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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Practical implications
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.
Originality/value
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.
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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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Practical implications
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.
Originality/value
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.
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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.
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Practical implications
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.
Originality/value
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.
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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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Practical implications
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.
Originality/value
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.
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Abdul Quadir, Alok Raj and Anupam Agrawal
The purpose of this paper is to investigate the impact of demand information sharing on products’ greening levels with downstream competition. Specifically, this study examine two…
Abstract
Purpose
The purpose of this paper is to investigate the impact of demand information sharing on products’ greening levels with downstream competition. Specifically, this study examine two types of green products, “development-intensive” (DI) and “marginal-cost intensive” (MI), in a two-echelon supply chain where the manufacturer produces substitutable products, and competing retailers operate in a market with uncertain demand.
Design/methodology/approach
The authors adopt the manufacturer-led Stackelberg game-theoretic framework and consider a multistage game. This study consider how retailers receive private signals about uncertain demand and decide whether to share this information with the manufacturer, who then decides whether to acquire this information at a certain given cost. This paper considers backward induction and Bayesian Nash equilibrium to solve the model.
Findings
The authors find that in the absence of competition, information sharing is the only equilibrium and improves the greening level under DI, whereas no-information sharing is the only equilibrium and improves the greening level under MI, an increase in downstream competition drives higher investment in greening efforts by the manufacturer in both DI and MI and the manufacturer needs to offer a payment to the retailers to obtain demand information under both simultaneous and sequential contract schemes.
Originality/value
This paper contributes to the literature by examining how the nature of products (margin intensive green product or development intensive green product) influences green supply chain decisions under information asymmetry and downstream competition.
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Xinbo Yu, Shuang Zhang, Liang Sun, Yu Wang, Chengqian Xue and Bin Li
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Xibing Li, Tian Cheng, Ming Li, Mingjian Li, Ruren Wu and Yingsi Wan
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.
Abstract
Purpose
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.
Design/methodology/approach
The research establishes the mathematical models of velocity, flux and pressure fields, etc., for lubrication performance distribution, and analyzes its load-bearing behavior.
Findings
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.
Originality/value
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.
Details
Keywords
Xibing Li, Tian Cheng, Ming Li, Mingjian Li, Ruren Wu and Yingsi Wan
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
Details
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Noel Scott, Brent Moyle, Ana Cláudia Campos, Liubov Skavronskaya and Biqiang Liu