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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.

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.

The purpose of this paper is to develop a novel interval Multi-Objective Optimization by a Ratio Analysis plus the Full Multiplicative Form(MULTIMOORA) with combination weights to evaluate the employment quality of college graduates, where the criteria are expressed by interval numbers and the weights of criteria are completely unknown.

Firstly, considering the subjective uncertainty of the weights of the criteria, the interval best worst method (I-BWM) was present to determine the subjective weights of the criteria. Secondly, by the improved interval number distance measure, an improved interval deviation maximization method (I-MDM) was introduced to detemine the objective weights. In the following, based on the I-BWM and the improved I-MDM, a combination weighting method that takes into account the subjective and objective weights is proposed. Finally, a multi-criteria decision-making method based on the interval MULTIMOORA with combination weights is present to evaluate the employment quality of college graduates, and then a comparative analysis with some of the existing distance measures of interval numberswas conducted to illustrate the flexibility.

According to the data of the Report on Employment Quality of Chinese College Graduats released by Mycos Research Institute in 2016–2020 and 2021–2022, the proposed method was used to evaluate the employment quality of college graduates during the period before and after the COVID-19 epidemic. The results verify that the method is more reasonable because the subjective and objective weights of the criteria can be fully considered. Finally, the feasibility and practicability of the proposed method are further verified by varying parameters.

Present an evaluation method on the employment quality of college graduates based on the Interval MULTIMOORA with combination weights considering the subjective and objective weights. And the proposed method is proved that it can provide a more reasonable evaluation results. At the same time, it is verified that the feasibility and the practicability of the proposed method are affected by varying parameters in the paper.

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.

This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

In this study, a novel framework was proposed to assess the trust in e-government (e-Gov) services under an uncertain environment. The proposed framework was applied in Iranian municipality websites of e-Gov services to evaluate the readiness score of trust in e-Gov services.

A unique hybrid research methodology was proposed. In the first phase, a comprehensive set of indices were determined from an extensive literature review and finalized by employing the fuzzy Delphi method. In the second phase, interval-valued intuitionistic fuzzy set (IVIFS) -was utilized to model the problem's uncertainty with analytic called IVIFS- hierarchy process (AHP) to determine the importance of indices and indicators by assigning the weights. In the third phase, the fuzzy evaluation method (FEM) is followed for assessing the readiness score of indices in case studies.

The findings indicated that “Trust in government” is the most significant index affecting citizen's trust in e-Gov services while “Maintenance and support” has the least impact on user's intention to use e–Gov services.

The study contributes by introducing a unique research methodology that integrates three phases, including fuzzy Delphi, IVIFS AHP and fuzzy evaluation method. Moreover, the fuzzy sets theory helps to reach a more accurate result by modeling the inherent ambiguity of indicators and indices. Interval-valued intuitionistic fuzzy models the ambiguity of experts' judgments in an interval.

The study helps policy makers to monitor wider aspects of trust in e-Gov services as well as understanding their importance. The study enables policy makers to apply the framework to any potential case studies to evaluate the readiness score of indices and recognizing strengths and weakness of trust dimensions as well as recommending advice for improving the situation.

The study is one of the few to indicate significant indices of trust in e-Gov services in developing countries. The study shows the importance of indicators and indices by assigning a weight. Additionally, the framework can assess the readiness score of various case studies.

Decision-making problems in emergency plan selection for epidemic prevention and control (EPAC) are generally characterized by risky and uncertainty due to multiple possible emergency states and vagueness of decision information. In the process of emergency plan selection for EPAC, it is necessary to consider several obvious features, i.e. different states of epidemics, dynamic evolvement process of epidemics and decision-makers' (DMs') psychological factors such as risk preference and loss aversion.

In this paper, a novel decision-making method based on cumulative prospect theory (CPT) is proposed to solve emergency plan selection of an epidemic problem, which is generally regarded as hybrid-information multi-attribute decision-making (HI-MADM) problems in major epidemics. Initially, considering the psychological factors of DMs, the expectations of DMs are chosen as reference points to normalize the expectation vectors and decision information with three different formats. Subsequently, the matrix of gains and losses is established according to the reference points. Furthermore, the prospect value of each alternative is obtained and the comprehensive prospect values of alternatives under different states are calculated. Accordingly, the ranking of alternatives can be obtained.

The validity and robustness of the proposed method are demonstrated by a case calculation of emergency plan selection. Meanwhile, sensitivity analysis and comparison analysis with fuzzy similarity to ideal solution (FTOPSIS) method and TODIM (an acronym in Portuguese for interactive and MADM) method illustrate the effectiveness and superiority of the proposed method.

An emergency plan selection method is proposed for EPAC based on CPT, taking into account the psychological factors of DMs.

Highlights

1. This paper proposes a new CPT-based EDM method for EPAC under a major epidemic considering the psychological factorsof DMs, such as risk preference, loss aversion and so on.

2. The authors' work gives approaches of normalization, comparison and distance measurement for dealing with the integration of three hybrid formats of attributes.

3. This article gives some guidance, which contributes to solve the problems of risk-based hybrid multi-attribute EDM.

4. The authors illustrate the advantages of the proposed method by a sensitivity analysis and comparison analysis with existing FTOPSIS method and TODIM method.

This paper proposes a new CPT-based EDM method for EPAC under a major epidemic considering the psychological factorsof DMs, such as risk preference, loss aversion and so on.

The authors' work gives approaches of normalization, comparison and distance measurement for dealing with the integration of three hybrid formats of attributes.

This article gives some guidance, which contributes to solve the problems of risk-based hybrid multi-attribute EDM.

The authors illustrate the advantages of the proposed method by a sensitivity analysis and comparison analysis with existing FTOPSIS method and TODIM method.

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.