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INTERNATIONAL JOURNAL OF c 2005 Institute for ScientificINFORMATION AND SYSTEMS SCIENCES Computing and InformationVolume 1, Number 3-4, Pages 406412

APPLYING FUZZY ANALYTIC HIERARCHY PROCESS TOEVALUATE SUCCESS FACTORS OF E-COMMERCE

FENG KONG AND HONGYAN LIU

Abstract. : With the fast development of the E-commerce, it becomes critical

to set up an E-commerce Evaluation criteria system. Fuzzy Analytic Hierarchy

Process is a new multi-criteria evaluation method evolved from Saatys AHP.

This paper aimed to find out the key factors that affect success in E-commerce

using fuzzy AHP, and give an evaluation method for E-commerce in order to

help researches and managers to determine the drawbacks and opportunities.

Key Words. E-commerce website, evaluation, fuzzy AHP.

1. Introduction

The Internet has been evolved from a basic tool of communications into a vastand interactive market of products and services involving over 240 million usersworldwide [1]. The Internet has the potential to market products and services tocustomers, to communicate information to a global community, to provide an elec-tronic forum for communications and to process business transactions such as ordersand payments. Naturally many enterprises across the world attempt to embracethe digital revolution and place a wide range of materials on the web, from infras-tructure to databases to actual services online for the convenience of customers.E-commerce is no longer just an option now but a necessity for enterprises aimingfor better performance.

Owing to the significance of E-commerce, the importance of measuring the qual-ity of E-commerce website cannot be overemphasized. With the fast developmentof the E-commerce, it becomes critical to set up an E-commerce Evaluation criteriasystem. The purpose of this paper is to develop an E-commerce website assessmentmethod to evaluate the success factors of E-commerce website.

The AHP was developed in the 1980s by Saaty [2]. It is a systematic decisionmaking method which includes both qualitative and quantitative techniques. It isbeing widely used in many fields for a long time. But one of the critical steps ofAHP method is to set up the comparison matrixes. When the number of attributes

(or alternatives) in the hierarchy increases, more comparisons between attributes(or alternatives) need to be made. This could easily cause confusion due to theexcess of questions and hence the efficiency of the model. So a consistency checkis required for the pair-wise comparison matrix. Therefore, whether the setting ofthe comparison matrix is scientific affects the correctness of AHP directly. Whenthe comparison matrices are not consistent, we should adjust the elements in thematrixes and carry out a consistency test until they are consistent. In this paper,

Received by the editors June 15, 2004 and, in revised form, January 22, 2005.This research is supported by the Doctorial Teachers Foundation of North China Electric

Power University.

406

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APPLYING FUZZY AHP TO EVALUATE SUCCESS FACTORS OF E-COMMERCE 407

we introduce a fuzzy AHP in which substitute membership scales for Saatys 1-9scales to reduce adjusting times needed.

This paper is organized as follows: section 2 gives the introduction to the

fuzzy analytic hierarchy process; in section 3 we evaluate the success factors ofE-commerce website; in section 4 is the conclusion of this paper.

2. The fuzzy Analytic Hierarchy Process

2.1. Definitions of the new fuzzy comparison matrices. The comparisonmatrix defined by Saaty employs 1-9 scales. The 1-9 scales are illustrated with thefollowing comparison matrix and table 1.

(1) A =

w1w1

w1w2

w1wn

w2w1

w2w2

w2wn

..

.

..

.

..

.wnw1

wn

w2

wn

wn

=

a11 a12 a1na21 a22 a2n

..

.

..

.

..

.an1 an2 ann

Saatys scale The relative importance of the two sub-elements1 Equally important3 Moderately important with one over another5 Strongly important7 Very strongly important9 Extremely important

2, 4, 6, 8 Intermediate values

Table 1. Saatys scale for pairwise comparison.

Our new fuzzy comparison matrix differs with Saatys in that we use membershipscales, instead of the 1-9 scales, as the values of the elements.

(2) A =

w1w1+w1

w1w1+w2

w1

w1+wnw2

w2+w1

w2w2+w2

w2

w2+wn...

... ...

wn

wn

+w1

wn

wn

+w2

wn

wn

+wn

=

r11 r12 r1nr21 r22 r2n

......

...rn1 rn2 rnn

If this comparison matrix is consistent, it should satisfy:

(3) rii = 0.5, rij + rji = 1,1

rij 1 = (

1

rik 1) (

1

rki 1).

This method compares weights in pairs and is more straightforward and easierto use for the decision-makers.

The meanings of our membership scales can also be expressed in the same wayas Saatys scale, see table 2.

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408 H. Y. LIU AND F. KONG

Scale values The relative importance of the two sub-elements0.5 Equally important

0.55(or0.5 0.6) Slightly important

0.65(or0.6 0.7) Important0.75(or0.7 0.8) Strongly important0.85(or0.8 0.9) Very strongly important0.95(or0.9 1.0) Extremely important

Table 2. Scale for fuzzy pair-wise comparison.

Theoretically, the membership scales put forward in this paper and Saatys scalesshould satisfy the following:

(4) rij =aij

aij + 1.

The difference of our membership scales with Saatys lies in that the values ofmembership scales falls within the range of [0,1].

2.2. Calculation of the priority weights. Let

(W = w1, w2, , wn),

(5) wi =bini=1

bi

.

where, bi =1

nj=1

1

rij

n

.

2.3. Consistency test of the comparison matrix. We can use the followingequation to calculate the consistency index:

(6) CI =

ni=1

(AW)inwi

n 1,

where the values of the elements in matrix A could be derived by applying equation(3) to matrix R.

The comparison matrix will be considered to be consistent if there exists CR =CIRI

< 0.1. The various values ofRI are shown in table 3.

Size of matrix 1 2 3 4 5 6 7 8 9 10RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49

Table 3. Values of RI.

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3. Evaluation of the success factors of E-commerce website

Now we use fuzzy AHP to evaluate the success factors of a commerce website

and then undertake a comprehensive evaluation of the website.We will use a numerical illustration to show our method.First, set up the analytic hierarchy model of E-commerce evaluation as the fol-

lowing:

The best success factor

Trust(C1)System

quality(C2)

Content

quality(C3)

Online

service(C4)Use (C5)

Security(C11)

Visualappearance

(C21)

Up-to-datedness(C31)

Tracking OrderStatus (C41)

Information(C51)

Privacy(C12)response time

(C22)

Understand

ability(C32)

Account

Maintenance

(C42)

Transaction

(C52)

page loading

speed (C23)timeliness (C33)

Payment

Alternatives

(C43)

the disabled

service (C53)

24-hour

availability

(C24)

Preciseness

(C34)FAQs (C54)

Figure 1. The hierarchy model of the evaluation of websites

Next, we give the fuzzy comparison matrixes of the criteria level and sub-criterialevel. For instance, Tables 4-9 show the original fuzzy pair-wise comparison ma-trixes for E-commerce website evaluation.

C1 C2 C3 C4 C5C1 0.5 0.8 0.7 0.5 0.9C2 0.2 0.5 0.4 0.1 0.4C3 0.3 0.6 0.5 0.3 0.7C4 0.5 0.9 0.7 0.5 0.7C5 0.1 0.6 0.3 0.3 0.5

Table 4. Fuzzy Comparison matrix at criteria level.

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C11 C12

C11 0.5 0.7C12 0.3 0.5

Table 5. Fuzzy Comparison matrix at sub-criteria level, for criterion C1.

C21 C22 C23 C24C21 0.5 0.6 0.7 0.4C22 0.4 0.5 0.6 0.3C23 0.3 0.4 0.5 0.2C24 0.6 0.7 0.6 0.5

Table 6. Comparison matrix at sub-criteria level, for criterion C2.

C31 C32 C33 C34C31 0.5 0.2 0.7 0.4C32 0.8 0.5 0.9 0.6C33 0.3 0.1 0.5 0.2C34 0.6 0.4 0.8 0.5


C41 C42 C43C41 0.5 0.7 0.6C42 0.3 0.5 0.4C43 0.4 0.6 0.5


C51 C52 C53 C54C51 0.5 0.25 0.7 0.5C52 0.75 0.5 0.6 0.7C53 0.3 0.4 0.5 0.4

C54 0.5 0.3 0.6 0.5

Table 9. Comparison matrix at sub-criteria level, for criterion C5

Then calculate the relative priority weights of each criterion and each sub-criterion. The results of the instance are shown in table 10.

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Criterion Priority Sub- Priority of final Priority of CR of CR of of criterion criterion sub-criterion sub-criterion Sub-criterion Criterion

C1 0.371 C11 0.7 0.260 0

C12 0.3 0.111C21 0.278 0.017

C2 0.061 C22 0.182 0.011 0.049C23 0.113 0.007C24 0.427 0.026C31 0.146 0.022

C3 0.153 C32 0.497 0.076 0.087 0.05C33 0.062 0.009C34 0.295 0.045C41 0.477 0.166

C4 0.348 C42 0.207 0.072 0C43 0.316 0.110

C51 0.193 0.013C5 0.067 C52 0.432 0.029 0.095C53 0.166 0.011C54 0.210 0.014

Table 10. Priority and Consistency ratios

We can see that the essential factors affecting the success of websites are factorsC1 and C4; while C11 is the most critical factor within C1 and C41 is the mostcritical factor within C4.

Let the evaluation ranking set be: Very good, Good, Moderate, Bad, Very bad.We can give priority ranking weights to the elements of the evaluation set as,respectively, 100, 80, 60, 40, and 20.

Suppose the evaluation matrix for the E-commerce website is:

Criterion Very Good Good Moderate Bad Very BadC11 0.7 0.2 0.1 0 0C12 0.6 0.3 0.1 0 0C21 0.2 0.6 0.2 0 0C22 0 0.3 0.4 0.2 0.1C23 0 0.5 0.3 0.2 0C24 0.6 0.2 0.2 0 0C31 0.6 0.1 0.2 0.1 0C32 0.4 0.3 0.1 0.2 0C33 0.8 0.2 0 0 0C34 0.7 0.2 0.1 0 0

C41 0.6 0.3 0.1 0 0C42 0.4 0.2 0.3 0.1 0C43 0.3 0.4 0 0.2 0.1C51 0 0.3 0.3 0.3 0.1C52 0.2 0.2 0.2 0.2 0.2C53 0 0.2 0.6 0.2 0C54 0 0 0.4 0.1 0.5

Result 0.517 0.263 0.129 0.094 0.025

Table 11. Evaluation matrix for websites

The comprehensive evaluation result is:

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0.517 100 + 0.263 80 + 0.129 60 + 0.094 40 + 0.025 20 = 83.57.Hence, the E-commerce website belongs to grade of good according to our eval-

uation.

4. Conclusion

In this paper, we put forward a subjective and objective integrated approach todetermine attributes weights in Fuzzy MADM problems. Since the approach takesinto account both subjective and objective factors, it retains the merits of bothsubjective and objective approaches, to determine weights by solving mathematicalmodels automatically and at the same time take into consideration the decisionmakers preferences, and overcomes the shortcoming which may happen when eithera subjective approach or an objective approach is used in Fuzzy MADM problems.

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Economics and Management Department, North China Electric Power University, Baoding,071003, China.

E-mail: [email protected] and [email protected]

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