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This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.

To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed.

The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results.

Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.

The aim of this paper is to solve the problem of low accuracy of traditional fatigue crack growth (FCG) prediction methods.

The GMSVR model was proposed by combining the grey modeling (GM) and the support vector regression (SVR). Meanwhile, the GMSVR model parameter optimal selection method based on the artificial bee colony (ABC) algorithm was presented. The FCG prediction of 7075 aluminum alloy under different conditions were taken as the study objects, and the performance of the genetic algorithm, the particle swarm optimization algorithm, the n-fold cross validation and the ABC algorithm were compared and analyzed.

The results show that the speed of the ABC algorithm is the fastest and the accuracy of the ABC algorithm is the highest too. The prediction performances of the GM (1, 1) model, the SVR model and the GMSVR model were compared, the results show that the GMSVR model has the best prediction ability, it can improve the FCG prediction accuracy of 7075 aluminum alloy greatly.

A new prediction model is proposed for FCG combined the non-equidistant grey model and the SVR model. Aiming at the problem of the model parameters are difficult to select, the GMSVR model parameter optimization method based on the ABC algorithm was presented. the results show that the GMSVR model has better prediction ability, which increase the FCG prediction accuracy of 7075 aluminum alloy greatly.

Karl Marx's social capital reproduction theory is his significant contribution to economics. The purpose of this paper is to review the contributions of the exploration of Chinese economists (especially Professor Liu Guoguang) in the concretization of Marx’s social capital reproduction theory combined with socialist construction since 1949.

During this process, Professor Liu Guoguang, a famous Chinese Marxist economist, has made an outstanding contribution by creating a Marxist social capital reproduction model with Chinese characteristics and a distinctive Marxist economic growth model. Professor Liu's exploration is still of crucial practical significance to building a socialist market economy today.

The process and achievements in the sinicization exploration of Marx's social capital reproduction theory were reviewed. With the reform and opening up, fundamental changes have occurred in China's economic system – the centralized planned economic system has been transformed into a socialist market economic system.

The planned management of the national economy is replaced by a macro-regulation system characterized by gross control gradually, and the concepts of agriculture, light industry, and heavy industry, and their intercorrelation are no longer applied in theory and policy. However, the sinicization exploration of Marx's social capital reproduction theory in the older generation of Marxist economists represented by Liu is not only of historical significance but also of important practical significance.

In this essay, a new NDAGM(1,N,α) power model is recommended to resolve the hassle of the distinction between old and new information, and the complicated nonlinear traits between sequences in real behavior systems.

Firstly, the correlation aspect sequence is screened via a grey integrated correlation degree, and the damped cumulative generating operator and power index are introduced to define the new model. Then the non-structural parameters are optimized through the genetic algorithm. Finally, the pattern is utilized for the prediction of China’s natural gas consumption, and in contrast with other models.

By altering the unknown parameters of the model, theoretical deduction has been carried out on the newly constructed model. It has been discovered that the new model can be interchanged with the traditional grey model, indicating that the model proposed in this article possesses strong compatibility. In the case study, the NDAGM(1,N,α) power model demonstrates superior integrated performance compared to the benchmark models, which indirectly reflects the model’s heightened sensitivity to disparities between new and old information, as well as its ability to handle complex linear issues.

This paper provides a scientifically valid forecast model for predicting natural gas consumption. The forecast results can offer a theoretical foundation for the formulation of national strategies and related policies regarding natural gas import and export.

The primary contribution of this article is the proposition of a grey multivariate prediction model, which accommodates both new and historical information and is applicable to complex nonlinear scenarios. In addition, the predictive performance of the model has been enhanced by employing a genetic algorithm to search for the optimal power exponent.

A nonclassical method, usually called memory-free approach, has shown promising potential to release arithmetic complexity and meets high memory-storage requirements in solving fractional differential equations. Though many successful applications indicate the validity and effectiveness of memory-free methods, it has been much less understood in the rigorous theoretical basis. This study aims to focus on the theoretical basis of the memory-free Yuan–Agrawal (YA) method [Journal of Vibration and Acoustics 124 (2002), pp. 321-324].

Mathematically, the YA method is based on the validity of two fundamental procedures. The first is to reverse the integration order of an improper quadrature deduced from the Caputo-type fractional derivative. And, the second concerns the passage to the limit under the integral sign of the improper quadrature.

Though it suffices to verify the integration order reversibility, the uniform convergence of the improper integral is proved to be false. Alternatively, this paper proves that the integration order can still be reversed, as the target solution can be expanded as Taylor series on [0, ∞). Once the integration order is reversed, the paper presents a sufficient condition for the passage to the limit under the integral sign such that the target solution is continuous on [0, ∞). Both positive and counter examples are presented to illustrate and validate the theoretical analysis results.

This study presents some useful results for the real performance for the YA and some similar memory-free approaches. In addition, it opens a theoretical question on sufficient and necessary conditions, if any, for the validity of memory-free approaches.

The purpose of this paper is to identify most favorable (or quasi-preferred) industry characteristics of remanufacturing industry and most favorable (or quasi-preferred) industry factors which have an effect on these characteristics so as to improve these factors.

Grey system theory has prominent advantage of using few data and uncertainty information to analyze many factors. Therefore, it is more suited for system analysis than traditional statistical analysis methods like regression analysis, variance analysis and principal component analysis, which require massive data, certain probability distribution in the data and few variant factors. So in this paper, grey incidence analysis method, which is an important part of grey system theory, is used to identify industry characteristics and key industry factor of remanufacturing industry in China and then put forward appropriate industrial policies and countermeasures to improve these industry factors.

According to the results of this study, it reveals that there are no most favorable industry characteristics and no most favorable industry factors in remanufacturing industry of China. “Annual sale of remanufacturing industry” is identified as quasi-preferred industry characteristic, and “total number of employees with master degree or above in remanufacturing enterprise” is identified as the quasi-preferred industry factor. “Total building area of remanufacturing enterprise” is referred as the most unfavorable industry factors.

Judging from the findings of this study, four practical implications are summarized as follows: “annual sale of remanufacturing industry” should be given great importance because it is a quasi-preferred industry characteristic. “Total number of employees with master degree or above in remanufacturing enterprise” and “total number of research institution and university participated in remanufacturing” should be further strengthened by establishing an industry-university-research institute collaboration network, due to the fact that they are the top two quasi-preferred industry factors. “Total investment of remanufacturing industry” and “total annual R&D expenditures” have not played their due role in improving remanufacturing industry, so they should be moderately controlled so as to reduce waste of investment. “Total building area of remanufacturing enterprise” must be strictly controlled because of its little impact on remanufacturing industry.

In this research, grey incidence analysis is applied to identify key industry factors of remanufacturing industry for the first time. It helps in finding industry factors which are in urgent need of improvement and assists in making appropriate industrial policies and countermeasures to improve them by studying relationships between industry characteristic and industry factors.

The paper aims to elucidate effective strategies for promoting the adoption of green technology innovation within the private sector, thereby enhancing the value of public–private partnership (PPP) projects during the operational phase.

Utilizing prospect theory, the paper considers the government and the public as external driving forces. It establishes a tripartite evolutionary game model composed of government regulators, the private sector and the public. The paper uses numerical simulations to explore the evolutionary stable equilibrium strategies and the determinants influencing each stakeholder.

The paper demonstrates that government intervention and public participation substantially promote green technology innovation within the private sector. Major influencing factors encompass the intensity of pollution taxation, governmental information disclosure and public attention. However, an optimal threshold exists for environmental publicity and innovation subsidies, as excessive levels might inhibit technological innovation. Furthermore, within government intervention strategies, compensating the public for their participation costs is essential to circumvent the public's “free-rider” tendencies and encourage active public collaboration in PPP project innovation.

By constructing a tripartite evolutionary game model, the paper comprehensively examines the roles of government intervention and public participation in promoting green technology innovation within the private sector, offering fresh perspectives and strategies for the operational phase of PPP projects.

The purpose of this paper is to study the grey decision model and distance measuring method of general grey number.

First, intuitionistic grey number (IGN) set and an IGN are defined by grey number probability function. Second, each interval grey number in general grey number is represented by an IGN and converts the general grey number into an IGN set. Final, the operation of two general grey numbers is defined as the operation between IGN sets, and the distance measure of the general grey number is given.

Up to now, the method of measuring the distance and the grey decision model of general grey number is established. Thus, the difficult problem for set up decision mode of general grey number has been solved to a certain degree.

The method exposed in this paper can be used to integrate information form a different source. The method that a general grey number converted to a set of IGNs could be extended to the case of grey incidence analysis models, grey prediction models and grey clustering evaluation models, which includes general grey numbers, etc.

The concepts of IGN and IGN set are proposed for the first time in this paper; The operation of two general grey numbers can be defined as the operation between IGN sets. On this basis, the algorithm of IGN, the integration operator of IGN and the distance measure between IGN sets are given.