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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 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.

Currently, China’s manufacturing industry chain still faces the danger of chain breakage due to the persistent “lack of technology” issue. The definition and detection of key nodes in the industry chain are significant to the enhancement of the stability of the industry chain. Therefore, detecting the key nodes in the manufacturing industry chain is necessary.

A complex network based on the links amongst listed manufacturing enterprises is built, and the authors analyse the network’s basic characteristics and vulnerability, taking into account the impact of scientific and technological innovation on the stability of the industry chain.

It is found that the high structural characteristic of midstream nodes in the naval architecture and marine engineering equipment industry chain determines their importance to stability, and the key status of upstream nodes is reflected in the weakness of technological innovation. The upstream nodes should focus on improving their independent innovation and R&D capability, whilst the midstream nodes should maintain a close supply–demand cooperation relationship.

The key node detection model for industry chain stability is constructed by considering various factors from the perspective of network and technological innovation. Empirical study is conducted to verify effectiveness of proposed method.

Natural disasters cause serious operational risks and disruptions, which further impact the food supply in and around the disaster-impacted area. Resilient functions in the supply chain are required to absorb the impact of resultant disruptions in perishable food supply chains (FSC). The present study identifies specific resilient functions to overcome the problems created by natural disasters in the FSC context.

The quality function deployment (QFD) method is utilized for identifying these relations. Further, fuzzy term sets and the analytical hierarchy process (AHP) are used to prioritize the identified problems. The results obtained are employed to construct a QFD matrix with the solutions, followed by the technique for order of preference by similarity to the ideal solution (TOPSIS) on the house of quality (HOQ) matrix between the identified problems and functions.

The results from the study reflect that the shortage of employees in affected areas is the major problem caused by a natural disaster, followed by the food movement problem. The results from the analysis matrix conclude that information sharing should be kept at the highest priority by policymakers to build and increase resilient functions and sustainable crisis management in a perishable FSC network.

The study suggests practical implications for managing a FSC crisis during a natural disaster. The unique contribution of this research lies in finding the correlation and importance ranking among different resilience functions, which is crucial for managing a FSC crisis during a natural disaster.

The purpose of this study is to analyse the magnetic field effect on Fe₃O₄/H₂O Ferrofluid flowing in a sudden expansion tube, which has specific behaviour in terms of rheology, with convex dimple fins. Because the investigation of flow separation is a prominent application in performance, the effect of magnetic field and convex dimple on the thermo-hydraulic performance of sudden expansion tube are examined, in detail.

During the solution of the boundary conditions of the sudden expansion tube, finite volume method was used. Analyses have been conducted considering the single-phase solution, steady-state, incompressible fluid and no-slip condition of the wall under forced convection conditions. In the analyses, it has been assumed that the flow was developing thermally and has been fully developed hydrodynamically.

The present study focuses on exploring the influence of the magnetic field, nanofluid concentration and convex dimple fins on the thermo-hydraulic performance of sudden expansion tube. The results indicate that the strength of the magnetic field, nanofluid concentration and convex dimple fins have a positive effect on the convective heat transfer in the system.

The authors conducted numerical studies, determining through a literature search that no one had yet investigated enhancing heat transfer on a sudden expansion tube using combinations of magnetic fields, nanofluids and convex dimple fins. The results of the numerical analyses provide valuable information about the improvement of heat transfer and system performance in electronic device cooling and heat exchangers.

The purpose of this study is to solve the issues of time-consuming and complicated computation of traditional measures, as well as the underutilization of two-dimensional (2D) phase-trajectory projection matrix, so a new set of features were proposed based on the projection of attractors trajectory to characterize the friction-induced attractors and to reveal the tribological behavior during the running-in process.

The frictional running-in experiments were conducted by sliding a ball against a static disk, and the friction coefficient was collected to reconstruct the friction-induced attractors. The projection of the attractors in 2D subspace was then mapped and the distribution of phase points was adapted to conduct the feature extraction.

The evolution of the proposed moment measures could be described as “initial rapid decrease/increase- midterm gradual decrease/increase- finally stable,” which could effectively reveal the convergence degree of the friction-induced attractors. Moreover, the measures could also describe the relative position of the attractors in phase–space domain, which reveal the amplitude evolution of signals to some extent.

The proposed measures could reveal the evolution of tribological behaviors during the running-in process and meet the more precise real-time running-in status identification.

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.

We attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.

In order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.

The results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.

By employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

The author identifies the traits of consumer resilience in emerging markets, classifies these major traits into five categories and analyses the influence relationships among them with distinctive focus on the psychological and personal resilience aspects.

The influence relations among the traits of consumer resilience from an expert perspective were identified with typical focus on electronic supply chains, and later the same was analysed through an intelligent influence modelling method, the grey causal modelling (GCM).

The major traits were analysed using the GCM, where the cause–consequence relations were observed for various objectives and the situational effects are noted. By constructing a magnitude plot and further a causal magnitude table, the important influence traits of consumer resilience for the considered case were observed and the same were auxiliary validated using an interpretive structural modelling (ISM) based approach.

As perceived from the results, it is evident that social support and recommendations from customers emerge as the principal influence traits of consumer resilience from an expert perspective, considering the case. The study can be further extended empirically to validate the findings.

Altogether, the author can recommend for practitioners that the influence of family, society, friends, peers as well as ratings from the customers can determine the level of consumer resilience. Hence, practitioners of customer relationship management can focus on improving the product and brand awareness among customers, so that more customers may recommend for typical products.

Consumer resilience depend on several factors, where the author has identified 25 major traits of the same and classified them into five major categories, including individual psychological factors, individual attitudes, individual socio demographic factors, micro environmental factors and macro environmental factors and the influence relations among them were studied from an expert perspective.

The aim of this research was to evaluate the maturity level of strategic communication management implemented by Brazilian startups.

This study employed the analytic hierarchy process (AHP), survey and Grey Fixed Weight Clustering modeling techniques. Three experts with extensive academic and practical experience in the subject participated in the AHP process, providing their opinions on the relative importance of eight variables associated with the topic under investigation, thus enabling their prioritization. Concurrently, data were collected through a survey from 23 respondents who have extensive knowledge about the realities of Brazilian startups. The weights derived from the AHP and the survey data were utilized in the Grey Fixed Weight Clustering modeling.

Based on the opinions of the 23 respondents, the level of implementation of practices related to strategic management, brand management, external image management and internal communication management is superficial. In addition, according to the majority of experts, Brazilian startups exhibited a medium level of maturity to address the key challenges related to communication management. Furthermore, this study reveals that the variables “financial resources allocation,” “stakeholder relationship” and “brand management” were deemed the most significant for the model.

The contributions presented herein can be beneficial for both researchers and startup managers seeking to enhance communication strategies in their organizations. This research also contributes by highlighting how grey systems theory can be extremely useful for conducting decision-making analyses in the context of startups, which is characterized by uncertainty and imprecise information.