Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 2, No. 3, 2021 

 

43 

A	Fuzzy	Evaluation	Approach	for	Scientific	Research	
Projects	with	2‐Tuple	Linguistic	Preference	Relations	
Huarong Zhang1, Xiangqian Feng2, * 

1Institute of science and technology, Nanjing Normal University, Nanjing, 210023, China 
2School of Business, Nanjing Normal University, Nanjing, 210023, China 
* Corresponding author: Xiangqian Feng (Email: xiangqianone@126.com) 

 

Abstract: Science and technology project evaluation is an important means of science and technology management. Whether 
the evaluation of science and technology projects is fair or not directly affects the development of national economy and the 
allocation of science and technology resources. Due to the complexity of the project and the fuzziness of human thinking, the 
expert information is often difficult to quantify in the process of project evaluation. Generally, the better choice is to express it 
in qualitative language. In this paper, the 2-tuple linguistic preference relation is proposed to evaluate scientific research projects. 
The reasonableness of the concept of complete consistency for the 2-tuple linguistic preference relation is discussed. Priority of 
2-tuple linguistic preference relation is set up based on the 2-tuple weighted geometric averaging operator. Finally, combined 
with Science and technology project evaluation problem, the effectiveness and feasibility of the method are verified. 

Keywords: Science and technology project evaluation; Linguistic preference relation; 2-tuple linguistic. 
 

1. Introduction 
Science and technology project initiation and evaluation is 

an important part of science and technology project 
management. It is an important means and guarantee to 
promote the sustainable and healthy development of national 
science and technology, promote the optimal allocation of 
science and technology resources, and improve the level of 
science and technology management [1]. Project initiation 
review is one of the core links of science and technology 
project evaluation. It is generally carried out in accordance 
with the procedures of preliminary review form review, peer 
expert communication review, comprehensive treatment of 
writing comprehensive review opinions, and discipline 
review meeting review. Peer expert review and 
comprehensive treatment are the two most important links in 
the review process [2]. Some scholars have studied using the 
uncertainty method to describe and gather the review opinions 
of peer experts. Dey [3] proposed a decision support system, 
which analyses projects with respect to market, technicalities, 
and social and environmental impact in an integrated 
framework using analytic hierarchy process, a multiple-
attribute decision-making technique. Zhu [4] proposed a 
project evaluation method for non-formatted Chinese text 
evaluation information based on multi-granular linguistic 
labels.  

In the actual decision-making process, due to the fuzziness 
and diversity of science and technology project evaluation 
information, each expert's personal preference, professional 
status and authority are not exactly the same and other factors, 
it is impossible for experts to express different projects with 
certain values when comparing them. It is usually expressed 
in fuzzy language evaluation. The 2-tuple linguistic model 
formalized by Herrera and Martínez in year 2000, has 
upgraded several linguistic processes for solving complex 
decision-making issues. Its successful application in different 
fields has impelled several researchers to work in its 
extension. Faizi and Nawaz [5] think that the intuitionistic 2-
tuple linguistic set accurately deals with the imprecise and 

unpredictable information in those decision-making problems 
where experts prefer the degree of membership and non-
membership values in the form of 2-tuple. Faizi and Saabun 
[6] proposed Linear Best-Worst Method (LBWM) and 
Euclidean Best-Worst method (EBWM) to achieve the best 
criteria priority vector for Multi-Criteria Group Decision 
Making (MCGDM) problems in the context of intuitionistic 
2-tuple linguistic information. Using 2-tuple to express the 
evaluation information of decision-makers is more practical, 
and more appropriately expresses the cognitive uncertainty 
with clear connotation and unclear extension in the process of 
scientific research project evaluation, which is conducive to 
the evaluation of scientific and technological projects with 
fuzzy characteristics. Therefore, this paper applies 2-tuple to 
the evaluation of science and technology projects, describes 
the evaluation information of science and technology projects 
with 2-tuple linguist terms, and puts forward a scientific and 
effective evaluation method of science and technology 
projects. 

The rest of paper is organized as follows. In Section 2, we 
review some concepts and operations related to 2-tuple 
linguistic terms. In Section 3, gives the definitions of 
consistency for 2-tuple linguistic preference relation and then 
proposes the approach to derive the priority weights from 2-
tuple linguistic preference relations. In Section 4, the 
proposed approach is demonstrated by using an illustrative 
example. Finally, conclusions of this paper are drawn in 
section 5. 

2. Preliminary 

Let  {0,1, , }iS s i T    �   be a finite and totally 
ordered linguistic term set with odd cardinality where is  

represents a possible value for a linguistic variable, and the 
following characteristics should be satisfied [7]: 

(1) 0min( ) , max( )i i
i T i T

s s s s 
   

(2) ( )k ks Neg s  ; 



 

44 

(3)    1 1k l k ls s s s       , where  1 is   is the 
index i  of the linguistic term ( , )is i k l ; 

(4) max( , )k l ks s s  , if k ls s   and min( , )k l ks s s  , if 

k ls s . 
And some operational laws of any two linguistic terms 
,k ls s S  are introduced as follows: 
(1) k l k ls s s   ; 
(2) k l k ls s s  ; 
(3) k ks s  ; 
(4) ( )k ks s 

  ; 

(5) ( )k l k ls s s s     ; 
(6) 1 2 1 2( ) k k ks s s       

Definition 1 Let  {0,1, , }iS s i T    �   be a 
linguistic term set and [ 0.5, 0.5]    denoting the symbolic 
translation, ( , )i is   is called a 2-tuple linguistic variable, and 
the following characteristics should be satisfied [8]: 

(1)  : [0, ] [ 0.5, 0.5)S    , ( ) ( , )i i is   ; 

(2) 1 [ 0.5, 0.5) [0, ]S    , 
1 ( , ) [0, ]i i i is i   
     ; 

(3) 1( , ) ( ( , ))k k k kneg s s  
   ; 

(4) ( , ) ( , )k k l ls s   if k l ; 
(5) if k l , ①if k l  , ( , ) ( , )k k l ls s  , 
②if k l  , ( , ) ( , )k k l ls s   
③if k l  , ( , ) ( , )k k l ls s  . 
where ( )i round    and , [ 0.5, 0.5)i ik       . 

Note “round” is the usual round operator. 
And some operational laws of any two 2-tuple linguistic 

terms ( , ), ( , )k k l ls s   are introduced as follows: 

(1) 1 1( , ) ( , ) (min{ , ( , ) ( , )})k k l l k k l ls s g s s   
        

(2)  1 1( , ) ( , ) max{0, ( , ) ( , )}k k l l k k l ls s s s           
(3) 1( , ) (min{ , ( , )})k k k ks g s   

   ; 

(4) 1( , ) (min{ , ( ( , )) })k k k ks g s
     . 

Definition 2. For linguistic 2-tuples ( , ), ( , )k k l ls s  , the 
deviation measure between ( , )k ks   and ( , )l ls  is defined as 
follows 

 
 1 1(( , ), ( , )) ( , ) ( , )k k l l k k l ld s s s s   

          (1) 

3. Consistency Measures and Priority 
for 2-Tuple Linguistic Preference 
Relation 

Definition 3 [9]. Let ( )ij n nP p   be a matrix. If ijp  is a 2-

tuple, and ( )ji ijp Neg p , then P  is called a 2-tuple linguistic 
preference relation. 

Definition 4 Let ( )ij n nP p  be a 2-tuple linguistic preference 

relation, then P  is called a consistent 2-tuple linguistic 
preference relation if there exists ik kj ijp p p   for 

, , {1, 2, , }i j k N n  � . 

Theorem 1 ( )ij n nP p   is called a consistent 2-tuple 

linguistic preference relation if and only if ( )ij n nQ q   is a 
consistent fuzzy preference relation, where 

1 ( )
0.5 , , 1, 2, ,

ij
ij

p
q i j n



 
   
  

� . 

Proof: Let ( )ij n nP p   is called a consistent 2-tuple 

linguistic preference relation, from Definition 4 ik kj ijp p p   

for , , {1, 2, , }i j k N n  � , so 
1 1 1( ) ( ) ( )ik kj ijp p p
       . 

Then 
11

1

( )( )
0.5 0.5

( )
           0.5 0.5 0.5

kjik
ik kj

ij
ij

pp
q q

p
q

 







  
      

    
 

     
  

 

Conversely, let ( )ij n nQ q   be a consistent fuzzy preference 
relation, then  

1 1

1

( ) ( ) ( 0.5) ( 0.5)

                            ( 0.5) ( )

ik kj ik kj

ij ij

p p q q

q p

 



 



      

   
 

So, ik kj ijp p p  ,which completes the proof of Theorem. 

Lemma 1 [10] Let ( )ij n nP p   be a 2-tuple linguistic 

preference relation and ( )n nijP p  , where 

1 1

1

1
( ( ) ( ) ; , 1, 2, ,

n

ik kjij
k

p p p i j n
n

 



 
      

 
 � , 

then P  is a consistent 2-tuple linguistic preference relation. 
Definition 5 Let ( )ij n nP p   be a 2-tuple linguistic 

preference relation, then we define the distance between P  and 

( )n nijP p   as follows: 

 

1 1

2
( , ) ( , )

( 1)

n n

ij ij
j i i

d P P d p p
n n   




          (2) 
 

We set 

-1 -1

1 1

1 2
( ) ( ( , )) ( ) ( )

( 1)

n n

ij ij
j i i

CI P d P P p p
n n    

   


  as the 
consistency index of the 2-tuple linguistic preference relation 
P . 

The above consistency index reflects the deviation degree 
between the linguistic preference relation P  and the consistent 
linguistic preference relations. Obviously, the smaller the value 
of ( )CI P  , the more consistent the linguistic preference 

relation P . If ( )CI P  =0, then P  is a consistent linguistic 

preference relation. If ( ) 0.1CI P  , we conclude that P  is of 
acceptable consistency; otherwise, we conclude that P  is of 
unacceptable consistency. 

Definition 6 [11]. Let TWGA: nS S , if 
 

  11 1 2 2
1

( , ), ( , ), , ( , ) ( ( , )) i
n

v
v n n i i

i

TWGA s s s s   


 
   

 
�   (3) 

 

where [0,1]iv   and 1 1
n

ii
v


 , then TWGA is called the 

2-tuple weighted geometric averaging operator. 



 

45 

Let ( )ij n nP p   be a 2-tuple linguistic preference relation, 

we can obtained the weight vector 1 2( , , , )nw w w w �  by the 
following formula 

 

 
 

1
1 2

1
1 21

( , , , )

( , , , )

n
v i i in

i n
n

v i i ini

TWGA p p p
w

TWGA p p p










�

�
        (4) 

 
where 1 niv  , {1, 2, , }i n � . 

4. An Illustrative Example 
In this section, taking the fund project evaluation of a basic 

research funding department as an example, it is assumed that 
there are 3 experts participating in the project evaluation. 
They give the following 2-tuple linguistic preference relation 
and try to select one for approval and funding from the four 
alternatives  1 2 3 4, , ,X x x x x  by using the linguistic terms 
in the set 

0 1 2

3 4 5

6 7 8

  ,

 , ,  ,

,  ,  

s extremely poor,s very poor,s poor

S s slightly poor s fair s slightly good

s good s very good s extremly good

   
 

    
    

 

4 4 5 3

4 4 5 4

3 3 4 2

5 4 6 4

( , 0) ( , 0.3) ( , 0.4) ( , 0.1)

( , 0.3) ( , 0) ( , 0,1) ( , 0.4)

( , 0.4) ( , 0.1) ( , 0) ( , 0.4)

( , 0.1) ( , 0.4) ( , 0.4) ( , 0)

s s s s

s s s s
P

s s s s

s s s s

  
  
 
 

  

 

Step 1 Consistency test for 2-tuple preference relationship. 

4 4 4 4

4 4 5 4

4 3 4 3

4 4 5 4

( , 0) ( , 0.2) ( , 0.3375) ( , 0.4375)

( , 0.2) ( , 0) ( , 0, 4625) ( , 0.2375)

( , 0.3375) ( , 0, 4625) ( , 0) ( , 0.225)

( , 0.4375) ( , 0.2375) ( , 0.225) ( , 0)

P

s s s s

s s s s

s s s s

s s s s



  
   
 
 

 

 

( ) 0.0495 0.1CI P    , we conclude that P  is of 
acceptable consistency. 

Step 2 Priority for 2-tuple linguistic preference relation by 
the formula (4) 

0.2407 0.2662 0.1970 0.( , , , )2961w   
which means the ranking of alternatives is 

4 2 1 3x x x x� � � . 

5. Conclusion 
2-tuple linguistic is an effective tool to express humans’ 

fuzzy information when providing linguistic evaluations, and 
have wide applications in MCDM. In this paper, we study the 
2-tuple linguistic preference relation, which aim to evaluate 
scientific research projects. A simple yet pragmatic approach 

for judging whether or not a 2-tuple linguistic preference 
relation is consistency. In case of acceptable consistent 2-
tuple linguistic preference relation, the approach of deriving 
priority vector is put forward. The numerical results show that 
the proposed evaluation approach provides us with a useful 
way for scientific research projects. 

Acknowledgment 
The author is most grateful to the referees and the editors 

for their constructive suggestions. The work was partly 
supported by University Social Sciences Project of Jiangsu 
Province (No. 2016SJD630014). 

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