Discovering clusters remains challenging when dealing with complex data structures, including those with varying densities, arbitrary shapes, weak separability, or the presence of noise. In this article, we propose a novel clustering algorithm called representative point-based clustering with neighborhood information (RPC-NI), which highlights the significance of neighborhood information often overlooked by existing clustering methods. The proposed algorithm first introduces a new local centrality metric that integrates both neighborhood density and topological convergence to identify core representative points, effectively capturing the structural characteristics of the data. Subsequently, a density-adaptive distance is defined to evaluate dissimilarities between these core representative points, and such distance is used to construct a minimum spanning tree (MST) over these points. Finally, an MST-based clustering algorithm is employed to yield the desired clusters. Incorporating neighborhood information enables RPC-NI to comprehensively determine representative points, and having multiple representative points per cluster allows RPC-NI to adapt to clusters of arbitrary shapes, varying densities, and different sizes. Extensive experiments on widely used datasets demonstrate that RPC-NI outperforms baseline algorithms in terms of clustering accuracy and robustness. These results provide further evidence for the importance of incorporating neighborhood information discovering clusters with complex structures.

In the context of severe global warming, accurately exploring the trend of carbon emissions intensity (CEI) changes is of great significance for mitigating climate change issues. The implementation of China's Carbon Emissions Trading Scheme (ETS) in 2013 is a policy intervention aimed at influencing CEI. The impact of intervention events makes forecasting a complex problem, which poses significant challenges to the construction of forecasting models. We first develop a quadratic time-varying nonlinear discrete grey model (QDNDGM(1,1)) to assess the intervention effect of the ETS policy. Then, a novel intervention effect-based quadratic time-varying nonlinear discrete grey model (IE-QDNDGM(1,1)) is developed to conduct the prediction under intervention effect, including an intervention term. The Whale Optimization Algorithm (WOA) is used to calculate a nonlinear parameter. We assess the intervention effect of the ETS policy in China and find that it can indeed reduce CEI. We verify the IE-QDNDGM(1,1) model’s superiority by comparing its predictive performance with that of three grey models, one statistical technique, and one artificial intelligence model. The comparative study shows the proposed model’s excellent fitting and prediction performance. An ablation experiment is conducted to validate the design of the IE-QDNDGM(1,1). Policy implications of the ETS intervention effect are discussed.

Classical clustering methods such as k-means, spectral clustering, DBSCAN, and DPC often operate under specific assumptions about data characteristics. However, the increasing diversity and complex characteristic of data, coupled with limited prior knowledge, hinder the direct application of these clustering algorithms. Existing data processing approaches, such as ReScale and CDF-TS, are capable of homogenizing cluster density, but tailor to density-based algorithms that does not perform well on weakly separated or manifold clusters. To overcome these issues, we propose a novel data processing method (ReShape) facilitating the direct application of well-known clustering algorithms without modifications. The ReShape integrates three key components: a homogenization factor for uniforming varying cluster densities, a separation factor for enhancing cluster separations, and a joint distance considering both global and local consistency to measure distances in manifold datasets. The proposed method is universally applicable, and can match implicit assumptions of existing clustering algorithms. Extensive experiments and a case study for fault diagnosis involving k-means, spectral clustering, DBSCAN, and DPC demonstrates the efficacy of the ReShape approach.

Different from conventional decision-making environments, decision makers (DMs) in a community setting usually exhibit the complex social preferences and intricate social interactions, which may lead to high-decision costs for group consensus reaching. To address this challenge, we design a minimum cost consensus-based social network group decision making (SNGDM) approach considering altruism-fairness preferences and ordered trust propagation. First, a trust propagation method with order effect and path length is proposed to estimate the completed trust relationships among DMs in order to determine the weights of DMs. Then, inspired by the interaction of altruism and fairness preferences, we define the individual altruism-fairness preference utility function and utility level for cost consensus, and explore some properties. Afterwards, a new minimum cost consensus-based SNGDM with individual altruism-fairness preference utility is constructed. Finally, the validity of the proposed consensus framework is confirmed through the carbon reduction consensus problem of China’s aviation enterprises. Moreover, the sensitivity studies and comparative analysis are conducted to further demonstrate the merits of our proposal.

The paper uses factor analysis and grey relational advantage analysis method to analyze the interactive relationship between regional scientific and technological strength and modern service industry development in Nanjing. Based on data of 1998-2008 in Nanjing, this paper calculates integrated development levels and subentry levels of scientific and technological strength and modern service industry. On this basis, the grey advantage analysis method is used to study the intrinsic relevance between scientific and technological strength and modern service industry. The results show that: the development of modern service industry in Nanjing, R&D makes the largest contribution, but the utilization of new technology is not ideal and affects the advantages of science and technology; in the upgrading of scientific and technological strength in Nanjing, a good foundation and development potential of modern service industry play a catalytic role, but there is no comparative advantage to play out. Nanjing should continue to strengthen the two-way leading role of scientific and technological strength and modern service industry, and take advantage of the mutual promotion between scientific and technological strength and modern service industry.

A model which meets the law of grey exponent has been constructed for sequences based on the analysis of modeling mechanism in grey systems theory. And data in these sequences also meet the law of grey exponent. After the model is constructed, we make some simulations and present a numerical example. The result indicates that the prediction accuracy from this new model is much higher than that from the traditional GM(1,1) model for sequences meeting the law of grey law. The conclusions from simulations and the numerical example also indicate that our proposed model in this paper is effective and applicable for sequences meeting the law of grey law.

Based on Wuxi city's data of R&D outlay, S&T personnel and GDP, this paper analyze the incidence of the S&T investment and economic growth used the relative degree incidences. The conclusion is that R&D Expenditure and S&T personnel investment both have a positive correlativity with economic growth, and R&D Expenditure investment is more important than others. This indicates that: in Wuxi, investment play more role than others in economic growth. Wuxi should pay more attention on talent introduction and education.

The grey forecast is one of the important parts in grey systems theory. According to the theory of prior using of new information, based on the present theories of buffer operators and some already existed weakening buffer operators, some new weakening buffer operators are established. Meanwhile, they are compared with the existing weakening buffer operators in effectiveness. The problem that there are some contradictions between quantitative analysis and qualitative analysis in pretreatment for vibration data sequences is resolved effectively. The research result shows the kind of new weakening buffer operators increase the forecast precision of grey forecast model remarkably.

To surmount the difficulty in solving the problem of linear programming with grey parameters (LPGP), a series of new conceptions such as the positioned linear programming, the ideal model, the critical model, and some other new ideas are put forward. The problem of how the optimum solution is affected by the variation of positioned coefficients and the range of the variation of the optimum positioned values are studied. The satisfying solution for the positioned programming and the satisfying degree of the solution were defined. Thus, the LPGP problem will be converted into several problems of ordinary linear programming. The difficulty in solving the LPGP problem and how to appraise the solution have been surmounted to a certain degree.

Grey cluster decision-making is an important part of grey system theory. And 2-tuple linguistic assessment resolves the calculation problems of the result of expert qualitative linguistic assessment. But both of them not mention how to calculate the weight of index. Based on the definitions of entropy, a method of getting weight is proposed, and considers the character of grey cluster decision-making and 2-tuple linguistic assessment, this paper proposed the method of 2-tuple linguistic assessment based on grey cluster. It can combine qualitative analysis and quantitative analysis well.

The GM(1,1) model assume the sequence is analogous to exponential law. Great error appears when it is used to simulate many nonlinear sequences. The paper proves that the growth rates of the simulated value of the GM(1,1) model and the discrete GM(1,1) model are both fixed value. If the growth rates of the primary sequence are equate, the fitted value deriving from the discrete GM(1,1) model the same as the primary sequence. The paper improves the discrete GM(1,1) model. Using the optimization method, the paper studies the initial value. The paper puts forward the solution arithmetic to the optimization and proves the efficiency of the arithmetic by means of a example. The research indicates the discrete grey extension model can greatly improve the simulated intensity and it can solve the simulated of the nonlinear nonnegative sequence.

The constraint conditions of some linear programming are presented with grey system, linear regression and qualitative analysis. Therefore, the linear programming model to adjust the internal structure of the first industry in China is developed. And its responding adjusting plans on the internal structure of the first industry in the period of “Eleven-Five” is advised. Lastly, the keys and the strategies of adjusting the internal structure of agriculture are analyzed.

By analyzing Grey decision, we think it will come down to benefits and effects of all parts during the decision. So, only if these benefits and effects are fully considered, the result of decision is scientific and rational. For multi-hierarchy decisions, the decision-makers must be endowed to different weight because of the different actions of them. In this paper, the authors deal with the A middot B-hierarchy decision. First we define the A middot B-hierarchy decision order sequences and A middot B-hierarchy decision order matrix, then compute the weighed grey incidence degree between neighbouring hierarchies of decision sequences. Furthermore, we made the integrated decision model of grey weighed hierarchy owning to the maximum principle, and develop the schemes to find the satisfied grey classes and satisfied items. Last, we illustrate the model.

This paper studies comprehension ex-post evaluation of multi-object and multi-layer projects by grey cluster evaluation model, analytical hierarchy process and experts investigation method. In order to study it, the ratio value index, before and after change threshold value index are constructed. At the same time, a comprehensive ex-post evaluation model is constructed and evaluation steps are given also. Finally, a sample is given to illustrate the rationality and validity of this model proposed in the paper. The results indicate that comprehensive ex-post evaluation model constructed in this paper can deal with problems of poor information and grey type coefficient without prominence differences better for projects comprehensive ex-post evaluation.

In this paper, the gray preference analysis of service brand extension is proposed based on A&K model, and a famous Chinese brand suning is experimented. The experimental evidence shows that complementary is a salient clue to evaluate extensions in a services context, the process quality is more important than functional quality, and brand extension strategies could probably be used more successfully for those with higher service quality.

By summarizing the recent degree of grey incidence calculating methods, the definition of the sequence similarity and degree of grey incidence axiom are pointed out ,then the absolute degree of grey incidence model in them is improved, the improved grey incidence model have some good properties and an example is given to prove the availability, rationality and practicability.

Based on the present theories of buffer operators, we established the ASBO (average strengthening buffer operator), GASBO (geometry average strengthening buffer operator), WASBO (weigh average buffer strengthening operator), and WGASBO (weigh geometry average buffer strengthening operator), etc. all of which possessed the universality and practicability. At the same time, we studied some characters and inherent relation among them, and effectively resolved some contradictions between quantitative analysis and qualitative analysis during the pretreatment of vibration data sequence. Then, we gave an example to illustrate its validity and practicability.

Grey fixed weight clustering decision-making is an important part of grey system theory. In traditional method, the weight of the indexes is given in advance. The study on how to get the weight of different indexes scientifically is not taken into account by people. In this paper, a method of getting weight is proposed based on the definition of entropy, and then the corresponding algorithm of grey fixed weight clustering decision-making based on entropy weight is given. Taken practical problem as empirical study, it indicates that the method exhibits better effect and be an effective development to grey clustering decision-making theory.

The distance of interval number and its characteristics were defined in this paper first, then based on the theories on the degree of grey incidence, namely, the more similar the curves are, the higher degree of incidence between sequences, we defined the incidence degree of interval number and discussed its characteristics. All this extended the degree of grey incidence from real number sequence to interval number sequence and widened the theories on degree of grey incidence. At the same time, not only did the grey incidence of interval number extended the applied fields, but also provided the theory basis for applying grey incidence analysis method.

A definition on degree of orderliness of industrial structure is put forward for the first time. And a concrete formula to calculate the degree of orderliness of industrial structure is given. The problems about how to choose and determine the objective structure are discussed. The degree of orderliness of industrial structure of China and each province is calculated according to statistical data from 1999 to 2002. And the outcome is analyzed. The Main viewpoint in this paper is as follows: (1) Different tactics for readjusting the industrial structure should be adopted on the basis of specific conditions in different areas. (2) To a certain degree, the process of economic growth is a process of spiral development with the industrial structure from disorderliness to orderliness, from lower-level orderliness to high-level orderliness. The growth is endless, and the readjusting is incessant.