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Aim to the limitations of grey relational analysis of interval grey number, based on the generalized greyness of interval grey number, this paper tries to construct a grey angle cosine relational degree model from the perspective of proximity and similarity.

Firstly, the algorithms of the generalized greyness of interval grey number and interval grey number vector are given, and its properties are analyzed. Then, based on the grey relational theory, the grey angle cosine relational model is proposed based on the generalized greyness of interval grey number, and the relationship between the classical cosine similarity model and the grey angle cosine relational model is analyzed. Finally, the validity of the model in this paper is illustrated by the calculation examples and an application example of related factor analysis of maize yield.

The results show that the grey angle cosine relational degree model has strict theoretical basis, convenient calculation and is easy to program, which can not only fully utilize the information of interval grey numbers but also overcome the shortcomings of greyness relational degree model. The grey angle cosine relational degree is an extended form of cosine similarity degree of real numbers. The calculation examples and the related factor analysis of maize yield show that the model proposed in this paper is feasible and valid.

The research results not only further enrich the grey system theory and method but also provide a basis for the grey relational analysis of the sequences in which the interval grey numbers coexist with the real numbers.

The paper succeeds in realizing the algorithms of the generalized greyness of interval grey number and interval grey number vector, and the grey angle cosine relational degree, which provide a new method for grey relational analysis.

This paper aims to investigate the grey scheduling, which is the combination of grey system theory and scheduling problems with uncertain processing time. Based on the interval grey number and its related definitions, properties, and theorems, the single machine scheduling with uncertain processing time and its general forms are studied as the research object. Then several single machine scheduling models are reconstructed, and an actual production case is developed to illustrate the rationality of the research.

In this paper, the authors first summarize the definitions and properties related to interval grey numbers, especially the transitivity of the partial order of interval grey numbers, and give an example to illustrate that the transitivity has a positive effect on the computational time complexity of multiple interval grey number comparisons. Second, the authors redefine the general form of the single machine scheduling problem with uncertain processing time according to the definitions and theorems of interval grey numbers. The authors then reconstruct three single machine scheduling models with uncertain processing time, give the corresponding heuristic algorithms based on the interval grey numbers and prove them. Finally, the authors develop a case study based on the engine test shop of K Company, the results show that the proposed single machine scheduling models and algorithms with uncertain processing time can provide effective guidance for actual production in an uncertain environment.

The main findings of this paper are as follows: (1) summarize the definitions and theorems related to interval grey numbers and prove the transitivity of the partial order of interval grey numbers; (2) define the general form of the single machine scheduling problem with interval grey processing time; (3) reconstruct three single machine scheduling models with uncertain processing time and give the corresponding heuristic algorithms; (4) develop a case study to illustrate the rationality of the research.

In the further research, the authors will continue to summarize more advanced general forms of grey scheduling, improve the theory of grey scheduling and prove it, and further explore the application of grey scheduling in the real world. In general, grey scheduling needs to be further combined with grey system theory to form a complete theoretical system.

It is a fundamental work to define the general form of single machine scheduling with uncertain processing time used the interval grey number. However, it can be seen as an important theoretical basis for the grey scheduling, and it is also beneficial to expand the application of grey system theory in real world.

In order to make full use of the generalized greyness of interval grey number, this paper analyzes the properties and its applications of generalized greyness.

Firstly, the static properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain are analyzed. Then, this paper gives the dynamic properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain and explains the dialectical principle contained in it. Finally, the generalized greyness is used to judge the effectiveness of interval grey number transformation.

The results show that the generalized greyness of interval grey number has relativity, normativity, unity, eternity and conservation. The static and dynamic properties of generalized greyness are the same in the infinite and infinitesimal background domain, while they are different in the bounded background domain. The generalized greyness can be used as an index to judge whether the grey number transformation is greyness or information preservation.

The research shows that the generalized greyness can be used as an index to judge the validity of the grey number transformation and also can be applied in grey evaluation, grey decision-making and grey prediction and so on.

The paper succeeds in realizing the mathematical principle of “white is black”, the “greyness clock-slow effect” of the value domain of interval grey number and the generalized greyness conservation principle, which provides a theoretical basis for the rational use of generalized greyness of interval grey number.

Assembly line is a common production form and has been effectively used in many industries, but the imprecise processing time of each process makes production line balancing and capacity forecasting the most troublesome problems for production managers. In this paper, uncertain man-hours are represented as interval grey numbers, and the optimization problem of production line balance in the case of interval grey man-hours is studied to better evaluate the production line capacity.

First, this paper constructs the basic model of assembly line balance optimization for the single-product scenario, and on this basis constructs an assembly line balance optimization model under the multi-product scenario with the objective function of maximizing the weighted greyscale production line balance rate, second, this paper designs a simulated annealing algorithm to solve problem. A neighborhood search strategy is proposed, based on assembly line balance optimization, an assembly line capacity evaluation method with interval grey man-hour characteristics is designed.

This paper provides a production line balance optimization scheme with uncertain processing time for multi-product scenarios and designs a capacity evaluation method to provide managers with scientific management strategies so that decision-makers can scientifically solve the problems that the company's design production line is quite different from the actual production situation.

There are few literary studies on combining interval grey number with assembly line balance optimization. Therefore, this paper makes an important contribution in this regard.

Competition in the banking sector is more complex than in the past, and survival has become more difficult than before. The purpose of this paper is to propose a grey methodology for evaluating, clustering and ranking the performance of bank branches with imprecise and uncertain data in order to determine the relative status of each branch.

In this study, the two-stage data envelopment analysis model with grey data is applied to assess the efficiency of bank branches in terms of operations. The result of grey two-stage data envelopment analysis model is a grey number as efficiency value of each branch. In the following, the branches are classified into three grey categories of performance by grey clustering method, and the complete grey ranking of branches are performed using “minimax regret-based approach” and “whitening value rating”.

The results show that after grey clustering of 22 branches based on grey efficiency value obtained from the grey two-stage DEA model, 6 branches are assigned to “excellent” class, 4 branches to “good” class and 12 branches to “poor” class. Moreover, the results of MRA and whitening value rating models are integrated, and a complete ranking of 22 branches are presented.

Grey clustering of branches based on grey efficiency value can facilitate planning and policy-making for branches so that there is no need to plan separately for each branch. The grey ranking helps the branches find their current position compared to other branches, and the results can be a dashboard to find the best practices for benchmarking.

Compared with traditional DEA methods which use deterministic data and consider decision-making units as black boxes, in this research, a grey two-stage DEA model is proposed to evaluate the efficiency of bank branches. Furthermore, grey clustering and grey ranking of efficiency values are used as a novel solution for improving the accuracy of grey two-stage DEA results.

This paper aims to provide a promising memetic algorithm (MA) for an unrelated parallel machine scheduling problem with grey processing times by using a simple dispatching rule in the local search phase of the proposed MA.

This paper proposes a MA for an unrelated parallel machine scheduling problem where the objective is to minimize the sum of weighted completion times of jobs with uncertain processing times. In the optimal schedule of the problem’s single machine version with deterministic processing time, the machine has a sequence where jobs are ordered in their increasing order of weighted processing times. The author adapts this property to some of their local search mechanisms that are required to assure the local optimality of the solution generated by the proposed MA. To show the efficiency of the proposed algorithm, this study uses other local search methods in the MA within this experiment. The uncertainty of processing times is expressed with grey numbers.

Experimental study shows that the MA with the swap-based local search and the weighted shortest processing time (WSPT) dispatching rule outperforms other MA alternatives with swap-based and insertion-based local searches without that dispatching rule.

A promising and effective MA with the WSPT dispatching rule is designed and applied to unrelated parallel machine scheduling problems where the objective is to minimize the sum of the weighted completion times of jobs with grey processing time.

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.

This paper investigates a problem in a reverse logistics (RLs) network to decide whether to dispose of unsold goods in primary stores or re-commercialize them in outlet centers. By deducting the costs associated with each policy from its revenue, this study aims to maximize the profit from managing unsold goods.

A new mixed-integer linear programming model has been developed to address the problem, which considers the selling prices of products in primary and secondary stores and the costs of transportation, cross-docking and returning unwanted items. As a result of uncertain nature of the cost and time parameters, gray numbers are used to deal with it. In addition, an innovative uncertain solution approach for gray programming problems is presented that considers objective function satisfaction level as an indicator of optimism.

According to the results, higher costs, including transportation, cross-docking and return costs, make sending goods to outlet centers unprofitable and more goods are disposed of in primary stores. Prices in primary and secondary stores heavily influence the number of discarded goods. Higher prices in primary stores result in more disposed of goods, while higher prices in secondary stores result in fewer. As a result of the proposed method, the objective function satisfaction level can be viewed as a measure of optimism.

An integral contribution of this study is developing a new mixed-integer linear programming model for selecting the appropriate goods for re-commercialization and choosing the best outlet center based on the products' price and total profit. Another novelty of the proposed model is considering the matching percentage of boxes with secondary stores’ desired product lists and the probability of returning goods due to non-compliance with delivery dates. Moreover, a new uncertain solution approach is developed to solve mathematical programming problems with gray parameters.

The effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.

First, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.

The predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.

Crude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

This study constructs a three-stage evaluation model for interdisciplinary organizations to solve their ranking problems effectively.

A three-stage interdisciplinary organization evaluation model abounds the key problems of “who will evaluate the projects?” and “how to evaluate the projects?”. In the first stage, the authors build a consensus maximization model to identify the selected experts based on the interval grey number because of the uncertainty in assessment. In the second stage, considering the reliability of the experts, the authors calculate the reliability of the experts based on historical data. Meanwhile, considering the gradual changes of the experts, the dynamic weighting method is obtained based on the clustering method. In the third stage, considering decision-makers regret psychological behavior, the authors construct a cross-organizational performance evaluation model based on consensus expectations.

First, for selecting the experts responsible for assessing interdisciplinary organizations, the consensus-reaching method can effectively avoid cognitive bias. Second, during the assessment, the authors obtained more reasonable results by considering the psychological changes of experts based on regret theory. Third, based on the results, the cross-organization of colleges focused on the achievements of talent training, cross effects, and system construction.

Our study could help organizations establish a suitable assessment mechanism and promote interdisciplinary development.

First, considering the importance of selecting the experts, the authors use the consensus-reaching process for expert selection. This method could guarantee most experts' preferences. Then, the authors propose a two-stage dynamic weighting method, including a pre-determined and adjusted process. The dynamic method can better perform the preferences of experts. Third, the authors studied the assessment in interdiscipline. In addition, based on the framework and considering the features of the interdiscipline, the authors use the grey number to perform the uncertain preferences of the experts using regret theory.