Generalised grey target decision method based on the Gini–Simpson index involving mixed attributes and uncertain numbers

Published date03 September 2019
Date03 September 2019
AuthorJinshan Ma
Subject MatterLibrary & information science
Generalised grey target decision
method based on the GiniSimpson
index involving mixed attributes
and uncertain numbers
Jinshan Ma
Henan Polytechnic University, Jiaozuo, China
Purpose The purpose of this paper is to investigate a novel generalised grey target decision method
(GGTDM) with index and weight involving mixed attribute values.
Design/methodology/approach The mixed attribute values are transformed into binary connection
numbers and also comprised of two-tuple (determinacy, uncertainty) numbers to fulfil the decision-making
task. The proposed method constructs the weight function to convert the mixed attribute-based weights into
the certain number-based weights and determines the alternatives ranking by the comprehensive weighted
GiniSimpson indices (CWGSIs).
Findings The result of decision making regarding the numerical example by the proposed approach is
somewhat different from that obtained by the reported vector-based method. The reasons for this are
threefold: the decision-making bases are different, the target centre indices are determined by different
mechanisms and certain number-based weights are calculated in different ways.
Research limitations/implications The proposed method ranks an alternative based on the
GiniSimpson index, as derived from the viewpoint of measuring the uncertainty (heterogeneity): however,
the vector-based GGTDM makes a decision based on proximity, as is the case whenmeasuring the similarities
between index vectors.
Practical implications The proposed approach is admissible to solving mixed attribute-based decision
making especially for alternative indices and attribute weights containing both uncertain numbers.
Originality/value The proposed method provides a new perspective on measuring the difference of
alternatives to the target centre via the CWGSI: the CWGSI is obtained by relying on the pseudo-probabilities
achieved by the ratios of the alternative indices to the target centre indices. It also builds a weight
function converting the mixed attribute-based weights into certain number-based weights. This method
provides a framework that should be tested in terms of its effective decision making using real data and an
actual problem.
Keywords Weight function, Binary connection number, Generalized grey target decision method,
GiniSimpson index, Interval number, Mixed attributes
Paper type Research paper
1. Introduction
Decision making by grey target method depends on the target centre distance. The certain
number-based grey target decision method arrives at the target centre distance mainly by
distance-based method such as Euclidean distance and Mahalanobis distance (Wang et al.,
2009; Song et al., 2010). The mixed attribute-based grey target decision method obtains the
target centre distance (including the generalised target centre distance) in the reported
literature as follows: by distance-based method mainly by Euclidean distance (Song et al.,
2009; Shen et al., 2010; Luo and Wang, 2012); using the equivalent method such as cobweb
area and incidence coefficient (Guan et al., 2015; Zeng et al., 2016); or by vector-based
method, entropy-based method, or GiniSimpson index (GSI)-based method, which are
referred to as generalised grey target decision methods (GGTDM) (Ma and Ji, 2014;
Data Technologies and
Vol. 53 No. 4, 2019
pp. 484-500
© Emerald PublishingLimited
DOI 10.1108/DTA-02-2019-0019
Received 4 February 2019
Revised 2 June 2019
30 July 2019
Accepted 19 August 2019
The current issue and full text archive of this journal is available on Emerald Insight at:
This research was supported by the Fundamental Research Funds for the Universities of Henan
Province (Grant No. SKJZD2019-05). The constructive criticism of the anonymous reviewers is
gratefully acknowledged.
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 GiniSimpson 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 GiniSimpson
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
KullbackLeibler 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)
grey target

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