Ma, 2018a, b, 2019). The GGTDM differs from its conventional counterparts in its
calculation process but follows the same principle as the conventional method (Ma, 2014,
2018a, b, 2019; Ma and Ji, 2014). Given that uncertainty originates from the uncertain
number, an effective tool is essential to measure it in a GGTDM. The Gini index was
proposed to quantify the inequality of income distributions (Fabrizi and Trivisano, 2016).
Now, the Gini index (coefficient) has been advanced and applied to a wide range of topics,
among which, the GSI is one of the forms of Gini index (Rao, 1982; Guiasu and Guiasu, 2012;
Casquilho, 2016; Pesenti et al., 2017). The GSI (also known as quadratic entropy in
information theory) has been reinvented by some scholars evolving to a few types of
expressions (Österreicher and Casquilho, 2018). Initially, GSI was used to measure
biodiversity (Rao, 1982; Guiasu and Guiasu, 2012; Pesenti et al., 2017); later, it was applied in
the detection of medical viruses (Gregori et al., 2016). In addition, it was also employed to
measure the uncertainty of information (Petry et al., 2015; Jiang et al., 2017). More recently,
the improved GSI was adopted in a decision-making task concerning mixed attribute values
(Ma, 2019). It should be noted that the weighted Gini–Simpson index (WGSI) appears in
different versions. Thus, the GGTDM concerning uncertain numbers could be rebuilt
relying on the different versions of GSI.
The novelty of this research is as follows: it presents a new viewpoint for measuring the
difference of the alternatives to the target centre involving uncertain numbers. Then the GSI
is improved to be as the generalised target centre distance. Next, it obtains the pseudo-
probability by the ratio method which connects the alternative index and the target centre
index, which is a core element in the calculation of comprehensive weighted Gini–Simpson
index (CWGSI). Finally, it also builds a weight function converting the mixed attribute-
based weights into the certain number-based weights. Besides, the following analysis is
crucial to make the readers learn (in a concrete fashion) the contribution of the proposed
approach to the mixed attribute-based generalised grey target decision making.
There are a few published articles on the topic of the proposed method: however, this
work has some major differences in comparison with the previous research. In general,
investigation of GGTDM lies in the following aspects. First, obtaining the target centre
distance is the most important step to arrive at a decision. Second, some factors such as data
types, attribute weights, target centre indices and various types of methods for obtaining
target centre distances may affect the decision making. Thus, the difference between this
research and the previous work is analysed as described below.
The GGTDM involving mixed attribute values was first proposed in Ma and Ji (2014).
Different from the conventional grey target decision method handling uncertain number, the
generalised method presented in Ma and Ji (2014) adopts the binary connection number
unifying different types of uncertain numbers into one and obtains the target centre
distance by substituting the vector-based method into the distance-based method.
Thereafter, the GGTDM with the alternative index and attribute weight denoted by mixed
values was addressed in Ma (2018a). Later, the entropy-based method (mainly using
Kullback–Leibler distance) was investigated in Ma (2018b), which works from the viewpoint
of measuring the uncertainty. Motivated by measuring the uncertainty of numbers, the
improved GSI-based method was proposed (Ma, 2019). It should be noted that the GSI used
in Ma (2019) is one of its many forms; this paper presents a different version of GSI-based
GGTDM concerning mixed attribute values. The proposed method makes improvements in
terms of achieving the target centre indices, converting uncertain number-based weights
into certain number-based weights, and especially calculating the CWGSI (generalised
target centre distance).
With respect to the published papers on GGTDM addressing mixed attribute values,
they could be divided into two categories: vector-based methods discussed in (Ma and Ji,
2014; Ma, 2018a) and other type of methods investigated in Ma, 2018b, 2019). Ma (2018a)