CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

Assessment of Organization Performance in the Human 
Resource Management 

Chao Ge*, Cun Li 

Agricultural University of Hebei Baoding, Hebei, China 
68219008@qq.com 

It is widely accepted that human resource management is very important in a company. Hereinto, Human 
resources represent, and for sure will represent also in the future, the greatest potential competitive advantage 
of companies. In addition, organization performance in human resource management is a key point that can 
influence the development of a company. Thus, how to assess organization performance in the human 
resource management is a new challenge that a company have to face. In this paper, interval valued 
intuitionistic fuzzy numbers are introduced to express the assessments of the decision maker for the 
organization performance of a company, which can be constructed based on some criteria or attributes. Then, 
the TOPSIS method is proposed to solve this assessment problem. The application of the proposed method is 
also demonstrated in this paper by considering a real problem. 

1. Introduction 

With the appearance of knowledge economy time, the administration and supervision authorities of an 
organization start to realize the importance of human resource management. Human resources represent, and 
for sure will represent also in the future, the greatest potential competitive advantage of companies. The 
condition of the materialization of this prerequisite is an effective management of human resources, such as 
careful planning, organizing, leading and controlling (Cech et al., 2016). The literature review of the human 
resource and its management will be signified in the next section. 
In human resource management, with the increasing complexity and changes of business environment, the 
enterprises are confronted with more and more severe challenges about increasing their organization 
performance. Obviously, it has been a significant problem for the enterprise to decide that how to promote 
their or organization performance such as abilities of adjusting, innovating, operating and adding their values. 
However, in real case, more and more enterprises have realized that those elements including capital and 
technology, which used to be their competitive advantages, are copied by their competitors quite soon or 
weeded out faster and faster. Thus, how to assess organization performance in the human resource 
management is a new challenge that a company have to face. 
In order to assess the organization performance in the human resource management, the decision maker who 
is often an expert in this field is needed to be invited. But how to express the assessments of the decision 
maker objectively is difficult. Many ways have been proposed including interval valued numbers, triangle fuzzy 
numbers, trapezoidal fuzzy numbers (Xu et al., 2010), general fuzzy numbers (Zadeh, 1965), intuitionistic 
fuzzy numbers (Atanassov, 1986) and especially interval valued intuitionistic fuzzy numbers (Tan, 2011; Tan 
and Chen, 2010; Long and Geng, 2015). Thus, interval valued intuitionistic fuzzy number as a popular way is 
introduced in this paper to help the decision maker construct the decision matrix based on their preferences. 
Then, TOPSIS method which is based on distance measure is proposed in this paper to help aggregate 
assessment with interval valued intuitionistic fuzzy numbers on each attribute. As we known, TOPSIS 
developed by Hwang and Yoon can represent that the chosen alternative should have the shortest distance 
from the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS). Many researchers 
devoted to the development of TOPSIS method. Baky (2014) extended the concept of the technique for order 
preference by similarity to ideal solution (TOPSIS) to develop a methodology for solving multi-level non-linear 
multi-objective decision-making (MLN-MODM) problems of maximization-type. Chen (2000) extended the 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651139

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Ge C., Li C., 2016, Assessment of organization performance in the human resource management, Chemical 
Engineering Transactions, 51, 829-834  DOI:10.3303/CET1651139   

829



concept of TOPSIS to develop a methodology for solving multi-person multi-criteria decision-making problems 
in a fuzzy environment and he defined the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal 
solution (FNIS). In the final, the proposed method is applied to a real problem which demonstrates the 
scientific and applicability of this method. 
The rest of the paper is organized as follows: Section 2 reviews the literatures related to the human resource 
management. Section 3 and Section 4 show the proposed TOPSIS method with interval valued intuitionistic 
fuzzy numbers. Section 5 applies the proposed method in a real case. Section 6 concludes this paper. 

2. The literature review  

As demonstrated in Introduction, human resource management is very important in a company (Voegtlin and 
Greenwood, 2016). Many research and literature in the area of human resource management focuses on the 
positive impact of human resource management practices. Results such as employee well-being, 
organizational effectiveness and wider societal contributions have long been the focus to argue that human 
resource management can make a positive contribution to the organization and society (Becker and Smidt, 
2016). In addition, considering the fact that the modern development trend of an organization is firmly based 
on the paradigm of innovativeness, an interest in practices aimed at directing human resource management to 
innovativeness becomes increasing. Moreover, risk and risk management related to human resource 
management is another topic attracting much attention from the researchers. Some researchers held that in a 
world of complexity and rapidly changing environments, effective risk management may be a source of 
competitive advantage in human resource management. 

3. Preliminaries 

As mentioned in Section 1 and Section 2, base on the concepts of intuitionistic fuzzy sets, interval valued 
intuitionisitc fuzzy sets are proposed to express the preferences of the decision makers more objectively. 
Definition 1(Atanassov. 1986). Given a finite set X, an intuitionisitc fuzzy set A in X can be defined in the 
following: 

 , ( ), ( )A AA x u x v x x X  ,                                                                                                           (1) 

where  : 0,1Au X   denotes the degree of membership and  : 0,1Av X   denotes the degree of non-

membership with the condition: 0 1
A A

u v   , for all elements x in the set X.  
For each intuitionistic fuzzy set A in X, if the amount  

( ) 1 ( ) ( ),
A A A

x u x v x x X      . Here, 0 ( ) 1A x  .  

Although the mentioned intuitionistic fuzzy sets can deal with many situations, it cannot be applied in all 
situations, especially the preferences of the decision maker are interval value such as interval valued 
intuitionistic fuzzy sets (Wang and Li, 1998) below. 
Definition 2 (Atanassov and Gargo, 1989). Given an ordinary finite non-empty set X, an interval valued 

intuitionisitc fuzzy set A  in X can be defined in the following: 

 , ( ), ( )A AA x u x v x x X  ,                                                                                                           (2) 

where  : 0,1
A

u X   denotes the degree of membership and  : 0,1
A

v X   denotes the degree of non-
membership for all elements in the set X.  

Here,      0 sup sup 1
A A

u x v x   . 

For each x X ,  
A

u x and  
A

v x can be represented as closed intervals lower and upper points denoted 

by  -
A

u x ,  +
A

u x ,  -
A

v x  and  +
A

v x , respectively. 

Thus, the hesitation (or uncertainty) degree of interval valued intuitionistic fuzzy sets can be obtained as 

 
   

inf
1 sup sup

A x
u x v x   

，
 and 

 
   

sup
1 inf inf

A x
u x v x   

，
. 

830



Here  -
A

x  is equal to 
 infA x


，

 and   +
A

x  is equal to 
 supA x


，

, where    - + [0,1]
A A

x x D  （ ， ） . 

Firstly, the operational laws of interval valued intuitionistic fuzzy numbers are defined as follows. 

Definition 3. Let - -1 1 1 1 1( , , , )a u u v v
          and 

- -

2 2 2 2 2
( , , , )a u u v v

          be two interval valued intuitionistic 

fuzzy numbers, then the following operational laws are valid. 

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

( , , , )a a u u u u u u u u v v v v
                       ;  

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

( , , , )a a u u u u v v v v v v v v
                       ; 

(3)    1 1 1 1 1( 1 (1 ) ,1 (1 ) , , ) 0a u u v v
 

 
 

              
;  

(4)      1 1 1 1 1( , , 1 (1 ) ,1 (1 ) 0a u u v v
   


              

） ; 

(5)          1 1 1 1 1( , , , 0a v v u u
   


       

      
） . 

Definition 4. Let - -1 1 1 1 1( , , , )a u u v v
          and 

- -

2 2 2 2 2
( , , , )a u u v v

          be two interval valued intuitionistic 

fuzzy numbers, then the following operations are valid. 

 (1) 
1 2 2 1

a a a a   ;  

(2)  1 1 2 1 1 1 2a a a a     ;  

(3) 
1 1 2 1 1 2 1

( )a a a      . 

The proof of the Definitions 3 and 4 can refer to the corresponding concepts in (Long and Geng, 2015). 

4. The proposed method based on hesitant fuzzy sets 

After the definition and the introduction of operational laws of interval valued intuitionistic fuzzy numbers, the 
proposed method to assess the performance of organizations can be proposed in this section. Hereinto, the 
model of the assessment is defined at first, then the distance measure is designed and the TOPSIS method is 
introduced.  

4.1 The model of the proposed method 

For an assessment problem, firstly a decision matrix [ ]
ij m n

D a , where all the assessments 
ij

a (i = 1, 2, ..., m; 
j = 1, 2, ..., n) are interval value intuitionistic fuzzy numbers provided by a decision maker who is often invited 
from famous experts. For each alternative 

i
A (i = 1, 2, ..., m), the decision maker is required to express his/her 

preference on each attribute 
j

C (j = 1, 2, ..., n) which is constructed by the specific problem. Then, the 
decision maker specifies the attribute weights of the n attributes denoted as w = (w1, w2, …, wn)T with 0 ≤ wj ≤ 

1 (j = 1, 2, ..., n) and 
1

1
n

ji
w


 . 

Finally, according to preference of the decision maker, a normal decision making matrix can be generated in 
the following, which is obvious the base of the next method:  

1 2

1 11 12 1

2 21 22 2

1 2

n

n

m n n

m m m mn

C C C

A a a a

D A a a a

A a a a



 
 


 
 
 
 

.                                                                                               (3) 

4.2 Distance measure 
Distance measure, as a popular tool to measure the deviation of two objects has been widely applied in many 
fields, such as decision making, pattern recognition, machine learning and marker prediction (Ahn, 2011; Joshi 

831



and Kumar, 2016). In this paper, we introduce a generalized distance measure between two interval valued 
intuitionisitc fuzzy numbers in order to measure the differences between these two numbers. Firstly, an axiom 
is demonstrated in the following.  
Definition 5. Let A1, A2 and A3 be three interval valued intuitionisitc fuzzy sets on X = {x1, x2, ..., xn}, then the 
distance measure between A1 and A2 is defined as d(A1, A2), which satisfies the following properties: 
(1) 0 ≤ d(A1, A2) ≤ 1; 
(2) d(A1, A2) = 0, if and only if A1 = A2; 
(3) d(A1, A2) = d(A2, A1); 
(4) if 

1 2 3
A A A , then 

1 3 1 2
, ,d A A d A A . 

Definition 6. Let Ai and Ak be two interval valued intuitionistic fuzzy sets on the alternatives Ai and Ak (i, k = 1, 
2, ..., m), then the generalized weighted distance measure between alternatives Ai and Ak can be defined as 
follows: 

 
1

1

1
( , )

4

n

i k j ij kj ij kj ij kj ij kj

j

d A A w u u u u v v v v
n


   

       



 
        
 

 ,                                             (4) 

where λ > 0, which can be obtained according to the decision maker's risk attitude. 
When λ = 2, the generalized weighted distance measure reduces to the weighted Euclidean distance between 
Ai and Ak as follows: 

 
1 2

2 2 2 2

1

1
( , )

4

n

i k j ij kj ij kj ij kj ij kj

j

d A A w u u u u v v v v
n

       



 
        
 

 ,                                             (5) 

When λ = 1, the generalized weighted distance measure reduces to the weighted Hamming distance between 
Ai and Ak as follows: 

 
1

1
( , )

4

n

i k j ij kj ij kj ij kj ij kj

j

d A A w u u u u v v v v
n

       



 
        
 

 .                                             (6) 

Obviously, the defined distance measure in Definition 6 satisfies the properties in Definition 5. So, the proof is 
omitted here. 

4.3 The TOPSIS method 
Technique for order preference by similarity to ideal solution (TOPSIS) proposed by Hwang and Yoon (1981), 
one of known classical decision making method, bases upon the concept that the chosen alternative should 
have the shortest distance from the positive ideal solution (PIS) and the farthest from the negative ideal 
solution (NIS). In this paper, based on the characteristic of interval valued intuitionisitc fuzzy sets, we use the 
ideal of TOPSIS to select the alternative with the shortest distance from the positive ideal solution (PIS). 
In interval valued intuitionisitc fuzzy context, the interval valued intuitionisitc fuzzy ideal position solution PIS, 
denoted by A+ and negative ideal solution NIS A- can be defined below. 

  * * U * * U, , , , 1, 2, ,        L Li j j j jA x u u v v j n .                                                                               (7) 

Here,    * * U, max , max      
L L U

j j ij ij
i i

u u u u  and    * * U, min , min      
L L U

j j ij ij
i i

v v v v   

  ^ ^ U ^ ^ U, , , , 1, 2, ,        L Li j j j jA x u u v v j n                                                              (8) 

Here,    ^ ^ U, min , min      
L L U

j j ij ij
i i

u u u u  and    ^ ^ U, max , max      
L L U

j j ij ij
i i

v v v v   

The relative closeness coefficient of an alternative Ai with respect to the hesitant fuzzy PIS A+ and NIS A- is 
expressed as follows: 



 




i

i

i i

d
CC

d d
,                                                                   ( 9 ) 

where 0 1, 1, 2,...
i

CC i m   . 

832



Obviously, when an alternative Ai is closer to the interval valued intuitionisitc fuzzy PIS, CCi will be closer to 1. 
Thus, based on the closeness coefficient CCi, the ranking of all alternatives can be determined and the best 
alternative can be selected. 

4.4 The process of the proposed method 

The procedure based on mentioned proposed methods is demonstrated in the following figure. 
Assessment of performance 

of organization

Identifying decision attributes

Determining attribute weights

Obtaining decision result 

based on TOPSIS

Achieving satisfaction ?

Promoting sustainable 

development

Yes

  

Figure 1:  The framework of green supply chain coordination mechanism 

5. A real problem 

Based on the analysis in Section 1 and Section 2, we introduce a real problem to help some companies 
assess their organization performance by using the proposed method in Section 3 and Section 4. In this 
problem, firstly we invite an expert as the decision maker to implement process of assessment. Three 
companies are selected as alternatives denoted by A1, A2 and A3. Then the decision maker identifies four 
attributes denoted as C1, C2, C3 and C4.  

Table 1:  Description of the four attributes 

Attributes Descriptions 
C1 risk management 
C2 organization design  
C3 staff management and training 
C4 innovation and social responsibility 
 
The attributes are generated from the analysis about existing literature. The decision maker gives 
assessments of each alternative on each attribute, respectively. Therefore, a decision matrix 

3 4
[ ]

ij
D a  can 

be constructed in Table 2. In addition, the attribute weight can be determined as w = (0.2, 0.25, 0.25, 0.2)T by 
the decision maker. 

Table 2:  Interval valued intuitionistic fuzzy decision matrix 

 A1 A2 A3 
C1 {[0.3,0.5],[0.4,0.5]} {[0.1,0.4], [0.2, 0.5]} {[0.3,0.5],[0.4,0.5]} 
C2 {[0.5,0.6],[0.2,0.4]} {[0.1,0.4],[0.4,0.5]} {[0.2,0.3],[0.5,0.6]} 
C3 {[0.5,0.7],[0.1,0.2]} {[0.3,0.6],[0.1,0.2]} {[0.7,0.8],[0.1,0.2]} 
C4 {[0.6,0.8],[0.1,0.2]} {[0.2,0.6],[0.1,0.3]} {[0.1,0.2],[0.5,0.7]} 
 
According to Eqs. (4)-(9), assessments on each attribute can be aggregated into that on each alternative. 
Thus, the ranking order is demonstrated as A1  A3 A2 which indicates that A2 is the optimum company.  

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6. Conclusion 

In general, human resource management is very important in a company. Hereinto, Human resources 
represent, and for sure will represent also in the future, the greatest potential competitive advantage of 
companies. In addition, organization performance in human resource management is a key point that can 
influence the development of a company. Thus, how to assess organization performance in the human 
resource management is a new challenge that a company have to face. In this paper, interval valued 
intuitionistic fuzzy numbers are introduced to express the assessments of the decision maker for the 
organization performance of a company, which can be constructed based on some criteria or attributes. Then, 
the TOPSIS method is proposed to solve this assessment problem. In the final, the proposed method is 
applied to a real problem which demonstrates the scientific and applicability of this method. 
In the future, this proposed method may be applied in more and more organizations to help them improve the 
organization performance from the perspective of the human resource management.  

Acknowledgement 

This work was supported in part by 2015 Program supported by Social Sciences Fund of Agricultural 
University of Hebei: Study on Operation Strategies and Effectiveness of Wechat Career Accounts(Grant 
No.SK2015344). Submitted 07 November 2015. Published as resubmitted by the authors 05 December 2015. 
University of Hebei.  

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