https://doi.org/10.31449/inf.v48i5.5169                                               Informatica 48 (2024) 1–14   1 
Enhanced CoCoSo Method for Intuitionistic Fuzzy MAGDM and 
Application to Financial Risk Evaluation of High-Tech Enterprises 
 
Huanwen Liu 
School of Finance and Management, Changsha Social Work College, Changsha, 410004, Hunan, China 
E-mail: csmz_huanwenliu@163.com 
Keywords: multiple attribute group decision making (MAGDM), intuitionistic fuzzy sets (IFSs), combined 
compromise solution (CoCoSo) method, financial risk evaluation of high-tech enterprises  
Received: September 8, 2023 
The continuous innovation of science and technology is the foundation for the survival and development 
of high-tech enterprises. In order to gain a foothold in the fierce market competition, enterprises must 
seize market share by developing new high-tech products tailored to the market, and obtain economic 
benefits for maintaining survival and development. However, to ensure the smooth progress of the 
development and research process, sufficient financial support is required. Fundraising is particularly 
important, even if the required funds are raised, its own high-risk needs to be given special attention. 
The financial risk evaluation of high-tech enterprises is a multiple attribute group decision making 
(MAGDM). Recently, the Combined Compromise Solution (CoCoSo) method has been employed to 
manage MAGDM issues. The intuitionistic fuzzy sets (IFSs) are used as a tool for portraying uncertain 
information during the financial risk evaluation of high-tech enterprises. In this paper, the intuitionistic 
fuzzy CoCoSo (IF-CoCoSo) method is cultivated to manage the MAGDM based on the Hamming 
distance and Euclid distance under IFSs. In the end, a numerical case study for financial risk evaluation 
of high-tech enterprises is supplied to validate the proposed method. The main contributions of this 
paper are outlined: (1) the CoCoSo method has been extended to IFSs; (2) Information Entropy is used 
to derive weight based on the Hamming distance and Euclid distance under IFSs. (3) the IF-CoCoSo 
method is founded to manage the MAGDM based on the Hamming distance and Euclid distance under 
IFSs; (4) a numerical case study for financial risk evaluation of high-tech enterprises and some 
comparative analysis is supplied to validate the proposed method. 
Povzetek: Predstavljena je  metoda IF-CoCoSo za oceno finančnega tveganja visokotehnoloških 
podjetij, temelječ na intuicionističnih mehkih množicah in večatributnem skupinskem odločanju.
1   Introduction 
In recent years, the role of science and technology in 
economic development has been continuously enhanced. 
The progress of technology has promoted the rapid 
development of high-tech industries, and the number of 
high-tech enterprises in China has increased from 49000 
more than a decade ago to 330000 in 2021[1-3]. The 
business operations of high-tech enterprises mainly 
revolve around technological research and development 
and the transformation of technological achievements. 
The products and services they provide have high value 
due to their high technological content, which makes the 
economic benefits generated by high-tech enterprises 
crucial in China's total economic output[4-6]. In order to 
accelerate the transformation of China's industrial 
structure, the national level has attached increasing 
importance to high-tech industries and provided tax 
incentives and financial support in many aspects, 
providing certain guarantees for the development of 
high-tech enterprises[7-9]. However, due to various 
factors, high-tech enterprises still face high financial 
risks. Financial security is the key to the operation and 
development of high-tech enterprises, and effective 
prevention of financial risks is a challenge that high-tech 
enterprises must overcome[10, 11]. Only by establishing 
a sound risk management system can the development of 
high-tech enterprises be safeguarded. In order to enhance 
the ability of high-tech enterprises to resist financial 
risks, it is necessary to understand the existing financial 
problems of high-tech enterprises, conduct in-depth 
research on the reasons behind financial risks, propose 
prevention and control measures for various sources of 
financial risks, promote the stable development of 
high-tech enterprises, and thereby increase the 
contribution of high-tech industries to economic 
development[12-14]. Overall, the financial risks of 
high-tech enterprises are mainly caused by external and 
internal environmental factors. From the perspective of 
external factors of the enterprise, factors such as market 
acceptance, industry competition, and policy systems can 
bring a certain degree of financial risk to high-tech 
enterprises[15, 16]. The imperfect internal risk control 
system and risk prevention mechanism, insufficient 
human resources, and organizational management 
deficiencies of enterprises may also be the sources of 
financial risks. The development of high-tech enterprises 
relies on technological research results, followed by the 
commercialization of technology. In this process, the 
economic environment in which high-tech enterprises 
operate is highly uncertain. Firstly, the uncertainty of 
market factors can cause financial risks for high-tech 

2   Informatica 48 (2024) 1–14                                                                         H. Liu 
enterprises[17, 18]. At present, the updates and upgrades 
of technology are constantly accelerating, and people's 
quality of life is constantly improving. In this situation, 
consumers' consumption concepts and habits are 
changing rapidly. When a company's products are put 
into the market, there is a great deal of uncertainty in 
consumer reactions and purchasing situations, leading to 
the inability to guarantee the expected returns of the 
company. Secondly, the industry situation of high-tech 
enterprises also presents great uncertainty[19, 20]. In the 
field of high-tech, competition in the industry is 
becoming increasingly fierce. When some enterprises 
obtain more funding and talent support, accelerating the 
speed of technology development and transformation, it 
will make other high-tech enterprises very passive, 
bringing more financial risks and corporate crises. 
Thirdly, many policies and systems of the country may 
also increase the requirements for high-tech enterprises. 
Nowadays, the country not only has strict regulations on 
the recognition of high-tech enterprises, but also restricts 
and regulates their financial activities such as loans. 
There are also many factors that can lead to financial 
risks within high-tech enterprises[21, 22]. Firstly, many 
high-tech enterprises have not established sound 
financial risk management systems. In the process of 
preventing and controlling financial risks, the 
responsible department lacks clear guidance and cannot 
implement the financial risk management system. In the 
prevention of financial risks, many steps have not been 
taken properly, and in reality, early warning and 
emergency handling of financial risks have not been 
achieved. Secondly, high-tech enterprises have human 
resource deficiencies[23, 24]. Due to the nature of the 
enterprise, there is insufficient reserve of management 
personnel and managerial talents within the enterprise, 
and many employees do not understand the financial risk 
control system, making it difficult to promote and 
implement related work. Many management employees 
overlook financial risks and lack the ability to handle 
them, resulting in poor coordination and cooperation 
among staff[25, 26]. Thirdly, the corporate governance 
structure is incomplete. Financial risk management is a 
highly professional task, but many high-tech enterprises 
have governance issues and do not have independent and 
specialized responsible departments, resulting in 
loopholes in financial risk management at all levels[27, 
28]. 
Decision making is one of the most common 
activities in daily life[29-32]. For example, an 
investment company needs to evaluate all possible 
alternative options and select the optimal investment 
plan to avoid investment risks and achieve maximum 
returns. A certain airline needs to evaluate the 
operational status of all routes in order to select the 
optimal route and promote successful experience to other 
routes, thereby improving the overall operational level of 
the airline. A manufacturing enterprise needs to select 
the best supplier from all raw material suppliers in order 
to obtain stable and reliable material sources. With the 
continuous development of the economy and society, 
decision-making issues have become increasingly 
complex[32-35]. Thus, in practical decision-making 
problems, it is often necessary to evaluate candidate 
methods from multiple perspectives, consider the overall 
performance of the candidate solutions, and then select 
the optimal solution[36-40]. In recent decades, 
multi-attribute decision-making (MADM), an important 
branch of management science and engineering, has 
received widespread attention from the academic 
community[41-44]. The so-called MADM refers to the 
evaluation of all decision plans by decision-makers from 
multiple dimensions, and then determining the optimal 
decision plan[45-49]. According to the experts’ number 
of participating in decision evaluation, MADM is 
subdivided into multi-attribute group decision-making 
(MAGDM)[50-54]. The financial risk evaluation of 
high-tech enterprises is classical MAGDM. The IFSs 
[55-58] are used as a tool for portraying uncertain 
information during the financial risk evaluation of 
high-tech enterprises. Furthermore, many decision 
algorithms use the typical CoCoSo method [59] 
separately to obtain the most optimal decision choice. 
Until now, no or few algorithms have been studied on 
information entropy and CoCoSo method based on the 
Hamming distance and Euclid distance under IFSs. 
Therefore, an integrated intuitionistic fuzzy CoCoSo 
(IF-CoCoSo) method is constructed to manage MAGDM 
based on the Hamming distance and Euclid distance 
under IFSs. An illustrative example for financial risk 
evaluation of high-tech enterprises and some 
comparative analysis is constructed to demonstrate the 
validity and reliability of IF-CoCoSo method. The main 
research goal and motivation of this paper is outlined: (1) 
the CoCoSo method has been extended to IFSs based on 
the Hamming distance and Euclid distance; (2) 
Information Entropy is used to derive weight based on 
the Hamming distance and Euclid distance under IFSs. 
(3) the IF-CoCoSo method is founded to manage the 
MAGDM based on the Hamming distance and Euclid 
distance under IFSs; (4) a numerical case study for 
financial risk evaluation of high-tech enterprises and 
some comparative analysis is supplied to validate the 
proposed method. 
   The structure of this paper is listed below. In Section 
2, the IFSs is introduced. In Section 3, IF-CoCoSo 
method is founded under IFSs with entropy based on the 
Hamming distance and Euclid distance. Section 4 gives 
an illustrative case for financial risk evaluation of 
high-tech enterprises and some comparative analysis. 
Some remarks are supplied in Section 5. 
2  Preliminaries 
Atanassov [60] constructed the IFSs. 
Definition 1[60]. The IFSs on  is: 
   ( ) ( )  
,,
HH
H u v     =   (1) 
where ( )   0,1
H
  is membership and 
( )   0,1
H
  is non-membership with information 

Enhanced CoCoSo Method for Intuitionistic Fuzzy MAGDM…                           Informatica 48 (2024) 1–14   3 
condition: ( ) ( ) 01
HH
     +  ,    . Then, 
( ) , h hu hv  = is denoted as an IFN. 
Definition 2[61, 62]. Let ( )
1 1 1
=, h hu hv  and 
( )
2 2 2
=, h hu hv  be IFNs, the score functions (SF) and 
accuracy functions (AF) of 
1
h  and 
2
h  is 
constructed: 
( ) ( )
1 1 1 2 2 2
, SF h hu hv SF h hu hv  = − = −                        
(2) 
( ) ( )
1 1 1 2 2 2
, AF h hu hv AF h hu hv  = + = +                      
(3) 
For two IFNs ( )
1 1 1
=, h hu hv  and 
( )
2 2 2
=, h hu hv  , then[63] 
( ) ( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
1 2 1 2
1 2 1 2 1 2
1 2 1 2 1 2
(1) , ;
(2) , , ;
(3) , , .
if SF h SF h h h
if SF h SF h AF h AF h h h
if SF h SF h AF h AF h h h
   
     
     

=  
= = =
Definition 3[64]. Let ( )
1 1 1
=, h hu hv  and 
( )
2 2 2
=, h hu hv  be IFNs, the IFN distanced measure 
(IFNDM) is supplied: 
 
( )
( ) ( )
( ) ( ) ( )
1 2 2 1 1 2
12
12
1 2 1 2 2 1 1 2
12
24
4
1
,
2
4 2 2
4
hu h hu h hu hu
hh
IFNDM h h
hv hv hv h hv h h h
hh



   


− − −

−

=

− + − + −

+

−


    (4) 
where 
1 1 1 2 2 2
1 , 1 h hu hv h hu hv  = − − = − − . 
Definition 4[63]. Let ( )
1 1 1
=, h hu hv  and 
( )
2 2 2
=, h hu hv  be two IFNs, the operation is 
constructed: 
( )
1 2 1 2 1 2 1 2
, h h hu hu hu hu hv hv   = + − (5) 
( )
1 2 1 2 1 2 1 2
, h h hu hu hv hv hv hv   = + − (6) 
( ) ( )
( ) 1 1 1
1 1 , , 0 h hu hv

   = − −       (7) 
( ) ( ) ( )
( ) 1 1 1
= ,1 1 , 0 h hu hv
  
 − −        (8) 
From the Definition 2, the useful operation laws are 
supplied. 
( )
( )
( )
2
1 1 2
1 2 2 1 1 2 2 1 1 1
(1) , , h h h h h h h h h h

  
           =   =  = ；          
( ) ( ) ( ) ( )
1 2 1 2 1 2 1 2
(2) , ; h h h h h h h h
  
            =   =                 
( ) ( ) ( ) ( )
( )
1 2 1 2
1 1 2 1 1 2 1 1 1 1
(3) , . h h h h h h
   
         
+
 = +  =
    The IFWA and IFWG operator is introduced. 
Definition 5[65]. Let 
( )
=,
j j j
h hu hv  be a group of 
IFNs, the IFWA operator is: 
( )
( ) ( )
12
1
11
1 1 ,
, ( , , )
jj
hw n
n
jj
j
j
nn
hw hw
j
j
j
IFWA h h h
hw
h
h
u hv
  

==
=

=

=
−−




   (9) 
where ( )
12
= , ,...,
T
n
hw hw hw hw be weight of 
j
h  ,
1
0, 1.
n
jj
j
hw hw
=
=

 
Definition 6[66]. Let 
( )
=,
j j j
h hu hv  be a group of 
IFNs, the IFWG operator is: 
 
( )
( ) ( )
1
1
1
2
1
,1 1
( , , , )
j
j
j
hw
hw n
n
hw
j
j
j
n
hw
j
n
jj
IFWG h h h
h
hu v h
  

=
=
=

= − −



=

   (10) 
where ( )
12
= , ,...,
T
n
hw hw hw hw be weight of 
j
h  ,
1
0, 1.
n
jj
j
hw hw
=
=

 
3   IF-CoCoSo method for MAGDM 
Then, IF-CoCoSo method is constructed for MAGDM. 
Let  
12
, , ,
m
HA HA HA HA = be alternative sets, 

4   Informatica 48 (2024) 1–14                                                                         H. Liu 
and attributes set  
12
, , ,
n
HG HG HG HG = with 
weight
( )
12
= , ,...,
T
n
hw hw hw hw , 
where   0,1
j
hw  ,
1
1
n
j
j
hw
=
=

and a set of invited 
experts 
 
12
, , ,
q
HE HE HE HE = , let expert’s 
weight be
( )
12
= , ,...,
T
n
h h h h     . 
 
Then, IF-CoCoSo model is constructed for 
MAGDM.  
 
Step 1. Build the intuitionistic fuzzy matrix 
( ) ( )
( )
tt tt
ij ij ij
mn
mn
IFM IFM hu hv


 ==

， and 
construct the average matrix 
ij
mn
IFM IFM

 =

: 
12
1 11 12 1
2 21 22 2
12
tt
ij
mn
n
t t t
n
t t t
n
t t t
m m m mn
IFM IFM
HG HG HG
HA IFM IFM IFM
HA IFM IFM IFM
HA IFM IFM IFM

 =




=




          
12
1 11 12 1
2 21 22 2
12
ij
mn
n
n
n
m m m mn
IFM IFM
HG HG HG
HA IFM IFM IFM
HA IFM IFM IFM
HA IFM IFM IFM

 =




=



                          
Based on IFWA technique, 
the
( )
,
ij ij ij
m n m n
IFM IFM hu hv

 ==

  is: 
 
( ) ( )
( )
12
12
11
= 1 (1 ) ,
t
t
q
ij ij ij q ij
qq
h
tt h
ij ij
tt
IFM h IFM h IFM h IFM
hu hv


  
==
=   

−−



                  (13) 
 
Step 2. Normalize 
the
( )
,
ij ij ij
m n m n
IFM IFM hu hv

 ==

into  
 
( )
,
ij ij ij
m n m n
NIFM NIFM nhu nhv

 ==

. 
For benefit attributes: 
 
  
( ) ( )
,
ij ij ij ij ij
NIFM nhu nhv hu hv == , (14) 
For cost attributes: 
 
( ) ( )
,
ij ij ij ij ij
NIFM nhu nhv hv hu == , (15) 
 
Step 3. Construct the intuitionistic fuzzy number 
negative ideal solution (IFNNIS): 
( )
,
j j j
IFNNIS nhu nhv = (16) 
( ) ( )
min ,
j ij ij
i
SF IFNNIS SF nhu nhv = (17) 
 
Step 4. Construct the weight values with entropy. 
The entropy[67] is used to define the weights. The 
calculating steps are defined. 
 
( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( )
1
1
1
,,
,,
1
  
ln
,,
ln
,,
ij j ij j
m
ij j ij j
i m
j
i
ij j ij j
m
ij j ij j
i
HD NIFM IFNNIS ED NIFM IFNNIS
HD NIFM IFNNIS ED NIFM IFNNIS
IFNE
n
HD NIFM IFNNIS ED NIFM IFNNIS
HD NIFM IFNNIS ED NIFM IFNNIS
=
=
=

+
  

+


=−



 +




+


 



 
 (18)
 
( )
1
1
,     1, ,
1
j
j n
j
j
IFNE
hw j n
IFNE
=
−
==
−

L 
                                                 (19) 
(12) 
(11) 

Enhanced CoCoSo Method for Intuitionistic Fuzzy MAGDM…                           Informatica 48 (2024) 1–14   5 
 
Step 5. Construct the IFN weighted arithmetic average (IFNWAA). 
 
( ) ( )
1
,,
2
n
ij j ij j
ij
j
HD NIFM IFNNIS ED NIFM IFNNIS
IFNWAA hw
=

+
 =



  (20) 
 
Step 6. Compute the IFN weighted geometric mean (IFNWGM). 
( ) ( )
1
,,
2
j
hw
n
ij j ij j
i
j
HD NIFM IFNNIS ED NIFM IFNNIS
IFNWGM
=

+
 =



  (21) 
 
Step 7. The three designed strategies are employed to 
obtain the relative importance: 
 
( )
1
i
i
i
i m
i
i
IFNWAA IFNWGM
IFN
IFNWAA IF
K
NWGM
A
=
+
+
=

                   
(22) 
 
min min
ii
ii
ii
i
IFNWAA IFNWGM
IFN
IFNWA F
KB
A I NWGM
=+              
(23) 
 
(1 )
,0 1.
max
(1 ) max
i
i
i
i
i
i
i
IFNWAA
IFNWGM
IFN
IFNWAA
IFNWGM
KC




 +



=



+−




−
    (24) 
 
where 
i
IFNKA is the arithmetic average of 
,
i i
IFNWAA IFNWGM , 
i
IFNKB is the relative 
scores of ,
i i
IFNWAA IFNWGM , and 
i
IFNKC is the 
compromise values of ,
i i
IFNWAA IFNWGM . 
Step 8. Compute the decision value
i
IFNK . 
 
3
3
i i i
i
i i i
IFN IFN IFN
IFN
IF
KA KB KC
K
KA K N IFN IF B KC N


=

+


+


+
    
(25) 
 
 
 
Step 9. Sort the alternatives 
with ( ) 1,2, ,
i
IFNK i m =    , and the higher the
i
IFNK , 
the better the decision alternative is. 
4  Numerical example and 
comparative analysis 
4.1  Numerical example for financial risk 
evaluation of high-tech enterprises 
In the 1970s, the concept of high-tech was born and 
widely spread, and its connotation continued to develop 
and derive in various countries around the world. With 
the development of economic globalization, high-tech 
enterprises play a crucial role in China's economic 
development. Technology is the internal driving force for 
the survival and development of an enterprise, especially 
high-tech enterprises. In the process of applying 
advanced technology or technological innovation, 
high-tech enterprises can obtain higher economic benefits 
by producing, selling, or providing innovative technology 
services through innovative products. However, 
compared with traditional enterprises, high-tech 
enterprises need to invest a lot of R&D funds and human 
and material resources, and this investment increases 
significantly with the increasing difficulty and 
complexity of R&D technology. Even when it comes to 
the development stage, the cost elasticity of investment 
increases, and there may be no gains. Sometimes, it 
requires repeated experimentation and continuous 
additional investment costs to succeed, while the cost 
level of the research and development process is very 
high. At the stage of product promotion, in order to 
increase market share and enable consumers to accept 
new products in a short period of time, it is inevitable to 
require a large amount of advertising investment. Overall, 
high-tech enterprises require high capital investment, 
with R&D investment intensity generally ranging from 
5% to 15%. However, it may vary depending on the 
industry, with R&D investment intensity reaching up to 
50%. In the later stage of the achievement transformation 
process, the investment will significantly increase, and 
the investment intensity in the process of transforming 
research and development achievements into goods or 
technologies is 5 to 10 times higher than that in the 
research and development process. This brings relatively 
high financial risks to high-tech enterprises. The 
continuous innovation of science and technology is the 
foundation for the survival and development of high-tech 
enterprises. In order to gain a foothold in the fierce 

6   Informatica 48 (2024) 1–14                                                                         H. Liu 
market competition, enterprises must seize market share 
by developing new high-tech products tailored to the 
market, and obtain economic benefits for maintaining 
survival and development. However, to ensure the 
smooth progress of the development and research process, 
sufficient financial support is required. Fundraising is 
particularly important, even if the required funds are 
raised, its own high-risk needs to be given special 
attention. The continuous innovation of science and 
technology is the foundation for the survival and 
development of high-tech enterprises. In order to gain a 
foothold in the fierce market competition, enterprises 
must seize market share by developing new high-tech 
products tailored to the market, and obtain economic 
benefits for maintaining survival and development. 
However, to ensure the smooth progress of the 
development and research process, sufficient financial 
support is required. Fundraising is particularly important, 
even if the required funds are raised, its own high-risk 
needs to be given special attention. The current world 
development pattern and economic environment have 
undergone significant changes, especially the 
development and innovation of science and technology, 
which have had a huge impact on the world economy and 
have had a certain impact on the development of 
enterprises. The establishment and growth of high-tech 
enterprises have their own characteristics. In the process 
of comparing the financial management work of 
high-tech enterprises with traditional enterprises, 
significant differences can also be found between the two. 
Therefore, high-tech enterprises should adopt financial 
management models that are more in line with the 
characteristics of the enterprise, use effective 
management methods to avoid various financial 
management risks, and actively respond to them based on 
a clear positioning of their own development. The 
financial risk evaluation of high-tech enterprises is a 
MAGDM. Therefore, the financial risk evaluation of 
high-tech enterprises is presented to show the developed 
approach in this paper. There are five high-tech 
enterprises ( ) 1,2,3,4,5
i
FA i = to select. The experts 
choose four attributes to evaluate the five small and 
medium sized financial institutions in rural areas[68]: ①
FG 1 is solvency for high-tech enterprises. ② FG 2 is 
financial risk management costs for high-tech enterprises. 
③FG 3 is operational capacity for high-tech enterprises. 
④FG 4 is profitability for high-tech enterprises. The five 
possible high-tech enterprises ( ) 1,2,3,4,5
i
FA i = are 
to be evaluated with linguistic scales (See Table 1[69]) 
with four attributes through three 
experts ( ) 1,2,3
t
FE t = (Suppose expert’s weight 
is ( ) 0.35,0.45,0.20 . 
The of the enterprise 
 
Table 1: Linguistic scale and IFNs[69] 
The IF-CoCoSo method is constructed to manage the financial risk evaluation of high-tech enterprises. 
Step 1. Construct the IFN-matrix
54
tt
ij
IFM IFM

 =

 (See Table 2-4). 
 
 
 
 
 
 
 
 

Enhanced CoCoSo Method for Intuitionistic Fuzzy MAGDM…                           Informatica 48 (2024) 1–14   7 
Table 2: Evaluation values by
1
HE 
 HG 1 HG 2 HG 3 HG 4 
HA 1 HT HW HM HVW 
HA 2 HVW HW HVT HM 
HA 3 HM HW HVT HVW 
HA 4 HM HT HVW HW 
HA 5 HVT HM HVW HT 
 
Table 3: Evaluation values by
2
HE 
  HG 1 HG 2 HG 3 HG 4 
HA 1 HM HW HVW HVT 
HA 2 HVT HVT HVW HM 
HA 3 HT HVW HVT HM 
HA 4 HVW HW HM HVT 
HA 5 HW HM HT HVW 
 
Table 4: Evaluation values by
3
HE 
 HG 1 HG 2 HG 3 HG 4 
HA 1 HT HVW HW HM 
HA 2 HVW HVT HT HW 
HA 3 HW HT HM HM 
HA 4 HVW HT HM HW 
HA 5 HVT HM HW HVT 
Then through the IFWA, the
54
ij
IFM IFM

 =

 is constructed (See Table 5). 
Table 5: The 
54
ij
IFM IFM

 =

 
 HG 1 HG 2 HG 3 HG 4 
HA 1 
(0.62 ，0.34) (0.86 ，0.12) (0.69 ，0.31) (0.64 ，0.25) 
HA 2 
(0.73 ，0.27) (0.67 ，0.24) (0.47 ，0.52) (0.49 ，0.51) 
HA 3 
(0.81 ，0.19) (0.53 ，0.38) (0.36 ，0.53) (0.31 ，0.42) 
HA 4 
(0.78 ，0.14) (0.52 ，0.46) (0.25 ，0.49) (0.54 ，0.38) 
HA 5 
(0.36，0.23) (0.73 ，0.17) (0.62 ，0.34) (0.46 ，0.23) 

8   Informatica 48 (2024) 1–14                                                                         H. Liu 
Step 2. Normalize the
54
ij
IFM IFM

 =

into 
54
ij
NIFM NIFM

 =

 (See Table 6). 
 
Table 6: The
54
ij
NIFM NIFM

 =

  
 HG 1 HG 2 HG 3 HG 4 
HA 1 
(0.62 ，0.34) (0.12 ，0.86) (0.69 ，0.31) (0.64 ，0.25) 
HA 2 
(0.73 ，0.27) (0.24 ，0.67) (0.47 ，0.52) (0.49 ，0.51) 
HA 3 
(0.81 ，0.19) (0.38 ，0.53) (0.36 ，0.53) (0.31 ，0.42) 
HA 4 
(0.78 ，0.14) (0.46 ，0.52) (0.25 ，0.49) (0.54 ，0.38) 
HA 5 
(0.36，0.23) (0.17 ，0.73) (0.62 ，0.34) (0.46 ，0.23) 
 
Step 3. Construct the IFNNIS (See Table 7). 
 
Table 7: The IFNNIS 
 HG 1 HG 2 HG 3 HG 4 
IFNNIS (0.36，0.23) (0.12 ，0.86) (0.25 ，0.49) (0.31 ，0.42) 
 
Step 4. Construct the weight values (See Table 8): 
 
 
Table 8: The weight values 
 HG 1 HG 2 HG 3 HG 4 
weight 0.2333 0.3355 0.2177 0.2135 
 
Step 5. Calculate the
i
IFNWAA (Table 9).  
Table 9: The
i
IFNWAA 
 HA 1 HA 2 HA 3 
HA 4 HA 5 
IFNWAA 0.5914 0.6066 0.7978 0.4914 0.4044 
 
Step 6. Calculate the
i
IFNWGM (Table 10). 
Table 10: The
i
IFNWGM 
 HA 1 HA 2 HA 3 
HA 4 HA 5 
IFNWGM 0.4339 0.4073 0.6097 0.3355 0.2505 
 
Step 7. Calculate the ,,
i i i
KA K IFN IF B N FNKC I (See Table 11). 
 
Table 11: Three designed strategies 
 
i
IFNKA 
i
IFNKB 
i
IFNKC 
HA 1 0.2080 3.1948 0.7285 

Enhanced CoCoSo Method for Intuitionistic Fuzzy MAGDM…                           Informatica 48 (2024) 1–14   9 
HA 2 0.2057 3.1259 0.7203 
HA 4 0.2856 4.4069 1.0000 
HA 4 0.1678 2.5548 0.5875 
HA 5 0.1329 2.0000 0.4653 
 
Step 8. Calculate the 
i
IFNK (See Table 12). 
Table 12: The
i
IFNK 
 HA 1 HA 2 HA 3 
HA 4 HA 5 
IFNK 2.1623 2.1244 2.9771 1.7349 1.3643 
 
Step 9. According to ( ) 1,2,3,4,5
i
IFNK i = , the 
order is 
3 1 2 4 5
HA HA HA HA HA     and the 
best high-tech enterprise is
3
HA . 
 
4.2   Comparative analysis 
Then, the IF-CoCoSo is compared with IFWA  
 
 
 
operator[70] and IFWG operator[63], intuitionistic 
fuzzy normalized weighted Bonferroni mean 
(IFNWBM) operator[71], dual generalized 
intuitionistic fuzzy weighted BM (DGIFWBM) 
operator[72], IF-Taxonomy method[73], 
IF-PROMETHEE method [74] and intuitionistic fuzzy 
FUCOM-WASPAS(IF-FUCOM-WASPAS) 
method[75]. The comparative information results are 
constructed in Table 13. 
 
Table 13: Order of the different methods 
 
Order 
IFWA operator[70] 
3 1 2 4 5
HA HA HA HA HA     
IFWG operator[63] 
3 1 4 2 5
HA HA HA HA HA     
IFNWBM operator[71] 
3 1 2 4 5
HA HA HA HA HA     
DGIFWBM operator[72]  
3 1 4 2 5
HA HA HA HA HA     
IF-Taxonomy method[73] 
3 1 2 4 5
HA HA HA HA HA     
IF- PROMETHEE method [74] 
3 1 2 4 5
HA HA HA HA HA     
IF-FUCOM-WASPAS method[75] 
3 1 2 4 5
HA HA HA HA HA     
 
From the above detailed analysis, it could be known that 
the order of these decision methods is slightly different, 
however, all these decision models have the same optimal 
high-tech enterprise and worst high-tech enterprise. This 
verifies the IF-CoCoSo model is reasonable and effective.  
5   Conclusion 
Under the new development situation, China has entered 
a new stage of economic development and is seeking a 
path of high-quality development. In recent years, the 
position of high-tech enterprises in the national economy 
and technological development has become increasingly 
prominent. Due to the high risk and high return 
characteristics of high-tech industries, more and more 
high-tech enterprises are paying attention to their own  
 
financial risk management. Financial risk management,  
as an important risk prevention measure for high-tech 
enterprises, helps to scientifically utilize and reasonably 
allocate the capital resources of high-tech enterprises, 
reduce operational risks, achieve overall strategic goals, 
and maximize value. Therefore, strengthening financial 
risk management is crucial for high-tech enterprises in 
China. The financial risk evaluation of high-tech 
enterprises is classical MAGDM. Recently, the CoCoSo 
method has been used to manage MAGDM. The IFSs are 
used as a tool for portraying uncertain information during 
the financial risk evaluation of high-tech enterprises. In 
this paper, the IF-CoCoSo method is founded to manage 
MAGDM under IFSs. Finally, a numerical case study for 
financial risk evaluation of high-tech enterprises is 

10   Informatica 48 (2024) 1–14                                                                         H. Liu 
supplied to validate the proposed method. The main 
contribution is outlined: (1) the CoCoSo method has been 
extended to IFSs; (2) Information Entropy is used to 
derive weight under IFSs. (3) the IF-CoCoSo method is 
founded to manage the MAGDM under IFSs; (4) a 
numerical case study for financial risk evaluation of 
high-tech enterprises and some comparative analysis is 
supplied to validate the proposed method.   
There may be some possible limitations for financial risk 
evaluation of high-tech enterprises, which can be further 
explored in future research: (1) It is a worthwhile 
research topic to apply prospect theory to financial risk 
evaluation of high-tech enterprises under IFSs [76, 77]; (2) 
It is also worthwhile to apply regret theory to the study of 
MAGDM under IFSs [78, 79]; (3) In subsequent studies, 
the application of IFSs needs to be studied with 
consensus measures for financial risk evaluation of 
high-tech enterprises [80-82]. 
 
Compliance with ethical standards 
Ethical approval 
This article does not contain any studies with human 
participants or animals performed by any of the authors. 
Conflict of interest 
The authors declare that they have no conflict of interest. 
Funding Information 
This study did not receive any funding in any form. 
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14   Informatica 48 (2024) 1–14                                                                         H. Liu