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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.
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
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.
Practical implications
The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.
Originality/value
On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.
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Keywords
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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Keywords
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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Keywords
Rafał Mierzwiak, Marcin Nowak and Naiming Xie
The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The theoretical…
Abstract
Purpose
The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The theoretical importance of the degree of greyness concept is also due to its application in a range of uncertainty modelling methods: predictive, relational and decision-making methods. Greyness, being a result of cognitive uncertainty, was recently subjected to axiomatization in the form of grey space with the use of the classical sets theory. The purpose of this article is to develop a new approach to the degree of greyness, being consistent with the grey space concept.
Design/methodology/approach
In order to realise the article’s goals, the research is divided into three stages described in particular sections. The first section of the article presents a theoretical framework of the degree of greyness and the grey space. The second part includes the assumptions of the new degree of greyness concept, along with the mathematical models for the first, the second and the third degree of greyness. The third section contains numerical examples for each degree of greyness.
Findings
As a result of the research, a concept of a degree of greyness was created and it was linked with a concept of grey space. This new approach to the issue of the degree of greyness has allowed the analysing of this category in three dimensions dependent on an accepted reference base. As a result, a concept of concrete and abstractive grey numbers was introduced and relationships between these categories of numbers and the degree of greyness were determined.
Originality/value
The proposed approach to the issue of the degree of greyness is a theoretical unification of the previous considerations in this area. The proposed three dimensions of greyness degree will be derived from the grey space, so they will also be a function of quantity. Thus, the degree of greyness was linked with a classical set theory. An original input in this article is also a differentiation of concrete and abstractive grey numbers, which give a basis for deliberations connected with interpretation of grey numbers in the context of real applications.
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San-dang Guo, Sifeng Liu and Zhigeng Fang
The purpose of this paper is to establish the algorithm rules of the interval grey numbers and propose a new ranking method of the interval grey numbers.
Abstract
Purpose
The purpose of this paper is to establish the algorithm rules of the interval grey numbers and propose a new ranking method of the interval grey numbers.
Design/methodology/approach
The definitions of “kernels” based on lower measure, upper measure or moderate measure are given according to the properties of the interval grey number problems. By means of the measurement error, the concept of the absolute degree of greyness and the relative degree of greyness corresponding to different “kernel” are given, and different simplified forms of the interval grey numbers are put forward.
Findings
The definitions of “kernel” and the degree of greyness in this paper not only take the upper limit, lower limit and the coverage of the interval grey numbers into account, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse.
Research limitations/implications
Though the method proposed in this paper has some deficiencies, such as the definition of relative degree of greyness is meaningless when the kernel of the interval grey number is 0, it provides a new idea for calculating and sorting the interval grey numbers and is conducive to the further development of the grey system theory.
Originality/value
The method proposed in this paper can not only distinguish interval grey numbers in different situations, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse. In this basis, the interval grey number algorithm is established and a new ranking method of interval grey numbers is given.
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Keywords
Shuaishuai Geng, Yu Feng, Yaoguo Dang, Junjie Wang and Rizwan Rasheed
This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according…
Abstract
Purpose
This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according to the principle of grey numbers operation. The domain means the emerging background of interval grey numbers, it is vital for the operational mechanism of such interval grey numbers. However, the criteria of selection of domain always remain same that is not only for the calculated grey numbers but also for the resultant grey numbers, which can be assumed as unrealistic up to a certain extent.
Design/methodology/approach
The existence of interval grey number operation based on kernel and the degree of greyness containing two calculation aspects, which are kernel and the degree of greyness. For the degree of greyness, it includes concepts of domain and calculation of the domain. The concepts of a domain are defined. The enhanced algorithm is also comprised of four deductive theorems and eight rules that are linked to the properties of the enhanced algorithm of the interval grey numbers based on the kernel and the degree of greyness.
Findings
Aiming to improve the algorithm of the degree of greyness for interval grey numbers, based on the variation of domain in the operation process, the degree of greyness of the operation result is defined in this paper, and the specific expressions for algebraic operations are given, which is relevant to the kernel, the degree of greyness and the domain. Then, these expressions are used to the algorithm of interval grey numbers based on the kernel and the degree of greyness, improving the accuracy of the operation results.
Originality/value
The enhanced algorithm in this paper can effectively reduce the loss of information in the operation process, so as to avoid the situation where the decision values are the same and scientific decisions cannot be made during the grey evaluation and decision-making process.
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In order to reflect the essential characteristics of interval grey number and study the ranking method of interval grey number as a whole, this paper aims to establish a ranking…
Abstract
Purpose
In order to reflect the essential characteristics of interval grey number and study the ranking method of interval grey number as a whole, this paper aims to establish a ranking method of interval grey number.
Design/methodology/approach
First, based on the generalised greyness of interval grey number, the definitions of referenced grey number and proximity degree are given. Second, based on the greyness distance of interval grey number, the proximity degree model is constructed and its properties are analysed. Finally, some examples are given to illustrate the effectiveness of the proximity degree model.
Findings
The results show that the index of proximity degree can better reflect the degree that the interval grey number is relatively close to the referenced grey number in different cases. The proximity degree model used to compare interval grey numbers is an extension of the model used to compare real numbers. The examples show that the proximity degree model of interval grey number proposed in this paper is feasible and effective.
Practical implications
The research studies show that the proximity degree model can be used for the ranking of interval grey numbers or real numbers and also for the ranking of numbers where interval grey numbers coexist with real numbers. In addition, the proximity degree model provides a theoretical basis for the establishment of grey comprehensive evaluation model.
Originality/value
The paper succeeds in putting forward the conceptions of referenced grey number and proximity degree based on the generalised greyness of interval grey number and constructing the proximity degree model for the ranking of interval grey number.
Details
Keywords
In order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute…
Abstract
Purpose
In order to solve the decision-making problem that the attributive weight and attributive value are both interval grey numbers, this paper tries to construct a multi-attribute grey decision-making model based on generalized greyness of interval grey number.
Design/methodology/approach
Firstly, according to the nature of the generalized gresness of interval grey number, the generalized weighted greyness distance between interval grey numbers is given, and the transformation relationship between greyness distance and real number distance is analyzed. Then according to the objective function that the square sum of generalized weighted greyness distances from the decision scheme to the best scheme and the worst scheme is the minimum, a multi-attribute grey decision-making model is constructed, and the simplified form of the model is given. Finally, the grey decision-making model proposed in this paper is applied to the evaluation of technological innovation capability of 6 provinces in China to verify the effectiveness of the model.
Findings
The results show that the grey decision-making model proposed in this paper has a strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application example shows that the grey decision model in this paper is feasible and effective. The research results not only enrich the grey system theory, but also provide a new way for the decision-making problem that the attributive weights and attributive values are interval grey numbers.
Practical implications
The decision-making model proposed in this paper does not need to seek the optimal solution of the attributive weight and the attributive value, and can save the decision-making labor and capital investment. The model in this paper is also suitable for the decision-making problem that deals with the coexistence of interval grey numbers and real numbers.
Originality/value
The paper succeeds in realizing the multi-attribute grey decision-making model based on generalized gresness and its simplified forms, which provide a new method for grey decision analysis.
Details
Keywords
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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Currently, for the evaluation of enterprise credit, many specific values of indexes are difficult to obtain, so decision makers tend to give a form of uncertain linguistic…
Abstract
Purpose
Currently, for the evaluation of enterprise credit, many specific values of indexes are difficult to obtain, so decision makers tend to give a form of uncertain linguistic variable. To solve this kind of problem, the purpose of this paper is to introduce an uncertain pure linguistic approach on evaluation of enterprise integrity based on grey information.
Design/methodology/approach
Initial uncertain linguistic variables given by experts are transferred into interval grey numbers, and their greyness of degree is computed. Then, the greyness of degree is applied to adjust the weights of experts. Moreover, the core of each interval grey number is calculated, and through giving the positive ideal point and negative ideal point, which are binary numbers, the comprehensive grey relational grade between the linguistic number and the two points is calculated, respectively, as well to get the ranking result of projects by considering both core and greyness of degree.
Findings
The model is applied to a case, and the result verifies the validity and practicability of the model which reveals high effectiveness.
Practical implications
This model provides a new feasible method in a growing number of fuzzy evaluation schemes in the fields of enterprise integrity and contributes to getting better and more accurate results.
Originality/value
In this paper, the greyness of degree is introduced to the model to adjust the experts’ weights, and it reflects the thought of “making full use of the information” in grey system theory and further enriches the system of grey decision-making theory as well as expanding its application scope.
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