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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.

Equally weighted factors and initial data from behavioural sequences are used for calculating the degree of grey incidence in Deng’s grey incidence analysis. However, certain grey information cannot be directly obtained, and the correlation coefficients of each sequence at different times are of different importance to the system. The purpose of this paper is to propose an improved grey incidence model with new grey incidence coefficients and weighted degree of grey incidence. Some grey information can be obtained more easily by using the grey transformation sequences, and the maximum entropy method is used to calculate the weights of new grey incidence coefficients, so the new degree of grey incidence was distinguished more effectively by the proposed model.

New grey incidence coefficients are defined using transformation sequences of the initial data. To overcome the shortcomings arising from the use of equal weights, the maximum entropy method is proposed for determining the weights of the grey incidence coefficients. The resulting model optimises the classical models and evaluates the influencing factors more effectively. The effectiveness of the model was verified by a numerical example. Furthermore, the model was used for analysing the main influencing factors of the tertiary industry in China.

The proposed model optimises the classical models, and the application example shows that urbanisation has the greatest effect on employment in the tertiary sector.

An improved grey incidence model is proposed that improves the grey incidence coefficients and their weights, and has better performance than the classical models. The model was successfully used in the analysis of the influence factors of the tertiary industry in China. The results indicate that the model can reflect the significance of incidence coefficients at different time points; therefore, their fluctuation can be effectively controlled.

In line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems.

Though the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept.

Four well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm.

The algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

The purpose of this paper is to propose a multi-scale extended grey target decision method for dealing with multi-attribute decision-making problems with interval grey numbers whose value distribution information is asymmetrical.

First, the whitenization weight function (WWF) was adopted to show the value distribution information of interval grey numbers. The definitions of kernel, degree of greyness, relative kernel and whitenization standard deviation of interval grey numbers were given based on the WWF. Then, the relative kernel grey target and whitenization standard deviation grey target were constructed to take full advantage of the owned decision information. Finally, the relative bull’s-eye coefficient was proposed to rank the preference order of all alternatives.

The relative bull’s-eye coefficient reflects the influence of the decision information on decision results with respect to the mean level and value distribution of attribute values. Thus, the decision-maker could set the return and risk adjustment coefficient according to their preferences and select the optimal alternative with a high expected return and low risk.

The paper considers the valve distribution information of interval grey numbers, and a novel definition for kernels, degrees of greyness, relative kernels and whitenization standard deviations, which are given based on the WWF. The paper not only considers the influence of mean levels of decision information over decision results, but also takes the value distribution information into account.

Alternating current (AC) corrosion is a type of corrosion that occurs in buried pipelines under AC stray current interference, which can increase the hydrogen embrittlement sensitivity of pipelines. However, rare research works have been conducted on the hydrogen permeability characteristics of pipeline steel under AC stray current interference. The purpose of this paper is to study hydrogen permeation behavior of X80 steel under AC stray current interference.

In this paper, the hydrogen permeation behavior of X80 steel under AC interference is studied by AC hydrogen charging experiment in a dual electrolytic cell. The relationship between hydrogen evolution rate and hydrogen permeation flux is studied using the gas collection method. The difference between AC hydrogen permeability and direct current (DC) hydrogen permeability is also discussed.

The anodic dissolution caused by AC corrosion promotes the chemical desorption reaction of the adsorbed hydrogen atoms on the surface, reducing the hydrogen atom absorption ratio by 70%. When the AC is smaller than 150░ A/m², the hydrogen permeation process is controlled by the hydrogen atom generation rate, and the hydrogen permeation flux increases with the increase in hydrogen atom generation rate. When the AC exceeds 400░ A/m², the hydrogen permeation process is controlled by the absorption ratio. The hydrogen permeation flux decreases with the decrease in the absorption ratio. Under AC interference, there is a maximum hydrogen permeation flux that linearly correlates to the H⁺ concentration in the solutions.

The high-strength steel is very sensitive to hydrogen embrittlement, and X80 steel has been widely used in oil and gas pipelines. To date, no research has been conducted on the hydrogen permeation behavior of pipeline steel under AC interference, and the hydrogen permeability characteristics of pipeline steel under AC interference are not clear. The research results of this paper are of great significance for ensuring the intrinsic safety of high-strength pipelines under AC stray current interference.

This study applied the GM(1,1) model of Grey theory to forecast sales of eight sub‐category non‐alcoholic beverages in Taiwan between 2001 and 2003. According to our measured results, the accuracy of the new forecasting model exceeds 95 per cent. The validity of predictions using the new model is clearly high. The model estimates that the total beverages market will grow, but growth rates will vary for individual sub‐categories. In relation to current growth, from 2001 to 2003, tea drinks, carbonated drinks, functional drinks and sports drinks will experience decreased market growth, while bottled water and fruit and vegetable juices will be a high growth market and coffee drinks and other drinks will enjoy improved sales. These results provide a valuable reference for the Taiwanese beverage industry developing marketing plans.

The knowledge of goals of the successor, who is preparing to take over the business, is extremely important for the succession process and further operation of a family enterprise. The aim of this study is to structure the goals of Polish family enterprises’ successors and to develop a Synthetic Model of the goals of Polish family enterprises' successors with the application of grey clustering evaluation models.

Research into the specifics of the diagnosis and assessment of the goals set for the successors of the first succession in family businesses in Poland was carried out in the third quarter of 2016 at two stages using two research methods: in-depth group interview and individual interview. The main aim of the first stage was the extraction of subjectively identified goals by family enterprises' successors (based on their succession experience). The statements were open and obtained during two in-depth group interviews (2 FGI) with successors being in the process of succession at its various stages (total, n = 14). The respondents presented their experiences connected with the succession process along with emotions that are associated with it. In one of the interview stages, the respondents were asked to enumerate their individual goals they set for themselves in the context of upcoming changes. Next, the group agreed on the most frequently mentioned goals by creating their verbal interpretation. The obtained list of 20 goals was recorded and discussed, and thanks to the application of the elimination rule in the collective decision-making process, that list was reduced to 10 goals, which was approved by all participating successors.

The results show the developed Synthetic Model of the goals of family enterprises’ successors. The study singled out four groups of successors: (1) successors who do not work in the family enterprise yet, (2) successors holding lower-level positions, (3) successors holding managerial positions, (4) successors who manage the entire company. As a result of the calculations, the developed Synthetic Model of the goals of family enterprises' successors was positively verified for successors working in higher-level positions and successors managing the entire family enterprise.

In order to use the results of clustering, e.g. for conducting studies on large samples with the use of statistical tools, a reduced number of goals should be taken into account. A thorough study of three goals may bring results similar to the study of the original ten successors of Polish family enterprises in the process of succession. The aim of future research is to develop a mathematical model using optimization functions that enable selection of elements representing individual clusters in such a way that it leads to the extraction of the elements with the highest value in relation to the accepted criterion for assessing their value.

In the future, conducting family business research in accordance with the developed methodology requires a look at the proposed list of successor goals obtained during the Focus Group Interview (FGI) as it could be shortened using the Cluster of Grey Incidence method. Shortening the list of goals has its analytic and practical justifications. The study of the full list of goals in subsequent (and numerous further studies) could lead to errors related to, for example, different interpretation of goals among the investigated successors. Furthermore, the full list of goals would increase costs and extend research time.

Given the maturation of the internet and virtual communities, an important emerging issue in the humanities and social sciences is how to accurately analyze the vast quantity of documents on public and social network websites. Therefore, this chapter integrates political blogs and news articles to develop a public mood dynamic prediction model for the stock market, while referencing the behavioral finance perspective and online political community characteristics. The goal of this chapter is to apply a big data and opinion mining approach to a sentiment analysis for the relationship between political status and economic development in Taiwan. The proposed model is verified using experimental datasets collected from ChinaTimes.com, cnYES.com, Yahoo stock market news, and Google stock market news, covering the period from January 1, 2016 to June 30, 2017. The empirical results indicate the accuracy rate with which the proposed model forecasts stock prices.