A comparative analysis of grey ranking approaches

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.

The Grey Ten-Element Analysis Method: A Novel Strategic Analysis Tool

“…There are different approaches to comparing/ranking the outputs of grey-based methods. Darvishi et al [88] reviewed the approaches employed to compare the grey numbers such as the Moore's approach [89], Ishibuchi and Tanaka's approach [90], Hu and Wang's approach [91], kernel and degree of greyness of grey numbers approach [92], grey possibility degree [92], and Xie and Liu's approach [93].…”

“…Grey numbers stand for numbers that are not crisp and carries some incomplete information yet bounded between two crisp values which demonstrate complete information [84]. The definition of a grey number has been provided as follows (Darvishi et al, 2019): An interval grey number is a number that is surrounded by two crisp upper and lower boundaries, but its position within the boundaries is not clear. Mathematically, an interval grey number is represented as ⊗G ∈ G, G = G ≤ t ≤ G where ⊗G is a grey number, t shows the information, G and G are the lower and upper boundaries, while G = G [85].…”

Exploitation of the advanced manufacturing machine tool evaluation model under objective-grey information: a knowledge-based cluster with the grey relational analysis approach

“…The grey information is GS 11,3 an obstacle to serve effective decision, and thus grasping grey information from system characteristics is enrolled in present work. Grey information is crucial for strategic network formation and deals with unclear, vague inaccurate and imprecise information, which exist in the system and can be utilize to make decision-making effectively (Liu et al, 2018;Javed and Liu, 2018;Mahmoudi, 2018;Salookolaei et al, 2018;Quartey-Papafio et al, 2019;Lui, 2019;Darvishi et al, 2019;Liu and Yang, 2019;Qian et al, 2019).…”

A dual simplex method for grey linear programming problems based on duality results

“…Ranking and comparing grey numbers represent a very important decision-making procedure in any given grey environment. Darvishi et al (2019) studied the existing approaches of ordering interval grey numbers in the context of decision-making by surveying existing definitions.…”