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CHEMICAL ENGINEERING TRANSACTIONS 
 

 VOL. 46,2015 

A publication of 

 

The Italian Association 
Of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Peiyu Ren, Yanchang Li, Huiping Song 
Copyright © 2015, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-37-2; ISSN 2283-9216 

Method of the Enterprise’s Supplier Selection Based on 

Interval Value TOPSIS of Triangular Fuzzy Numbers 
Lin Li, Guanqun W ang* 
School of Humanities and Economic Management, China University of Geosciences, Beijing 
Law and Public Affairs, Jiangsu Normal University. 
wgqpolitics@126.com 

Supplier selection is an important task when an enterprise establishes a supply chain. For an enterprise’s raw 

material supply, the assessment index system of supplier selection is established by analyzing its basic 
principles and method. An enterprise’s m ulti-objective supplier selection method is put forward based on 
triangular fuzzy numbers and interval value TOPSIS. This method can fully reflect the requirements of supplier 
capacity and enterprise demands, and provides an effective approach for enterpri ses to select suppliers. 

1. Introduction 

Supply chain management is one of the important competitive strategies of modern enterprises. The main 
purpose for supply chain management is to integrate different enterprise resources in the supply chain so as 
to respond to market changes and satisfy the customer needs. Supplier selection is one of the important tasks 
for an enterprise to establish a supply chain because the supplier has a great influence on product cost and 
quality, technology and timescales of new product launch. Based on research data, the sales volume for the 
products and services purchased by one enterprise from its suppliers accounts for 50 to 90 percent of the 
sales of the whole enterprise. Thus, scientifically and reasonably selecting an enterprise’s suppliers is crucial 
of its operation management.  
There are many decision-making methods to evaluate a supplier. This paper concludes the types of supplier 
selection methods and analyzes characteristics and application conditions of various decision -making 
methods by summing up previous supplier selection and decision-making methods employed experts. 
Furthermore, it proposes supplier selection methods based on TOPSIS of triangular fuzzy numbers and will 
provide helpful references for enterprise supply chain management and supplier selection.  

2. Principles and Methods of Supplier Selection 

2.1 Principles 
Generally speaking, the buyer and the supplier have a mutually conflicting relation, which has been replaced 
by the cooperative win-win relation between them in modern chain management.  
Houshyar(1992) divided the systematized supplier selection procedures into the following steps: a. Supplier 
selection criteria; b. Establishment of supplier selection criteria; c. Weight of supplier selection criteria; d. 
Processing of supplier selection data; e. Calculation and ranking of the supplier’s performances. Therefore, 

the supplier selection is a series of management and decision behaviors such as screening of candidate 
suppliers, establishment of evaluation criteria, weight of evaluation criteria, candidate suppliers’ performances 

in evaluation criteria and overall assessment in their alternative schemes. 
According to Carter’s study (1995, it is found that when the relation between the supplier and the buyer 
becomes more intimate with more cooperative relations, the buyer tends to reduce the number of suppliers 
and enter into strategic alliance with the remaining suppliers. Forster (1961) thought the buyer intended to 
cooperate with a single supplier in place of previous cooperative relations with several suppliers. So according 
to these studies on methods of supplier selection, Swift (1995) classified the different evaluation factors in 
single supplier or several supplier selection. It is found by F-test that the buyer pays more attention to price, 
quality and delivery time in selection of several suppliers however, in the single supplier selection more 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1546214

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Li L., Wang G.Q., 2015, Method of the enterprise’s supplier selection based on interval value topsis of triangular 
fuzzy numbers, Chemical Engineering Transactions, 46, 1279-1284  DOI:10.3303/CET1546214  

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emphasis is placed upon the technology-supporting effectiveness and reliability of products. In addition, the 
buyer selecting several suppliers pays more attention to price, while the buyer selecting the single supplier 
lays more emphasis on total cost of products. 
After studying considerations in selection of suppliers in the US automobile industry, Choi et al. (1996) 
performed analysis on questionnaires in their study. The results show that the main influencing factors for the 
manufacturers to select direct suppliers are the suppliers’ design and manufacturing capacity. When they 
select indirect suppliers what manufacturers often consider is price. In the analysis, supplier selection 
encompasses 26 evaluation factors, and eight factors are selected through the factorial analysis.  
It is known from the above literatures that indexes for supplier selection and evaluation are mostly aimed at 
specific industries and the general supplier selection method is difficult to determine. The supplier selection 
standard has developed to multi-objective orientation. Thus, the indexes determined in the study should be the 
important evaluation criteria recognized by scholars generally so as to gain the enterprise’s supplier evaluation 

criteria in consideration of the practical domestic iron and steel industry. 

2.2 Method of Supplier Selection 
Different enterprises have different criterion in selection of suppliers: the selecting criterion for enterprises 
taking the cost advantage as their competitive strategy is mainly cost; selecting criterion for the ones taking 
quality differentiation as their competitive strategy is mainly in consideration of quality. It is known by summing 
up foreign and domestic supplier selection methods in literatures that the supplier evaluation modes are 
mostly probability and statistics, mathematical programming, supplier profile analysis, multi -attribute utility, 
cost proportion, analytical hierarchy process, multi-objective decision-making method and fuzzy 
comprehensive judgment.  
The multi-objective decision-making method is to simplify the complex evaluation of multi-attribute utility 
function as evaluation of a series of single-attribute utility numbers to get value function and weight and 
performances of suppliers. This method allows for the following criteria: price a nd delivery time, production 
technology and quality, financial status and reputation, company’s organization and conception, and after -sale 
services and cooperation; the supplier selection system is structured based on multi -objective decision to gain 
ranking of suppliers’ performances. 

3. Design of Multi-Attribute Decision Method Based on Interval Number TOPSIS 

3.1 Interval Number Decision Matrix and its Normative Approach 
(1) Structuring the Interval Number Decision Matrix 
The multi-attribute decision for an attribute as an interval number is set as a scheme set, 

1 2
)（ ， ，

n
x x x x and 

1 2
, )（ ,

m
u u u u  which is an attribute value. The scheme 

i
x  is measured by 

the attribute vale 
j

u  to get 
i

x ’s attribute value ija  ( ,   
L U

ij ij ij
a a a )on 

j
u , so as to constitute the decision 

matrix ( )



ij n m

A a .  

As for multi-attribute decision of an interval number, the decision matrix information ( )



ij n m

A a is obtained 

first, then it is processed normatively to get the normative decision matrix ( ) , ij n mR r .  

(2)Normative Approach 

In order to eliminate influences of different physical dimensions on decision results, the decision matrix A  is 

translated into a nominative matrix ( ) , ij n mR r where, ,   
L U

ij ij ij
r r r . As the decision attributes are 

divided into efficiency and cost types, ( 1, 2)
j

I j  is set as the subscript sets representing efficiency and 

cost types. The normative methods for two types are as follows:  

1

1

/ , ,


  
n

ij ij ij

j

r a a i N j I
                                  

(1) 

2

1

(1 / ) / (1 / ), ,


  
n

ij ij ij

j

r a a i N j I                                 (2) 

Based on the rules of operation related to interval numbers, Formulas (1) and (2) are rewritten as follows: 

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1

1

1

,

, ,

,






 


  








n
L L U

ij ij ij

i

n
U U L

ij ij ij

i

r a a

i N j I

r a a

                     (3)   

1

2

1

(1 / ) (1 / ),

, ,

(1 / (1 / ),






 


  








n
L U L

ij ij ij

i

n
U L U

ij ij ij

i

r a a

i N j I

r a a

                   (4) 

3.2 Determination of the Weight of Interval Number Attribute Based on Triangular Fuzzy Numbers  

(1) Determining the weight vector 
1 2

, )（ ,   
m

 of attribute values 

The fuzzy AHP proposed by Buckley (1985) is adopted in this paper to establish a fuzzy positive reciprocal 
matrix by the triangular fuzzy numbers according to experts’ opinions. Then, the weight is solved by the fuzzy 

geometric method to calculate the total fuzzy score of schemes via hierarchical series. Finally, the priority level 
of the schemes is ranked based on the total fuzzy score of schemes.  

3.3 TOPSIS Method Whose Attribute Value is an Internal Value  

(1) Determine the positive and negative ideal points (
,

 
y y

) of interval number attribute values based on 
weighting a normative interval number matrix.  

, max( ), max( ) ,
          

L U L U

j j j ij ij
i i

y y y y y j M
 

, min( ), min( ) ,
          

L U L U

j j j ij ij
i i

y y y y y j M  
(2) Calculate the distances of each scheme to positive and negative ideal points respectively: 

1 1

,
   

 

       
  

m m
L L U U

i ij j ij j ij j

j j

D y y y y y y i N

 

1 1

,
   

 

       
  

m m
L L U U

i ij j ij j ij j

j j

D y y y y y y i N

 
(3) Calculate the close degree ( )

i
c i N  of each scheme to the ideal point, and make a sequence of the 

schemes based on close degrees. The bigger 
i

c  is, the better the scheme 
i

x is. 

,


 
 



i
i

i i

D
c i N

D D
 

4. Determination and Calculation of Assessment Index System for Enterprises to Select 
Suppliers 

4.1 Establishment of Assessment Index System for Enterprises to Select Suppliers 
(1) Design and Handout of Questionnaires 
There were 14 indexes as shown in Table 1 for the enterprise’s supplier selection determined preliminarily 
based on research results, and the supplier selection index system was established according to 
questionnaires and factor analysis.  
In this paper, the middle-level and senior executives, purchasing staff and QC personnel in medium and large 
iron and steel enterprises were selected as respondents. They scored these indexes by 5 levels (1-Leaving 
out; 2-Considered but not important; 3-Important; 4-Very important; 5-Extremely important). The investigators 
gave explanations to the respondents about questionnaires in person, and asked them to complete the 
questionnaires on site. The questions that the respondents couldn’t understand were explained by the 

investigators. In this way 3580 questionnaires were given out, and 257 completed questionnaires were 
collected, of which 232 were effective. The recovery rate and effective rate for questionnaires were up to 
73.43% and 66.29% respectively.  

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Table 1 Descriptive statistics of questionnaires 

Index  Mean value SD 

Enterprise qualification 2.9515 0.9020 
Guarantee and compensation  2.6153 0.6984 
Product quality 3.1403 0.8834 
Geographic position 3.0217 0.6389 
Service attitude 1.7280 1.0190 
Response to service 3.0809 0.7984 
Cooperative relation 3.1359 0.6169 
Pricing policy 2.6200 0.5220 
Historical performance 3.1729 0.5915 
Production equipment and capacity 1.7804 0.8300 
Coordination mechanism 3.0160 1.1084 
Reputation in the industry 1.8611 0.8074 
Guarantee for transportation 2.6766 0.3156 
Delivery rate on time 2.7766 1.3156 

 
The “Service Attitude”, “Production Equipment and Capacity” and “Reputation in the Industry” are below 2 

based on their mean values and standard deviations. This indicates that the investigators generally consider 
that importance degree for these indexes is lower. Thus, the other 11 indexes should be reserved as shown in 
Table 2.  

Table 2: Index weight for the enterprise’s supplier selection 

1-level Index Weight  2-level weight Weight  Total weight 

Basic requirement C1 0.4131 
Enterprise qualification C11 0.3844 0.1588 
Historical performance C12 0.2945 0.1217 
Geographic position C13 0.3211 0.1326 

Requirement for product C2 0.3125 

Pricing policy C21 0.3121 0.0975 
Delivery rate on time C22 0.2322 0.0726 
Product quality C23 0.1814 0.0567 
Guarantee for transportation C24 0.2743 0.0857 

Requirement for service C3 0.2744 

Cooperative relation C31 0.2145 0.0589 
Coordination mechanism C32 0.3181 0.0873 
Response to service C33 0.2153 0.0591 
Guarantee and compensation C34 0.2521 0.0692 

 
 (2) Factor Analysis 
The factor analysis was carried out by the other 11 indexes to determine the enterprise’s supplier selection 

index system structure. Applicability of factor analysis was tested at first. The test methods for the applicability 
were: the Bartlett Test of Sphericity and the Kaiser-Meyer-Olkin (KMO) tests.  
SPSS18.0was used to conduct the KMO and Bartlett Sphericity tests for the supplier selection index 
questionnaire results. The testing result KMO value was 0.814. This value was used for the exploratory factor 
analysis based on standards offered by Statistician Kaiser. Meanwhile, the accompanied probability from the 
Bartlett Sphericity test was 0.000, less than the significant level of 0.05. Thus, the null hypothesis for Bartlett t 
sphericity test was refused, and the exploratory factor analysis could be carried out.  
There are two criteria for determining factor number by the exploratory factor analysis: one is selecting the 
factor whose characteristic value is greater than 1; the other is that the accumulated SD contribution rate is 
greater than 70%. The variables have factor load capacity in common factors. The factor load capacity 
determines a variable should be assigned to the common factor. Generally speaking, it is significant if the 
absolute value of the factor load capacity is greater than 0.3; it is more important if the capacity is greater than 
0.3; it is very significant if the capacity is greater than 0.5. Thus, the factor load value being greater than 0.4 
means that it has significant load capacity to determine the items contained for each factor. The value was 
less than 0.4 but rounded, the load for the factors is shown in Table 3.  
(3) Explanation of Index Naming 
Determine the enterprise’s supplier selection index system based on results of factor analysis.  

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Table 3 Load matrix for supplier selection index factors 

Supplier selection index Component 

1 2 3 
Enterprise qualification 0.7399   
Historical performance 0.6929   

Geographic position 0.5479   
Pricing policy  0.7258  
Delivery rat on time  0.6258  
Product quality  0.5860  
Guarantee for transportation  0.4956  
Cooperative relation   7.0223 
Coordination mechanism   6.6706 
Response to service   6.3730 
Guarantee and compensation   5.1579 
SD explanation proportion 34.17% 21.66% 17.15% 

Total SD explanation proportion 72.98% 

 
(4) W eight Determination of the Enterprise’s Supplier Selection Evaluation Index System 
10 experts were employed to carry out fuzzy judgment to relative importance at different levels. The index 
weight was calculated by Formulas (5—9) as shown in Table 2.  

4.2 Cases of the Enterprise’s Supplier Selection 
(1) Problem Description 
One enterprise determined three potential suppliers (named as x1, x2 and x3 respectively) by preliminary 
screening. Experts were employed to evaluate each index, and the scores were represented by interval values 
(scoring by the hundred mark system); the original data was obtained.  
(2) Normalize original data and get the weighting normative decision matrix based on the index weight, and 

the weighting normative matrix is available, i.e. ( )  ij n mY y . 

(3) Determine positive and negative ideal points ,
 

y y  of interval number attribute values: 

 0.01813, 0.02635 jy ,  
0.00421, 0.00633




j
y  

(4) Calculate each supplier to be evaluated and the distance between positive and negative ideal points; 
calculate the close degree ( )

i
c i N  for each evaluation object to the ideal point and make a sequence for 

suppliers by their close degrees.  

Table 4: Close degrees for evaluation object’s ideal points 

Supplier to be evaluated 
1

x  
2

x  
3

x  



i
D  0.1756 0.2238 0.1812 



i
D  0.1622 0.1426 0.2119 

i
c  0.4802 0.3891 0.5391 

It can be seen from the calculated results that 
3

c >
1

c >
2

c . The conclusions are that Supplier 3 is the best 
option with Supplier 1 ranked second and Supplier 2 ranked poorest. 

5. Conclusions 

Aiming at the enterprise’s practical supplier selection, a multi-subjective supplier selection method for 
enterprises is established based on interval value TOPSIS and triangular fuzzy numbers. The method 
describes the supplier level by the interval numbers, which more accords with the enterprise’s practical 
supplier evaluation. In addition, by determining index weight by triangular fuzzy numbers the information is 

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more complete and can be directly applied to practical supplier selection. The study results show that this 
method can measure the enterprise’s supplier level effectively, and provide valuable information for the 

enterprise in the selection of suppliers. 

Acknowledgements 

This paper is supported by “the Fundamental Research Funds for the Central Universities”, No: 2652013068. 

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