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The purpose of this paper is to establish the grey‐weighted relationship prediction pattern of the soil organic matter content spectral inversion under the uncertainties between soil organic matter contents and spectral characteristics and the theory of grey system.

At first, according to grey‐weighted distance, a new grey relationship model is presented. Second, in order to make full use of the information of grey relationship sequences, the maximum grey relationship discrimination principle is improved and then the soil organic matter content spectral inversion pattern is put forward based on weighted grey recognition theory. A numeric example of Hengshan County in Shanxi Province is also computed in the last part of the paper.

The results are convincing: not only that soil organic matter content spectral inversion pattern based on the weighted grey recognition theory is valid, but also the model's prediction accuracy is higher; the sample's average prediction accuracy is 94.917 per cent.

The method exposed in the paper can be used at soil organic matter content hyper‐spectral inversion and even for other similar forecast problems.

The paper succeeds in realising both prediction pattern and application of soil organic matter content hyper‐spectral inversion by using the newest developed theories: weighted grey recognition theory.

The purpose of this paper is to construct a novel grey dominance variable precision rough model.

To deal with the problems that the attribute values of the decision-making object are often not exact numbers but interval grey numbers, and the decision-making attributes satisfy a certain preference relationship in the decision-making information because of the complexity and uncertainty of the real world, the authors take advantage of the theoretical thinking of the grey systems, dominance rough set theory and variable precision rough set theory, and construct a novel dominance variable precision rough set model. On the basis of the thinking logic of grey systems, the authors first define the concepts of balance degree, dominance degree and inferior degree, and then the grey dominance relationship based on the comparison of interval grey numbers. Then the authors use the grey dominance relationship to substitute for the indiscernibility relationship of the variable precision rough set so that the grey dominance variable precision rough model is naturally utilized to reduce the system's attributes in order to derive the needed decision rules. At the end, the authors use a decision-making example of the radar target selection to demonstrate the feasibility and effectiveness of the novel model.

The results show that the proposed model possesses certain fault tolerance ability and can well-realize decision rule extraction and knowledge discovery out of a given incomplete information system.

The method exposed in the paper can be used to deal with the decision-making problems with the grey information, preference information and noise data.

The paper succeeds in realizing both the grey decision-making information with preference information and noise data and the extraction of decision-making rules.

This research aims to identify, examine and evaluate barriers to the adoption of digital servitization in manufacturing firms in the case of the Sri Lankan manufacturing sector and analyze the inter-relationships among digital servitization barriers.

Based on the comprehensive literature review, 13 barriers were identified. The grey decision-making trial and evaluation laboratory (grey-DEMATEL) approach was used to uncover and analyze the relationships among barriers in terms of their overall influence and dependencies.

A prominent barrier to the success of adopting digital servitization in the Sri Lankan manufacturing sector is the lack of digital strategy in developing activities related to the design of digital service packages, organizational structures and processes. Supply chain integration is the most influential factor, which plays an important role in developing a competitive advantage by encouraging innovation process capabilities in servitized companies.

Industry practitioners can develop guidelines for adopting digital servitization practices based on the importance and interdependencies of different barriers and thereby prioritize projects within a program of digital servitization adoption in their organizations.

Research studies on barriers to digital servitization are limited to exploratory nature and have adopted mainly the qualitative approach, such as in-depth interviews. No empirical study has investigated the inter-relationships among digital servitization adoption barriers in the manufacturing sector. This study provides a holistic view of different barriers to the adoption of digital servitization in the manufacturing sector as a basis for developing comprehensive digital servitization strategies to manage and leverage complexity in digital transformation.

The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Based on the axiomatic definition of a grey number and its greyness degree in grey system theory, the whitenization mean, whitenization difference, whitenization covariance of sequences with interval grey numbers and their greyness degrees are defined in turn. In addition, the whitenization correlation coefficient and its greyness degree of sequences with interval grey numbers are also defined. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenization value and greyness degree of correlation coefficient to form of interval grey numbers are put forward further.

The whitenization value of correlation coefficient efficient of two arbitrary sequences with interval grey numbers have symmetry, with same greyness degree but without normalization in the interval [−1, 1]; the mean, difference, covariance and correlation coefficient defined in statistics are all the special cases of those in sequences with interval grey numbers.

Due to the complexity of operation of grey numbers, the reliability of correlation coefficient of interval numbers sequence is difficult to be tested by constructing statistics at present. The further research is needed.

The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.

On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.

This paper attempts to extend classic absolute degree of grey incidence so that the extended model can be used for grey number sequences.

The classic absolute degree of grey incidence was extended according to basic principles of grey incidence analysis. First, modelling methods and theories of the classic grey incidences were summarized. Then, the zeroing starting operator in grey incidence was extended for grey sequence. Third, the parameters in classic incidence degree were redefined, and an absolute degree of grey incidence for grey number sequences was proposed. The degree can not only be applied to grey number sequence, but also contains the uncertain information of analysis result. Fourth, two non‐linear programming models were constructed to estimate the grey coverage interval of absolute degree of incidences. Finally, the comparison method of grey numbers was introduced for sorting the different absolute degrees of incidences.

A theoretically feasible absolute degree of grey incidence was constructed for grey sequence. A case study showed that the proposed incidence degree was an effective method for grey sequence incidence analysis.

The method exposed in the paper can be used for grey sequences clustering, grey decision making, multi‐attribute decision making theory, uncertain target recognition and other related fields.

The paper succeeded in establishing an incidence analysis model for grey sequences which was still a research gap in grey system theory.

It is important to understand the factors that are significant in supply chain (SC) collaboration decision making and whether supply chain collaborative factors that are considered in the literature are still valid. To date, SC collaboration has not been extensively studied in the literature with supply chain finance (SCF) factors to evaluate SCF performance. Therefore, in this paper, the authors investigate the interrelationships between SCF and supply chain collaborative (SCC) factors for achieving SCF performance. The authors identified the most important factors from the literature on SCF and SCC and with inputs from experts in the textile industry in Pakistan.

The authors employed the Gray-Decision Making Trial and Evaluation Laboratory approach to help examine the cause-and-effect relationship between the factors and identify the influence of each factor on the others.

The findings showed that the most prominent factors of the study are “level of digitalization”, “information sharing”, and “collaborative communication”, and “most effect factors of this study are incentive alignment” and “information quality”. Furthermore, the “Level of digitalization” was identified as the factor with the central role and most significant correlation with other factors.

The major implication of the study is that textile industries should effectively develop their supply chain decisions after analyzing their internal and external factors, which will help in developing strategies that will facilitate better management of SCF relationships. The limitations of the study are that only 15 SCF and supply chain collaborative factors were considered, and time and scope are also limited. This study is only applied in the textile industry, so generalization may be limited.

To date, this study is the only one that has taken into consideration SCC with SCF factors to evaluate supply chain performance. This paper therefore makes this initial attempt and original contribution to this discussion, which can be helpful for those working to enhance supply chain performance, such as practitioners and policymakers.

Many current video games feature virtual worlds inhabited by autonomous 3D animated characters. These characters often fall short in their ability to participate in social interactions with each other or with people. Increasing the social capabilities of game characters could increase the potential of games as a platform for social learning. This article presents advances in the area of social autonomous character design. Specifically, a computational model of social relationship formation is described. This model formed the basis for a game entitled “AlphaWolf” that allows people to play the role of newborn pups in a pack of virtual wolves, helping the pups to find their place in the social order of the pack. This article offers the results from a 32‐subject user study that assessed the social relationship model, showing that it effectively represents the core elements of social relationships in a way that is perceivable by people. Additionally, this article proposes a game that will allow parents, teachers and children to experiment with computational social behavior through social virtual characters. This research contributes to the development of games for social learning by offering a set of viable algorithms for computational characters to form social relationships, and describing a project that could utilize this model to enable children to learn social skills by interacting with game characters.

The purpose of this paper is to study the extensive method of grey target based on multi‐stage linguistic label, which is a hypothesis of incomplete information of the weight of stage and decision maker.

For the incomplete weight information case, the weight model for the stage and decision maker is put forward based on the requirement of maximum difference among the alternatives. Also, the weight of the decision maker is estimated by the grey relationship method and the Euclid distance method.

As a result, the method of multiple stage grey target decision making based on linguistic label is suggested. In the incomplete information case, the weight model is suggested and the aggregation is put forward. The suggested method is clear and simple, which can be used in multi‐criteria decision making fields.

This paper offers a very useful result for multi‐attribute decision making.

This paper succeeds in studying the extensive method of grey target based on multi‐stage linguistic label, which is a hypothesis of incomplete information of the weight of stage and the decision maker.

As the grey systems theory has been used over the time in different economic areas, in the following, a short literature review will be put forward, starting from the usage of these theory in the supply chain management, decision-making process, financial performance evaluation, credit risk, energy consumption, investment efficiency, etc. The purpose of this paper is to identify some key studies from all the economic areas in which the grey systems can be used in order to open and to bring to the researchers new domains in which they can manifest their interest and in which they can successfully use the methods offered by the grey systems theory.

Using the search engine offered by the Web of Science, a literature review has been performed for the economic grey systems applications developed over the time on both economic diagnosis and system’s forecasting. In addition, some hybrid grey systems theory – artificial intelligence techniques models have also been presented.

The grey systems theory has brought its contribution to numerous economic application from various fields such as: supply chain management, decision-making process, financial performance evaluation, credit risk, energy consumption, investment efficiency, firms’ bankruptcy, product development, consumer income, monetization ratio, etc.

The present paper identifies the some of the most representative examples in which the grey theory has been used, but, in the same time, there are a lot of studies that have not been mentioned here due to the lack of space.

Unlike other review papers written on the grey systems theory area, the present paper is only focusing on the economic applications in which this theory has been successfully used, bringing to the reader a general overview on this field and, in the same time, enabling new research perspectives.

This study has two main objectives: (1) to expand the application areas of grey system theory and (2) to select the most livable city in Turkey.

Choosing the most livable city is a complex problem that requires many criteria to be considered. It is important to select decision points according to which the criteria selection will be made and to what extent the criteria will affect the evaluation. For this purpose, a questionnaire was prepared to determine the criteria to be used in the assessment. The survey results were evaluated by the factor analysis (FA) and it was found that the criteria included in the survey were grouped under seven factors. Then, criteria weights were assigned to the determined criteria using the analytic hierarchy process (AHP). At the last stage, Turkey's six most popular cities are graded using the grey relational analysis (GRA) to reduce the uncertainty existing in the process of evaluation.

The obtained results indicated that the most livable city in Turkey is Istanbul. Istanbul is followed by Izmir, Antalya, Eskisehir, Bursa and Ankara, respectively. Considering that Istanbul is a center of attraction in many respects, this result is not a surprise for many people. It is also observed that the results obtained overlap with similar studies in the literature.

Grey system theory and grey numbers have not been previously used to select the most livable city. With this aspect, this study has expanded the application of grey system theory and made an important contribution to the literature.