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A comparative analysis of grey ranking approaches

Davood Darvishi (Department of Mathematics, Payame Noor University, Tehran, Iran)
Jeffrey Forrest (School of Business, Slippery Rock University, Slippery Rock, Pennsylvania, USA)
Sifeng Liu (Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Publication date: 14 October 2019

Abstract

Purpose

Ranking and comparing grey numbers represent a very important decision-making procedure in any given grey environment. The purpose of this paper is to study the existing approaches of ordering interval grey numbers in the context of decision making by surveying existing definitions.

Design/methodology/approach

Different methods developed for comparing grey numbers are presented along with their disadvantages and advantages in terms of comparison outcomes. Practical examples are employed to show the importance and necessity of using appropriate methods to compare grey numbers.

Findings

Most the available methods are not suitable for pointing out which number is larger when the nuclei of the grey numbers of concern are the same. Also, these available methods are also considered in terms of partial order and total order. Kernel and degree of greyness of grey numbers method is more advantageous than other methods and almost eliminates the shortcomings of other methods.

Originality/value

Different methods for ranking grey numbers are presented where each of them has disadvantages and advantages. By using different methods, grey interval numbers are compared and the results show that some methods cannot make grey number comparisons in some situations. The authors intend to find a method that can compare grey numbers in any situation. The findings of this research can prevent errors that may occur based on inaccurate comparisons of grey numbers in decision making. There are various research studies on the comparison of grey numbers, but there is no research on the comparison of these methods and their disadvantages, advantages or their total or partial order.

Keywords

  • Grey systems theory
  • Grey number
  • Interval grey numbers
  • Order relations
  • Decision making
  • Ranking

Acknowledgements

This work was partially supported by Institute for Grey System Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China.

Citation

Darvishi, D., Forrest, J. and Liu, S. (2019), "A comparative analysis of grey ranking approaches", Grey Systems: Theory and Application, Vol. 9 No. 4, pp. 472-487. https://doi.org/10.1108/GS-05-2019-0014

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

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