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Algorithm rules of interval grey numbers based on different “kernel” and the degree of greyness of grey numbers

San-dang Guo (Department of Management Science, Henan Agricultural University, Zhengzhou, China) (College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Sifeng Liu (Institute for Grey Systems Studies, College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Zhigeng Fang (College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 7 August 2017

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.

Keywords

Acknowledgements

This work was supported by “the key project of the National Social Science Fund”, No. 10zd&014; “Funding of Jiangsu Innovation Program for Graduate Education, the Fundamental Research Funds for the Central Universities”, No. CXLX12_0177.

Citation

Guo, S.-d., Liu, S. and Fang, Z. (2017), "Algorithm rules of interval grey numbers based on different “kernel” and the degree of greyness of grey numbers", Grey Systems: Theory and Application, Vol. 7 No. 2, pp. 168-178. https://doi.org/10.1108/GS-10-2015-0073

Publisher

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Emerald Publishing Limited

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