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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.

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.

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.

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.

When the probability of each model is known, a natural idea is to select the most probable model. However, in many practical situations, the exact values of these probabilities are not known; only the intervals that contain these values are known. In such situations, a natural idea is to select some probabilities from these intervals and to select a model with the largest selected probabilities. The purpose of this study is to decide how to most adequately select these probabilities.

It is desirable to have a probability-selection method that preserves independence. If, according to the probability intervals, the two events were independent, then the selection of probabilities within the intervals should preserve this independence.

The paper describes all techniques for decision making under interval uncertainty about probabilities that are consistent with independence. It is proved that these techniques form a 1-parametric family, a family that has already been successfully used in such decision problems.

This study provides a theoretical explanation of an empirically successful technique for decision-making under interval uncertainty about probabilities. This explanation is based on the natural idea that the method for selecting probabilities from the corresponding intervals should preserve independence.

Financial performance has been paid attention at an unprecedented level, which can be confirmed as a fact that the quantitative expansion of financial performance evaluation work. The purpose of this study is to propose a more appropriate model for financial performance evaluation under the unbalanced development.

This paper introduces the differentiation criteria to eliminate the deviation caused by the same principle for multiple performance evaluation objects whose development are unbalanced; Then the generalized grey number is adopted to describe the value of performance evaluation index; and the information entropy weight is used to obtain the index weight to reduce the artificial judgment error; Finally, the generalized grey information entropy weight TOPSIS evaluation model is constructed.

Empirical research shows that in the new evaluation model, the differentiated possibility function effectively eliminates the deviation caused by the same principle, the application of information entropy weight reduces the human judgment error, and the value of generalized grey number further enhances the closeness of the results. Moreover, it is also found that in different scenarios, an adaptive performance evaluation model should be selected to match scientifically reasonable results.

The proposed model offers a solution for financial performance evaluation considering unbalanced development among cities. It can be realized by determining the differentiation possibility function matrix, and then the information entropy weight TOPSIS evaluation model can be constructed. This model reflects the actual situation, improves the performance evaluation accuracy, and can be used under similar conditions.

This study aims to propose a facilitating methodology for the application of Fuzzy FMEA (Failure Mode and Effect Analysis), comparing the traditional approach with fuzzy variations, supported by a case application in the aeronautical sector.

Based on experts' opinions in risk analysis within the aeronautical sector, rules governing the relationship between severity, occurrence, detection and risk factor were defined. This served as input for developing a fuzzyfied FMEA tool using the Matlab Fuzzy Logic Toolbox. The tool was applied to the sealing process in a company within the aeronautical sector, using triangular and trapezoidal membership functions, and the results were compared with the traditional FMEA approach.

The results of the comparative application of traditional FMEA and fuzzyfied FMEA using triangular and trapezoidal functions have yielded valuable insights into risk analysis. The findings indicated that fuzzyfied FMEA maintained coherence with the traditional analysis in identifying higher-risk effects, aligning with the prioritization of critical failure modes. Additionally, fuzzyfied FMEA allowed for a more refined prioritization by accounting for variations in each variable through fuzzy rules, thereby improving the accuracy of risk analysis and providing a more realistic representation of potential hazards. The application of the developed fuzzyfied FMEA approach showed promise in enhancing risk assessment in the aeronautical sector by considering uncertainties and offering a more detailed and context-specific analysis compared to conventional FMEA.

This study emphasizes the potential of fuzzyfied FMEA in enhancing risk assessment by accurately identifying critical failure modes and providing a more realistic representation of potential hazards. The application case reveals that the proposed tool can be integrated with expert knowledge to improve decision-making processes and risk mitigation strategies within the aeronautical industry. Due to its straightforward approach, this facilitating methodology could also prove beneficial in other industrial sectors.

This paper presents the development and application of a facilitating methodology for implementing Fuzzy FMEA, comparing it with the traditional approach and incorporating variations using triangular and trapezoidal functions. This proposed methodology uses the Toolbox Fuzzy Logic of Matlab to create a fuzzyfied FMEA tool, enabling a more nuanced and context-specific risk analysis by considering uncertainties.

Supply chain management (SCM)-embedded valuable resources, such as capital, raw-materials, products, partners, customers and finished inventories, where the evaluation of environmental texture and flexibilities are needed to perceive sustainability. The present study aims to identify and evaluate the directory of green and agile (G-A) attributes based on decision support framework (DSF) for identifying dominating measures in SCM.

DSF is developed by exploiting generalized interval valued trapezoidal fuzzy numbers (GIVTFNs). Two technical approaches, i.e. degree of similarity approach (DSA) and distance approach (DA) under the extent boundaries of GIVTFNs, are implicated for data analytics and for recognizing constructive G-A measures based on comparative study for robust decision. A fuzzy-based performance indicator, i.e. fuzzy performance important index (FPII), is presented to enumerate the weak and strong G-A characteristics to manage knowledge risks in allied business environment.

The modeling is illustrated from the insights of decision-makers for augmenting business value based on cognitive identification of measures, where the best performance score is identified by the “sustainable packaging” under the traits of green supply chain management (GSCM). “The use of Web-based applications” under the traits of agile supply chain management (ASCM) and “Outsourcing flexibility” under traits of ASCM is found as the second and third most significant performance characteristics for business sustainability. Additionally, the “Reutilization (recycling) and reprocessing” under GSCM in manufacturing and “Responsiveness and speed toward customers needs” under ASCM are found difficult in attainment.

The G-A evaluation will assist in attaining performance excellence in day-to-day operations and overall functioning. The outcomes will help executives to plan strategic objectives and attaining success.

To reinforce the capabilities of SCM, wide extent of G-A dimensions are presented, concept of FPII is reported to manage knowledge risks based on identification of strong attributes and two technical approaches, i.e. DSA and DA under GIVTFNs are presented for attaining robust decision and directing managerial decision-making process.