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Grey set is the important foundation of the grey mathematics and grey system theory, and the possibility function is the way of expressing grey set. This paper aims to establish the method of determining the possibility function of grey set and discusses its extended applications.

First, the grey kernel and the grey support set of grey set are defined, and the properties of grey kernel are analyzed. Second, according to the decomposition theorem of grey set, a method of determining the possibility function of grey set is put forward in this paper, which is called the method of increasing information and taking maximum and minimum (IITMM), and then it is further simplified as the method of increasing information and taking maximum (IITM), and an simple example is given to illustrate the calculation procedure. Finally, the grey information cluster method (GICM) based on IITM is proposed and applied to the ecological and geographical environment analysis of pine caterpillar.

The results show that the grey kernel of grey set still has grey uncertainty; the method of IITM has simple calculation and strict mathematical basis, and it can synthesize the information of the research object and accords with the principle of using minimum information; the GICM and the fuzzy cluster method have the same classification effect.

The researches show that method of IITM can be used not only to determine the possibility function of the grey set effectively, but also be used for the evaluation and cluster analysis of connotative objects. The classification result of the GICM presented in this paper is more precise than that of the fuzzy cluster method.

The paper succeeds in realizing both the IITM method for determining the possibility function of grey set and the GICM based on IITM for the connotative objects.

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.

In order to make full use of the generalized greyness of interval grey number, this paper analyzes the properties and its applications of generalized greyness.

Firstly, the static properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain are analyzed. Then, this paper gives the dynamic properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain and explains the dialectical principle contained in it. Finally, the generalized greyness is used to judge the effectiveness of interval grey number transformation.

The results show that the generalized greyness of interval grey number has relativity, normativity, unity, eternity and conservation. The static and dynamic properties of generalized greyness are the same in the infinite and infinitesimal background domain, while they are different in the bounded background domain. The generalized greyness can be used as an index to judge whether the grey number transformation is greyness or information preservation.

The research shows that the generalized greyness can be used as an index to judge the validity of the grey number transformation and also can be applied in grey evaluation, grey decision-making and grey prediction and so on.

The paper succeeds in realizing the mathematical principle of “white is black”, the “greyness clock-slow effect” of the value domain of interval grey number and the generalized greyness conservation principle, which provides a theoretical basis for the rational use of generalized greyness of interval grey number.

In order to make grey relational analysis applicable to the interval grey number, this paper discusses the model of grey relational degree of the interval grey number and uses it to analyze the related factors of China's technological innovation ability.

First, this paper gives the definitions of the lower bound domain, the value domain, the upper bound domain of interval grey number and the generalized measure and the generalized greyness of interval grey number. Then, based on the grey relational theory, this paper proposes the model of greyness relational degree of the interval grey number and analyzes its relationship with the classical grey relational degree. Finally, the model of greyness relational degree is applied to analyze the related factors of China's technological innovation ability.

The results show that the model of greyness relational degree has strict theoretical basis, convenient calculation and easy programming and can be applied to the grey number sequence, real number sequence and grey number and real number coexisting sequence. The relational order of the four related factors of China's technological innovation ability is research and development (R&D) expenditure, R&D personnel, university student number and public library number, and it is in line with the reality.

The results show that the sequence values of greyness relational degree have large discreteness, and it is feasible and effective to analyze the related factors of China's technological innovation ability.

The paper succeeds in realizing both the model of greyness relational degree of interval grey number with unvalued information distribution and the order of related factors of China's technological innovation ability.

This paper aims to propose cooperative control strategies for dual-arm robots in different human–robot collaborative tasks in assembly processes. The authors set three different regions where robot performs different collaborative ways: “teleoperate” region, “co-carry” region and “assembly” region. Human holds the “master” arm of dual-arm robot to operate the other “follower” arm by our proposed controller in “teleoperation” region. Limited by the human arm length, “follower” arm is teleoperated by human to carry the distant object. In the “co-carry” region, “master” arm and “follower” arm cooperatively carry the object to the region close to the human. In “assembly” region, “follower” arm is used for fixing the object and “master” arm coupled with human is used for assembly.

A human moving target estimated method is proposed for decreasing efforts for human to move “master” arm, radial basis functions neural networks are used to compensate for uncertainties in dynamics of both arms. Force feedback is designed in “master” arm controller for human to perceive the movement of “follower” arm. Experimental results on Baxter robot platform show the effectiveness of this proposed method.

Experimental results on Baxter robot platform show the effectiveness of our proposed methods. Different human-robot collaborative tasks in assembly processes are performed successfully under our cooperative control strategies for dual-arm robots.

In this paper, cooperative control strategies for dual-arm robots have been proposed in different human–robot collaborative tasks in assembly processes. Three different regions where robot performs different collaborative ways are set: “teleoperation” region, “co-carry” region and “assembly” region.

This paper aims to research the lubrication performance of large-size rectangular oil pad in hydrostatic thrust bearing for heavy computer numerical control (CNC) vertical lathe.

The research establishes the mathematical models of velocity, flux and pressure fields, etc., for lubrication performance distribution, and analyzes its load-bearing behavior.

When hydrostatic thrust bearing’s rotating speed is within ω₁-ω₂, the oil flow generated by plate’s relative motion is greater than that generated by pressure difference and centrifugal force, and in the opposite direction, making it not easy to emit friction heat, so the rotating speed range ω₁-ω₂ should be avoided for bearing.

The research provides powerful theoretical basis for the structure design, operating reliability and practical application of large size rectangular oil pad hydrostatic thrust bearing, and realizing the prediction of its lubrication performance.

The purpose of this study with the rapid development of the heavy/large mechanical equipment, the heavy computer numerical control (CNC) vertical lathe has become the ideal processing equipment for the parts of those mechanical equipments. The main factor which affects the machining quality and efficiency of heavy CNC vertical lathe is the mechanical properties of the hydrostatic thrust bearing.

This paper did the research based on the large size sector oil pad’s lubrication performance of the hydrostatic thrust bearing in the heavy/large equipments, establishing the lubrication performance distribution mathematical model of the velocity field, flow field, pressure field and so on, analyzing the bearing behavior of the large size sector oil pad.

The results show that the oil flow generated by the plate relative motion will be greater than that generated by the pressure difference in area B, with the rotational speed’s increasing of the hydrostatic thrust bearing, and the direction is opposite. The oil flow generated by the centrifugal force will be greater than that generated by the pressure difference in area C, with the rotational speed’s increasing of the hydrostatic thrust bearing, and the direction is opposite. When the rotational speed of the hydrostatic thrust bearing is too high, the friction heat will be not easy to be sent out. The bearing rotating speed should be lower than the comparatively smaller one of ω1 and ω2, which can help avoid the rise of too high temperature.

The research provides powerful theoretical foundation for practical application of the large size sector oil pad hydrostatic thrust bearing, its structure design and operating reliability, realizing the lubrication performance prediction of the large size hydrostatic thrust bearing.

The application of the traditional failure mode and effects analysis (FMEA) technique has been widely questioned in evaluation information, risk factor weights and robustness of results. This paper develops a novel FMEA framework with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment to solve these problems.

This paper introduces innovatively interval-value Pythagorean fuzzy weighted averaging (IVPFWA) operator, Tchebycheff metric distance and interval-value Pythagorean fuzzy weighted geometric (IVPFWG) operator into the MULTIMOORA submethods to obtain the risk ranking order for emergencies. Finally, an illustrative case is provided to demonstrate the practicality and feasibility of the novel fuzzy FMEA framework.

The feasibility and validity of the proposed method are verified by comparing with the existing methods. The calculation results indicate that the proposed method is more consistent with the actual situation of project and has more reference value.

The research results can provide supporting information for risk management decisions and offer decision-making basis for formulation of the follow-up emergency control and disposal scheme, which has certain guiding significance for the practical popularization and application of risk management strategies in the infrastructure projects.

A novel approach using FMEA with extended MULTIMOORA method is developed under IVPF environment, which considers weights of risk factors and experts. The method proposed has significantly improved the integrity of information in expert evaluation and the robustness of results.

This paper aims to find an effective and standardized function transformation method to apply in both high-growth original data sequences and low-growth original data sequences, which can improve the accuracy of model prediction in GM(1, 1) forecast.

In GM(1, 1) forecast, many original data sequences need to meet the quasi-exponential characteristic by methods of function transformation. However, many methods of function transformation have complex transformation processes or narrow application range. On the basis of the research results of Ye and Li, the paper presents a standardized approach based on to original data sequences and designs four situations of the standardized approach. By using high-growth and low-growth original data sequences as the objects, respectively, the paper verifies the effectiveness of the proposed method and compares the forecasting effects of GM(1, 1) based on function transformation with the original GM(1, 1).

Most of the results show that function transformations can improve the accuracy of the conventional GM(1, 1) forecast, and transform is a powerful tool to effectively process original data sequence of GM(1, 1) modeling.

GM(1, 1) forecast have been widely used in many fields such as agriculture, economy, meteorology, and geology. The proposed method in this paper can effectively apply to prediction of high-growth original data sequences and low-growth original data sequences, to some extent, enrich and deepen application of GM(1, 1) forecast.

The paper succeeds in providing a standardized approach based on and designs four intensity levels for different data sequences based on the standardized approach.

Grey modeling technique is an important element of grey system theory, and academic articles applied to agricultural science research have been published since 1985, proving the broad applicability and effectiveness of the technique from different aspects and providing a new means to solve agricultural science problems. The analysis of the connotation and trend of the application of grey modeling technique in agricultural science research contributes to the enrichment of grey technique and the development of agricultural science in multiple dimensions.

Based on the relevant literature selected from China National Knowledge Infrastructure, the Web of Science, SpiScholar and other databases in the past 37 years (1985–2021), this paper firstly applied the bibliometric method to quantitatively visualize and systematically analyze the trend of publication, productive author, productive institution, and highly cited literature. Then, the literature is combed by the application of different grey modeling techniques in agricultural science research, and the literature research progress is systematically analyzed.

The results show that grey model technology has broad prospects in the field of agricultural science research. Agricultural universities and research institutes are the main research forces in the application of grey model technology in agricultural science research, and have certain inheritance. The application of grey model technology in agricultural science research has wide applicability and precise practicability.

By analyzing and summarizing the application trend of grey model technology in agricultural science research, the research hotspot, research frontier and valuable research directions of grey model technology in agricultural science research can be more clearly grasped.