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The purpose of this paper is to explore a new approach to solve the problem of positive and negative offset in the calculation process of integral elements, then propose a series of new grey relational degree model for cross sequences.

The definitions of cross sequences and area elements have been proposed at first. Then the concept of difference degree between sequences has been put forward. Based on the definition of difference degree between sequences, various modified grey relational degree models for cross sequences have been proposed to solve the measurement problem of cross sequence correlation relationships.

(1) The new definition of cross sequences; (2) The area element; (3) Various modified grey relational degree models for cross sequences based on the definition of difference degree between sequences.

The grey relational analysis model of cross sequences is a difficult problem in grey relational analysis. The new model proposed in this article can effectively avoid the calculation deviation of grey relational analysis model for cross sequences, and reasonably measure the correlation between cross sequences. The new model was used to analyse the food consumer price index in Shaanxi Province, clarifying the relationship between different types of food consumer price indices, some interesting results that are not completely consistent with general economic theory were obtained.

The new definition of cross sequences, the area element and various modified grey relational degree models for cross sequences were proposed.

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 establishes a quality model for automation assembly of range hood impeller based on generalized grey relational degree, it improves the debugging efficiency of the newly developed assembly workstation.

First, spot check the trial production impellers and obtain three indexes that reflect the assembly quality of the impellers. Then, analyze the parameters that affect the assembly quality of the impeller using grey relational analysis (GRA), establish a model for the assembly quality of the range hood impeller based on the generalized grey relational degree and identify the main parameters. After that, analyze the transmission structure of automation assembly workstation, identify the reasons that affect parameters and propose improvement plans. Finally, a trial production is conducted on the automation assembly workstation after adopting the improved plan to verify the quality model of impeller automation assembly.

The research shows that compared to manual assembly, the automation assembly quality of the impeller using GRA model has been improved, shortening the debugging cycle of the newly developed assembly workstation.

The newly developed automation equipment will have some problems in the trial production stage, which often rely on the experience of engineers for debugging. In this paper, the automation assembly quality model of range hood impeller based on GRA is established, which can not only ensure the quality of finished impeller but also shorten the debugging cycle of the equipment. In addition, GRA can be widely used in the commissioning of other automation equipment.

This study has developed a set of impeller automation assembly workstation. The debugging method in the trial production stage is beneficial to shorten the trial production time and improve the economic benefits.

With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

In many of today’s manufacturing industries, such as automobile, aerospace, defence, die and mould making, medical and electrical discharge machining (EDM) has emerged as an effective material removal process. In this process, a series of discontinuous electric discharges is used for removing material from the workpiece in the form of craters generating a replica of the tool into the workpiece in a dielectric environment. Appropriate selection of the tool electrode material and combination of input parameters is an important requirement for performance enhancement of an EDM process. This paper aims to optimize an EDM process using single-valued neutrosophic grey relational analysis using Cu-multi-walled carbon nanotube (Cu-MWCNT) composite tool electrode.

This paper proposes the application of grey relational analysis (GRA) in a single-valued neutrosophic fuzzy environment to identify the optimal parametric intermix of an EDM process while considering Cu-MWCNT composite as the tool electrode material. Based on Taguchi’s L9 orthogonal array, nine experiments are conducted at varying combinations of four EDM parameters, i.e. pulse-on time, duty factor, discharge current and gap voltage, with subsequent measurement of two responses, i.e. material removal rate (MRR) and tool wear rate (TWR). The electrodeposition process is used to fabricate the Cu-MWCNT composite tool.

It is noticed that both the responses would be simultaneously optimized at higher levels of pulse-on time (38 µs) and duty factor (8), moderate level of discharge current (5 A) and lower level of gap voltage (30 V). During bi-objective optimization (maximization of MRR and minimization of TWR) of the said EDM process, the achieved values of MRR and TWR are 243.74 mm³/min and 0.001034 g/min, respectively.

Keeping in mind the type of response under consideration, their measured values for each of the EDM experiments are expressed in terms of linguistic variables which are subsequently converted into single-valued neutrosophic numbers. Integration of GRA with single-valued neutrosophic sets would help in optimizing the said EDM process with the Cu-MWCNT composite tool while simultaneously considering truth-membership, indeterminacy membership and falsity-membership degrees in a human-centric uncertain decision-making environment.

The importance of consumer experience in service industries, particularly healthcare, is widely acknowledged as it captures the intricacies of quality management. In tandem with the emerging research trends that evaluate service excellence through user experience, this study renders a performance analysis of the dimensions of consumer experience that individually or collectively shape healthcare consumers’ perceptions of service quality.

A cross-sectional study was conducted across 13 mid-tier corporate hospitals to collect data from 438 patients. The data was processed through factor analysis in SPSS to confirm sample adequacy and factor extractability. Further, two independent multi-criteria decision-making (MCDM) tools, Fuzzy Technique for Order Performance by Similarity to Ideal Solution (F-TOPSIS) and Grey Relational Analysis (GRA), were executed to render performance analysis of identified factors.

Using F-TOPSIS, factors such as “information” and “hospital environment” received higher performance ratings, while items related to “communication with doctors” and “humanistic care” received lower rankings. Minor yet anticipated deviations were observed while verifying performance scores using GRA. Nonetheless, both outcomes exhibited a strong correlation coefficient of 97.14%, confirming analytical consistency.

Hitherto, such usages of hybrid MCDM techniques have rarely been executed to convey a clear understanding of consumers’ experiences in healthcare services. Moreover, the findings provide a clear insight into consumers’ key response areas, which can further be translated to maximize consumer gratification, thus assisting healthcare managers in improving service performance and clinical decision-making.

This paper compares traditional and digital banks in nine categories of complaints and provides insights to improve complaint management performance.

A sample of the major Brazilian banks was defined, with four traditional and four digital banks. The grey relational analysis (GRA) method was applied as an analytical tool to compare the most frequent complaints of traditional and digital banks. The most critical complaints identified were considered to discuss potential improvements in complaint management using quality and service management system concepts.

The GRA method enabled the development of a ranking of nine complaint categories, considering the uncertainty involved in the data and differentiating between traditional and digital banks. The most critical complaint categories, regardless of business model, were “unauthorized charges” and “poor service,” which were ranked first and second in the frequency rankings. Traditional and digital banks differed the most in the complaint category “unfair charge,” ranking third and eighth in the rankings, respectively.

Managers from traditional and digital banks can improve complaint management performance by applying ISO 9001 and ISO 20000 concepts such as incident, problem, change, service level, availability, capacity, information technology service continuity and financial management.

The study's findings can help bank managers improve service levels in the face of technological competition. Improving these organizations is an important factor for developing countries such as Brazil.

This paper reveals the differences between two business models regarding complaint management. It also considers a methodological approach to include the uncertainty related to customers' perception and subjectivity inherent to complaints.

The criteria importance through intercriteria correlation (CRITIC) and range of value (ROV) combined methods were used to determine a single index for all multiple responses.

This paper used cold metal transfer (CMT) and pulse metal-inert gas (MIG) welding processes to study the weld-on-bead geometry of AA2099-T86 alloy. This study used Taguchi's approach to find the optimal setting of the input welding parameters. The welding current, welding speed and contact-tip-to workpiece distance were the input welding parameters for finding the output responses, i.e. weld penetration, dilution and heat input. The L9 orthogonal array of Taguchi's approach was used to find out the optimal setting of the input parameters.

The optimal input welding parameters were determined with combined output responses. The predicted optimum welding input parameters were validated through confirmation tests. Analysis of variance showed that welding speed is the most influential factor in determining the weld bead geometry of the CMT and pulse MIG welding techniques.

The heat input and weld bead geometry are compared in both welding processes. The CMT welding samples show superior defect-free weld beads than pulse MIG welding due to lesser heat input and lesser dilution.

Supplier selection along with continuous evaluation of their performance is a crucial activity in healthcare supply chain management for effective utilization of scarce resources while providing quality service at an affordable price, and minimizing chances of stock-out, avoiding serious consequences on the illness or fatality of the patients. Presence of both qualitative and quantitative evaluation criteria, set of potential suppliers and participation of different stakeholders with varying interest make healthcare supplier selection a challenging task which can be effectively solved using any of the multi-criteria decision making (MCDM) methods.

To deal with various qualitative criteria, like cost, quality, delivery performance, reliability, responsiveness and flexibility, this paper proposes integration of grey system theory with a newly developed MCDM tool, i.e. mixed aggregation by comprehensive normalization technique (MACONT) to identify the best performing supplier for pharmaceutical items in a healthcare unit from a pool of six competing alternatives based on the opinions of three healthcare professionals.

While assessing importance of the six evaluation criteria and performance of the alternative healthcare suppliers against those criteria using grey numbers, and exploring use of three normalization procedures and two aggregation operations of MACONT method, this integrated approach singles out S5 as the most compromised healthcare supplier for the considered problem. A sensitivity analysis of its ranking performance against varying values of both balance parameters and preference parameters also validates its solution accuracy and robustness.

This integrated approach can thus efficiently solve healthcare supplier selection problems based on qualitative evaluation criteria in uncertain group decision making environment. It can also be deployed to deal with other decision making problems in the healthcare sector, like supplier selection for healthcare devices, performance evaluation of healthcare units, ranking of physicians etc.

This paper aims to enable the analysts of reliability and safety systems to evaluate the risk and prioritize failure modes ideally to prefer measures for reducing the risk of undesired events.

To address the constraints considered in the conventional failure mode and effects analysis (FMEA) method for criticality assessment, the authors propose a new hybrid model combining different multi-criteria decision-making (MCDM) methods. The analytical hierarchy process (AHP) is used to construct a criticality matrix and calculate the weights of different criteria based on five criticalities: personnel, equipment, time, cost and quality. In addition, a preference ranking organization method for enrichment evaluation (PROMETHEE) method is used to improve the prioritization of the failure modes. A comparative work in which the robust data envelopment analysis (RDEA)-FMEA approach was used to evaluate the validity and effectiveness of the suggested approach and simplify the comparative analysis.

This work aims to highlight the real case study of the automotive parts industry. Using this analysis enables assessing the risk efficiently and gives an alternative ranking to that acquired by the traditional FMEA method. The obtained findings offer that combining of two multi-criteria decision approaches and integrating their outcomes allow for instilling confidence in decision-makers concerning the risk assessment and the ranking of the different failure modes.

This research gives encouraging outcomes concerning the risk assessment and failure modes ranking in order to reduce the frequency of occurrence and gravity of the undesired events by handling different forms of uncertainty and divergent judgments of experts.