PurposeIn 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/approachFirst, 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.FindingsThe 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 implicationsThe 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/valueThe 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.

Purpose – According to the grey uncertainty and the connotation of different types weights, the purpose of this paper is to establish the pattern of multi-dimensional grey fuzzy decision making with feedback based on weight vector and weight matrix, and applies this pattern to evaluate the regional financial innovation ability. Design/methodology/approach – At first, this paper analyzes the connotation of financial innovation ability and establishes the evaluation system of regional financial innovation ability. Second, the formula of computing the multi-objective weighted comprehensive value based on weight vector and weight matrix is put forward. In view of the object function with supervised factor and stability coefficient, this paper gives the formulas to compute weight vector and weight matrix. Moreover, the algorithm of the multi-dimensional grey fuzzy decision making pattern with feedback based on weight vector and weight matrix is expressed. At last, this paper uses the presented pattern to evaluate the financial innovation ability of thirty-one provinces in China. Findings – The results are convincing: the development of regional financial innovation is not balanced in China, having obvious spatial clustering feature. The comparisons of evaluation results based on different forms of weights show that the calculating convergence speed of the pattern presented in this paper is fast. The pattern enhances the rationality of the demarcation point between categories, and the convergence within categories, making the evaluation more reasonable. Practical implications – The method exposed in the paper can be used at evaluating the regional financial innovation ability and even for other similar evaluation problem. Originality/value – The paper succeeds in realising both the pattern of multi-dimensional grey fuzzy decision making with feedback and evaluating the regional financial innovation ability by using the newest developed theories: weighted grey and fuzzy recognition theory based on weight vector and weight matrix.

PurposeIn 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/approachFirst, 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.FindingsThe 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 implicationsThe 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/valueThe 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.

PurposeThis study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.Design/methodology/approachBased on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model.FindingsThe results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82; the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R2 = 0.924, and the average relative error is 6.608%.Practical implicationsStudies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.Originality/valueThe paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

The study on decision making is of important guide for theory and practice. Based on the theories of fuzzy recognition, the pattern of multiple objects and multiple dimensional grey-fuzzy decision making with self feedback is presented in this paper. Firstly, according to the given weights, weighting integrated value of decision making is computed. Secondly, the method of fuzzy recognition with single index is employed to calculate the fuzzy classification of the integrated value. At last, according to the cause analysis, the fuzzy classification of the integrated value is used to compute the cluster center and the weights of indexes. In a similar way, repeating the above processes, the weighting integrated value and fuzzy classification with given accuracy are gotten at the same time;the classification and sequence of decision making set are also gained. The example of steelmaking enterprise evaluation show that the model presented in this paper is valid.