing with such scenarios.

This is the first time, formulation of a decentralized bi-level multi-objective model under a grey environment is carried out as per the best knowledge of the authors. A solution approach is developed for bi-level MOP under grey uncertainty.

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 grey target decision model based on cobweb area in order to overcome the effect and influence from the extreme value of the index on the decision result. However, it does not take into account the impact of the correlation between indicators on the angle of the index, and produce a certain degree decision information distortion as a result of the equal angle between the indicators. In order to solve the above problems, a novel grey decision-making model based on cone volume is proposed.

In this paper, the model uses the whitening weight function to whiten the interval grey number, and the Delphi method and the maximal entropy method are exploited to integrate the weight of the index. On the basis of this, the center of the bull’s eye, the weight and the index value are constructed as the center circle, the radius, and the high cone, respectively. The scheme is selected by the volume of the cone, the decision is made according to the order relation, and the example is utilized to prove and analyze the validity of the proposed model.

The results show that the proposed model can well improve the traditional grey target decision-making model from the modeling object and modeling method.

The method exposed in the paper can be used to deal with the grey target decision-making problems which characteristics are multi-indexes, and the attribute values are interval grey numbers.

The paper succeeds in overcoming the disadvantages of grey target decision making based on the target center distance and the cobweb area.

The purpose of this paper is to propose an integrated decision-making model for multi-attributes decision-making (MADM) problems in additive manufacturing (AM) process planning and for related MADM problems in other research areas.

This research analyzed the drawbacks of former methods and then proposed two sub-decision-making models, “deviation model” and “similarity model”. The former sub-model aimed to measure the deviation extent of each alternative to the aspired goal based on analyzing Euclidean distance between them, whereas the latter sub-model applying grey incidence analysis was used to measure the similarity between alternatives and the expected goal by investigating the curve shape of each alternative. Afterwards, an integrated model based on the aggregation of the two sub-models was proposed and verified by a numerical example and simple case studies.

The calculating results of the cited numerical example and the comparison to former related research showed that this proposed model is more practical and reasonable than former methods applied in MADM problems of AM. In addition, the proposed model can be applied in other fields where MADM problems exist.

This proposed integrated model not only considered the deviation extent of alternatives to the aspired goal but also investigated the similarity between alternatives and the expected goal. The similarity analysis compensates the drawbacks of traditional “distance-based” models or methods that cannot distinguish alternatives which have the same distance-based index value.

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.

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

With respect to multi-stage group risk decision-making problems in which all the attribute values take the form of grey number, and the weights of stages and decision makers are unknown, the purpose of this paper is to propose a new decision-making method based on grey target and prospect theory.

First, the sequencing and distance between two grey numbers are introduced. Then, a linear operator with the features of the “rewarding good and punishing bad” is presented based on the grey target given by decision maker, and the prospect value function of each attribute based on the zero reference point is defined. Next, weight models of stages and decision makers are suggested, which are based on restriction of stage fluctuation, the maximum differences of alternatives and the maximum entropy theory. Furthermore, the information of alternatives is aggregated by WA operator, the alternatives are selected by their prospect values.

The comprehensive cumulative prospect values are finally aggregated by WA operator, alternatives are selected or not are judged by the sign of the comprehensive prospect theory, if the prospect value of alternative is negative, the corresponding alternative misses the group decision makers’ grey target, on the contrary, if the prospect value of alternative is positive, the corresponding alternative is dropped into the group decision makers’ grey target, the alternative with positive prospect value whose value is the maximum is selected.

Compared with the traditional decision-making methods using expected utility theory which suppose the decision makers are all completely rational, the proposed method is based on irrational which is more in line with the decision maker’s psychology. And this method considers the decision maker’s psychological expectation values about every attribute, different satisfactory grey target about attributes will directly affect decision-making result.

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.

In this study, a hybrid rough and grey set-based rule model is designed for diagnosis of one type of blood cancer called multiple myeloma (MM). The grey clustering method is used to combine the same condition attributes and to improve the validity of the final model.

Some tools of the rough set theory (RST) and grey incidence analysis (GIA) are used in this research to analyze the serum protein electrophoresis (SPE) test results. An RST-based rule model is extracted based on the laboratory SPE test results of patients. Also, one decision attribute and 15 condition attributes are used to extract the rules. About four rule models are constructed due to the different algorithms of data complement, discretization, reduction and rule generation. In the following phases, the condition attributes are clustered into seven clusters by using a grey clustering method, the value set of the decision attribute is decreased by using manual discretizing and the number of observations is increased in order to improve the accuracy of the model. Cross-validation is used for evaluation of the model results and finally, the best model is chosen with 5,216 rules and 98% accuracy.

In this paper, a new rule model with high accuracy is extracted based on the combination of the grey clustering method and RST modeling for diagnosis of the MM disease. Also, four primary rule models and four improved rule models have been extracted from different decision tables in order to define the result of SPE test of patients. The maximum average accuracy of improved models is equal to 95% and related to the gamma globulins percentage attribute/object-related reducts (GA/ORR) model.

The total number of observations for rule extraction is 115 and the results can be improved by further samples. To make the designed expert system handy in the laboratory, new computer software is under construction to import data automatically from the electrophoresis machine into the resultant rule model system.

The main originality of this paper is to use the RST and GST together to design and create a hybrid rule model to diagnose MM. Although many studies have been carried out on designing expert systems in medicine and cancer diagnosis, no studies have been found in designing systems to diagnose MM. On the other hand, using the grey clustering method for combining the condition attributes is a novel solution for improving the accuracy of the rule model.