不完全語意偏好關係預測導入企業資源規劃成功率架構

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不完全語意偏好關係預測導入企業資源規劃成功率架構

研究成果報告(精簡版)

計畫類別：個別型

計畫編號： NSC 98-2410-H-151-006-

執行期間： 98 年 08 月 01 日至 99 年 07 月 31 日

執行單位：國立高雄應用科技大學國際企業系

計畫主持人：王天津

計畫參與人員：碩士班研究生-兼任助理人員：高禾淳

博士班研究生-兼任助理人員：彭淑珍

報告附件：出席國際會議研究心得報告及發表論文

公開資訊：本計畫涉及專利或其他智慧財產權，2 年後可公開查詢

中華民國 99 年 10 月 31 日

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行政院國家科學委員會補助專題研究計畫

; 成果報告

□期中進度報告

不完全語意偏好關係預測導入企業資源規劃成功率架構

Applying Incomplete Linguistic Reference Relations to Forecast the

Success Possibility of Implementing ERP Systems

計畫類別：

;

個別型計畫 □整合型計畫

計畫編號：

NSC 98-2410-H-151-006

執行期間： 98 年 8 月 1 日至 99 年 7 月 31 日

執行機構及系所：國立高雄應用科技大學國際企業系

計畫主持人：

王天津

共同主持人：

計畫參與人員：

彭淑珍、高禾淳 (兼任助理二人)

成果報告類型(依經費核定清單規定繳交)：;精簡報告 □完整報告

本計畫除繳交成果報告外，另須繳交以下出國心得報告：

□赴國外出差或研習心得報告

□赴大陸地區出差或研習心得報告

;出席國際學術會議心得報告

□國際合作研究計畫國外研究報告

處理方式：

除列管計畫及下列情形者外，得立即公開查詢

□涉及專利或其他智慧財產權，□一年□二年後可公開查詢

中華民國 99 年 10 月 30 日

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Abstract—This study applies an analytic hierarchical prediction model based on Multi-Criteria Decision Making with Incomplete Linguistic Preference Relations(InLinPreRa) to help the organizations become aware of the essential factors affecting the Enterprise Resource Planning(ERP), as well as identify the actions necessary before implementing ERP. The subjectivity and vagueness in the prediction procedures are dealt with using linguistic terms quantified in an interval scale[- , ]t t . Then predicted success/failure values are obtained

to enable organizations to decide whether to initiate ERP, inhibit adoption or take remedial actions to increase the possibility of successful ERP. The empirical results not only demonstrate the senior manager support degree, organizational and coordination are the three most important influential factors in the ERP initiative process, but also reveal the applicability and feasibility of reciprocal Incomplete Linguistic Preference Relation(InLinPreRa) for solving complicated hierarchical multiple attribute prediction problems.

Keywords: InLinPreRa, Incomplete Linguistic Preference Relations, ERP, Multi-Criteria Decision Making, Analytical Hierarchy process.

I. INTRODUCTION

nterprise resource planning (ERP) is an enterprise-wide application software package that integrates all necessary business functions into a single system with a common database. In order to implement an ERP project successfully in an organization, it is necessary to select a

suitable ERP system[1-3]. This study uses Incomplete

Linguistic Preference Relations under Multi-Criteria Decision Making to predict the success/failure values of the ERP system. The method uses simple calculation and speeds up the process of comparison and selection of alternative. Decision makers obtain the matrix by choosing a finite and fixed set of alternatives and set a pairwise comparison based on their different preferences and knowledge. The next section discusses the literatures related to ERP, fuzzy preference relation, and Incomplete Linguistic Preference Relations. An analytic hierarchy framework based on the Multi-Criteria Decision Making with Incomplete Linguistic Preference Relations for predicting ERP implementation is described in Section 3. In Section 4, an empirical case of ERP initiative in Taiwan is presented. Finally conclusions are given in Section 5.

II. LITERATURE REVIEW

A. Enterprise Resource Planning(ERP)

In the dynamic and unpredictable business environments, companies face the tremendous challenge of expanding markets and rising customer expectations. This compels them to lower total costs in the entire supply chain, shorten

throughput times, reduce inventories, expand product choice, provide more reliable delivery dates and better customer service, improve quality, and efficiently coordinate globe demand, supply and production. Due to high cost and complication of the implementing process, it is not easy to install ERP system successfully. Thus, for most companies, being able to predict the rates of success before installing the system and finding the factors that influence the ERP success are important .

B. Fuzzy Preference Relations

Herrera-Viedma et al. (2004)[4]proposed Fuzzy Preference

Relations to understand the inconsistent problems in analytic hierarchy process that are caused by multi-decision-makers, multi-criteria, and multi-alternatives. Preference Relation means that the decision maker counters a set of criteria or alternatives according to the linguistic variables so as to carry out the pairwise comparison, then a mapping value can be derived; this value represents the degree of preference of the first alternative over the second alternative. Wang and

Chen (2007) [5]utilized fuzzy preference relations to

criticize the fuzzy analytical approach to partnership selection.

C. The Decision Making Matrix of Incomplete Linguistic Preference Relations

Linguistic preference relations are usually used by decision makers to express their linguistic preference information based on pairwise comparisons (Xu, 2005) [6]. Xu (2006)[7]

proposed the Incomplete Linguistic Preference Relations. The relevant definitions are described as follows.

1) Definition 1: Incomplete

Linguistic

Preference Additive Relation

Let A=(a_{ij n n})× be linguistic preference relation, if A is an incomplete linguistic preference relation, it counters the fact that decision makers can carry out pairwise comparison for attributes so as to satisfy Eq. (1)

0 0 , ,

ij ij ji ii

a ∈S a ⊕a =S a =S (1)

2) Definition 2: Incomplete

Linguistic

Consistent Additive Preference Relation:

Let A=(aij n n) × be complete consistent additive preference

relation, which counters all of the i j k, , decision makers for pairwise comparison, if a >Sik 0 represents xi is better

than xk; while a >Skj 0 represents xk is better than xj,

then a >S_ij ₀ can be derived the equation of x_i better than

j

x is

=

ij ik kj

a a ⊕a (2)

3) Definition 3: The Algorithm Rules of Three

Different Kinds of Pairwise Comparison Decision

Application of Incomplete Linguistic Preference Relations in

predicting the success of ERP Implementation

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Making Matrices

Then based on equations, preference relation matrix is generated. For different known factors of decision-making expert’s choice, it could obtain few matrices. The algorithm rules of the three different decision making matrices are shown as below:

Type 1: Horizontal pairwise comparison

13 1 12 14 1 2 1 2 3 4 ( ) ( ) ( ) ( ) ( ) ( ) 3 4 A A A A A A 0 ... A 0 ... A 0 ... D A ₀ _... ... A ... 0 m m r e r e r e r e r e r e ij _{m m} m m m a a a a a _× × ⎡ ⎤ ⎢ ⎥ ⎢_× _× _× _× ⎥ ⎢ ⎥ ⎢× × × × ⎥ ⎡ ⎤ =_⎣ _⎦ = _⎢ _⎥ ⎢× × × × ⎥ ⎢ ⎥ × × × × × ⎢ ⎥ ⎢_× _× _× _× ⎥ ⎣ ⎦ L M

×

represents the unknown variables.

Type 2: Vertical pairwise comparison

13 1 23 2 43 3 1 2 3 4 ( ) ( ) ( ) ( ) 3 ( ) 4 ( ) A A A A A A 0 ... A 0 ... A 0 ... D A ₀ _... A ... 0 m m r e r e r e r e ij _r _e m m r e m m m a a a a a × × ⎡ _× _× _×⎤ ⎢ ⎥ ⎢_× _× _×⎥ ⎢ ⎥ ⎢× × × ×⎥ ⎡ ⎤ =_⎣ _⎦ = _⎢ _⎥ ⎢× × ×⎥ ⎢ ⎥ × × × × ⎢ ⎥ ⎢ ⎥ × × × ⎣ ⎦ L M _M _O

Type 3: Oblique pairwise comparison

1 12 1 23 2 34 1 2 3 4 ( ) ( ) ( ) ( ) ( ) 3 4 ( ) A A A A A 0 ... A 0 ... A A 0 ... D A ₀ A ... 0 m m m r e r e r e r e r e ij _{m m} r e m m m a a a a a₋ × × ⎡ _× _× _× ⎤ ⎢ ⎥ ⎢_× _× _× ⎥ ⎢ ⎥ ⎢_× _× _× ⎥ ⎡ ⎤ ⎢ ⎥ =_⎣ _⎦ = ⎢_× _× _× _× ⎥ ⎢ ⎥ ⎢_× _× _× _× ⎥ ⎢ ⎥ ⎢_× _× _× _× ⎥ ⎣ ⎦ L O M O

III. FRAMEWORK FOR PREDICTING ERP IMPLEMENTATION

This section comprises four subsections: investigating the influential factors on ERP initiative, determining the priority weights of influential factors, determining the priority ratings for possible out regarding factors, and obtaining the priority weight for prediction.

A. Investigating the influential factors on ERP implementation

The influential factors are derived though widespread investigation and consultation with several experts, including two professionals , three senior mangers, three Systems Analysts and three random sampling staff to analyze the chance if successful ERP implementation. Synthesizing the literature review from, the opinions of these experts are utilized to yield the seven key influential factors used in this study.

B. Determining the priority weights of influential factors Subjectivity and vagueness within the measuring process are dealt with using linguistic variables quantified in a scale of

[- , ]t t . This study are used linguistic to express their strength of preference among influential factor.

1) Linguistic variables

This study provides the evaluators simple linguistic terms quantified on a scale of [-8,8] to express their strength of preference among influential factors (see Table 1). Linguistic variables [8] are simultaneously used to measure the likelihood of success/failure regarding each influential factor (see Table 2).

Table 1 Linguistic terms for the importance weights of influential factors

Definition value value

Absolutely more

important (AB) 8

Less Weakly more important

(LWK) -2

Very strongly more

important (VS) 6

Less Strongly more

important (LST) -4 Strongly more important

(ST) 4

Less Very strongly more

important (LVS) -6 Weakly more important

(WK) 2

Less Absolutely more

important (LAB) -8 Equally important (EQ) 0

Table 2 Linguistic variables for the priority ratings of possible outcome Definition value Very high (VH) 5 4 High (H) 2 Fair (F) 0 Less High (LH) -2

Less Very high (LVH) -4

2) Obtaining priority weights of influential factor

Although Xu’s method made the evaluating process more flexible, he only focused on comparing one unique standard.

Wang and Hsu[9] improved Xu’s method with multi-criteria

and applied to a selection of hearing aids. The following describes the procedures for obtaining the prioritise of influential factors.

♦ Construct pairwise comparison matrices amongst the influential factors ( C_r ,r=1, 2,...,k ). The evaluators

( E_e , e=1, 2,...,n ) used three types of pairwise

comparisons algorithm which are horizontal vertical and oblique to construct pairwise comparison matrices. Three kinds of matrices are as below.

1 2 3 4 ( ) ( ) ( ) ( ) 1 12 13 14 1 2 3 ( ) ( ) 4 ... 0 ... 0 ... 0 ... 0 ... ... ... ... ... ... 0 ... 0 k k k e e e e k e e ij k _kxk C C C C C C a a a a C C C a C C × ⎡ ⎤ ⎢ ⎥ × × × × ⎢ ⎥ ⎢_{× ×} _× _× ⎥ ⎡ ⎤ =_⎣ _⎦ = ⎢ ⎥ × × × × ⎢ ⎥ ⎢ _× ⎥ ⎢ ⎥ × × × × ⎢ ⎥ ⎣ ⎦

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1 2 3 4 1 ( ) 21 2 ( ) 3 31 ( ) ( ) ( ) 4 ₄₁ ( ) 1 ... 0 ... 0 ... 0 ... 0 ... ... _... _{... ... ...} ₀ ... 0 k k k e e e e ij _e e k k _kxk C C C C C C a C a C C a C a C _a × × × × × ⎡ ⎤ ⎢ _{× ×} _×⎥ ⎢ ⎥ ⎢ _× _× _×⎥ ⎢ ⎥ ⎡ ⎤ =_⎣ _⎦ = ⎢ _{× ×} _×⎥ ⎢ ⎥ × ⎢ ⎥ ⎢ _{× × ×} ⎥ ⎣ ⎦ 1 2 3 4 ( ) 12 1 ( ) 2 23 ( ) 3 ( ) ( ) 34 4 ( ) -1 ... 0 ... 0 ... 0 ... 0 ... ... _{... ...} _... _... ₀ ... 0 k k k e e e e e ij e k k k kxk C C C C C a C C a C _a C a C a C × ⎡ × × × ⎤ ⎢ ⎥ × × × ⎢ ⎥ ⎢_{× ×} _× ⎥ ⎢ ⎥ ⎡ ⎤ =_⎣ _⎦ = ⎢_{× ×} _× _× ⎥ ⎢ ⎥ ⎢ ⎥ ⎢_{× ×} _× _× ⎥ ⎣ ⎦ The remaining ( ) ij e

a can be calculates using Eq.(1) and

Eq.(2) to obtain the other known

×

of triangular second

half. Finally, obtain the full preference matrix.

♦ Transform the preference value ( )

ij e a into ( ) ij e b in an

interval scale [0,1] ,then the matrix Ct obtained as

( )

( e)

Ct=f C . The transformation function is given by

: [ , ] [0,1] f −a a → , ( ) 2 x a f x a + = (3a) 1 2 3 4 ( ) ( ) ( ) ( ) 12 13 14 1 1 _{( )} _{( )} _{( )} _{( )} 21 23 24 2 2 _{( )} _{( )} _{( )} _{( )} ( ) ( ) 3 31 32 34 3 ( ) ( ) 4 ₄₁ ₄₂ ₄₃ ... 0 ... 0 ... 0 ... ... ij k e e e e k e e e e k e e e e e e _k e e kxk k C C C C C b b b b C b b b b C C b b b b Ct b _C b b b C ⎡ ⎤ =_⎣ _⎦ = _{( )} _{( )} 4 ( ) ( ) ( ) ( ) 1 2 3 4 0 ... ... ... ... ... ... ... ... 0 e e k e e e e k k k k kxk b b b b b ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (3b)

♦ Utilize the method of average value to integrate the judgment values of n evaluators, namely

[ _{ij kxk}] C= p (4a) 1₍ (1) (2) _... ( )₎ 1 ( ) 1 1,2,..., , =1,2,..., ij ij ij ij n n e p_ij b b b b n n e i k j k = + + + = = =

∑

(4b)

♦ Use

h

_ij to indicate the normalized preference values of each influential factor, such as

1 2 3 4 ( ) ( ) ( ) ( ) 12 13 14 1 1 ( ) ( ) ( ) ( ) 21 23 24 2 2 ( ) ( ) ( ) ( ) 3 ₃₁ ₃₂ ₃₄ ₃ ( ) ( ) ( ) ( ) 4 41 42 43 4 ... 0 ... 0 ... 0 ... [ ] = 0 ... ... k e e e e k e e e e k e e e e k ij kxk e e e e k k C C C C C h h h h C h h h h C C h h h h C h C _h _h _h _h C = ( ) ( ) ( ) ( ) 1 2 3 4 ... ... ... ... ... ... ... 0 e e e e k k k k _kxk h h h h ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (5a) 1 1,2,... , 1,2,..., ij ij k ij i p h i k j k p = = = =

∑

(5b) ♦ Given the r

w

denoting the priority weight of

influential factor

r

, the priority weight of each factor can be obtained that is

1 1 1 1, 2,..., k rj j r k k ij i j h w i k h = = = =

∑

=

∑∑

(6) 1_{w w}_,2 _,...,k w , rw∈[0,1]_, 1 1 k r r w = =

∑

C. Determining the priority ratings for possible outcome regarding factors

The evaluators are asked to express their subjective judgments regarding the preference ratings of possible outcome(A ii, =1,2,...,m) regarding each influential factor in

linguistic terms, as listed in Table 2.

♦ The evaluators useed three types of pairwise comparisons algorithm to choose the best of two possible

outcome for a set of m-1preference. data under each

influential factor, three kinds of matrices are below.

12 23 34 -1 1 2 3 4 m ( ) 1 ( ) 2 ( ) 3 ( ) ( ) 4 ( ) ... 0 ... 0 ... 0 ... 0 ... ... ... ... ... ... ... 0 m m m m e r e r e r r e r e uv e r m m m A A A A A a A a A a A D a A a A × × ⎡ ⎤ ⎢ × × × ⎥ ⎢ ⎥ ⎢_× _× _× ⎥ ⎢ ⎥ ⎢ ⎥ × × × ⎢ ⎥ ⎡ ⎤ =_⎢ _⎥ = _⎢ _⎥ ⎣ ⎦ ⎢_× _× _× _× ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢_× _× _× _× ⎥ ⎣ ⎦ M 23 34 -1 12 1 2 3 4 m ( ) ( ) ( ) ( ) 1 2 3 ( ) ( ) 4 ... 0 ... 0 ... 0 ... 0 ... ... ... ... ... ... ... 0 m m m m e e e e r r r r r e r e uv m m m A A A A A a a a a A A A D a A A × × ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢_× _× _× _× ⎥ ⎢ ⎥ ⎢ ⎥ × × × × ⎢ ⎥ ⎡ ⎤ =_⎢ _⎥ = _⎢ _⎥ ⎣ ⎦ ⎢_× _× _× _× ⎥ ⎢ ⎥ ⎢ ⎥ × ⎢ ⎥ ⎢ ⎥ ⎢× × × × ⎥ ⎣ ⎦ M 2 1 31 4 1 1 1 2 3 4 1 ( ) 2 ( ) 3 ( ) ( ) ( ) 4 ( ) ... 0 ... 0 ... 0 ... 0 ... ... ... ... ... ... ... 0 m m m m r e r e r e r e uv _r _e r e m m m A A A A A A a A a A D a A a A _a × × ⎡ _× _× _× _×⎤ ⎢ ⎥ ⎢ ⎥ × × × ⎢ ⎥ ⎢ ⎥ × × × ⎢ ⎥ ⎡ ⎤ =_⎣ _⎦ = _⎢ _⎥ × × × ⎢ ⎥ ⎢ ⎥ × ⎢ ⎥ ⎢ ⎥ ⎢ × × × ⎥ ⎣ ⎦ M

Using Eq.(1) and Eq.(2) to obtain the corresponding value. Finally, obtain the full preference matrix.

♦ Next, the preference value r ( )e uv

a is transformed in the

range [-4,4] into rbuv( )e in an interval scale [0,1] ,then the

matrix r_Dt _{obtained as} r_Dt₌ _f₍r_D( )e₎ _{. The}

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]

1 ,

0 [

]

,

[

:

− a

a

→

f

, ( ) 2 x a f x a + = ( ) [ ] , 1,2,..., r r e uv mxm Dt= b u v= m (7)

♦ Utilize the method of average value to integrate the judgment values of n evaluators, namely

[ ] r uv mxm D = q (8a) 1₍ (1) (2) _... ( )₎ 1 ( ) _{1,2,..., ,} _1,2,..., 1 e r r r q_uv b_uv b_uv b_uv n n e rb_uv u m v m n e = + + + = = = =

∑

(8b) ♦ Use r uv

λ to indicate the normalized preference values of each influential factor, such as

[ ] r r uv mxm D= λ _(9a) 1 , 1,2,..., r uv uv m uv u q u v m q λ = = =

∑

(9b) ♦ Consequently, r u

ϕ denoting the average rating of

possible outcome

u

with respect to influential factor

r

is provided. The desired rating of each possible outcome can be obtained for each influential factor that is 1 1 m r r u uv v ϕ λ π = =

∑

(10)

D. Obtaining the priority weight for prediction Multiplying the priority weights of influential factors by the ratings of possible outcomes, a predicted value Zu

for chance in success/failure implementation is obtained as:

r r

u u

Z =ϕ ⊗ w (11)

IV. NUMERICAL EXAMPLE

A steel manufacture company located in Taiwan wishes to increase benefit and gain competitive by initiating ERP implement. Due to high cost and complication of the implementing process, it is not easy to install ERP system successfully. Thus, CEO asks a group comprising two professionals , three senior mangers, three Systems Analysts and three random sampling staff to analyze the chance if successful ERP implementation.

A. Weighting calculation of the influential factors Seven major influential factors are considered in this problem of predicting the success of ERP implementation. The sequences of these seven influential factors are randomly assigned, namely, (C1)project procedure time, (C2)function of information system, (C3)user's cooperation, (C4) senior manager support degree, (C5)coordination, (C6)organizational, (C7)cost. The pairwise comparisons for these seven factors are obtained via a series of interviews with the assessment representatives.

1)

Based on the interviews with 11 members

regarding the importance on seven influential

factors, the pairwise comparison matrices for a set

of 6 factors are listed below.

(1) (1) (1) (1) (1) (1) (1) 12 23 34 45 56 67 { , , , , , } {VS, LSLV, LVLA, VT, LAB,ST} C a a a a a a = = (3) (3) (3) (3) (3) (3) (3) 21 23 24 25 26 27 { , , , , , } { , , , , , } C a a a a a a AV LST LAB VS LSLV WK = = (4) (4) (4) (4) (4) (4) (4) 21 31 41 51 61 71 { , , , , , } { , , , , , } C a a a a a a WK LVS LVLA VS LAB LSLV = = (5) (5) (5) (5) (5) (5) (5) 12 32 42 52 62 72 { , , , , , } { , , , , , } C a a a a a a LSLV LST WK ST LVLA LVLA = = (6) (6) (6) (6) (6) (6) (6) 31 32 34 35 36 37 { , , , , , } { , , , , , } C a a a a a a AV VS LST LVS LVLA LWK = = (7) (7) (7) (7) (7) (7) (7) 13 23 43 53 63 73 { , , , , , } { , , , , , } C a a a a a a SW WE LST LVS LAB WE = (8) (8) (8) (8) (8) (8) (8) 41 42 42 45 46 67 { , , , , , } { , , , , , } C a a a a a a AB LST LVLA LSLV LVS VT = = (9) (9) (9) (9) (9) (9) (9) 14 24 34 54 64 74 { , , , , , } { , , , , , } C a a a a a a ST LST LAB LWK LVLA VS = (10) (10) (10) (10) (10) (10) (10) 57 51 52 53 54 56 { , , , , , } { , , , , , } C a a a a a a AB LWK LVLA WE LVS WK = = (11) (11) (11) (11) (11) (11) (11) 57 17 27 37 47 67 { , , , , , } { , , , , , } C a a a a a a AV LWK LAB WK LVS SW = =

The evaluator 1 is used as an example base on Eq.(1) and Eq.(2) to obtain the other known × . Finally, obtain the full preference matrix.

(1) (1) 1 2 3 4 5 6 7 1 2 3 4 5 6 7 C 0 6 1 -6 -1 -9 -5 -6 0 -5 -12 -7 -15 -11 -1 5 0 -7 -2 -10 -6 6 12 7 0 5 -3 1 1 7 2 -5 0 -8 -4 9 15 k k ij a C C C C C C C C C C C C C C × ⎡ ⎤ = ⎣ ⎦ = 10 3 8 0 4 5 11 6 -1 4 -4 0 ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

2)

Transform the preference value ( )

ij e a into ( ) ij e b in

an interval scale [0,1] ,then the matrix

Ct

.

(1) (1) 1 2 3 4 5 6 7 1 2 3 4 5 6 7 0.500 0.700 0.533 0.300 0.467 0.200 0.333 0.300 0.500 0.333 0.100 0.267 0.0 k k ij Ct b C C C C C C C C C C C C C C × ⎡ ⎤ = ⎣ ⎦ = 00 0.133 0.467 0.667 0.500 0.267 0.433 0.167 0.300 0.700 0.900 0.733 0.500 0.667 0.400 0.533 0.533 0.733 0.567 0.333 0.500 0.233 0.367 0.800 1.000 0.833 0.600 0.767 0.500 0.633 0.667 0.867 0.700 0.467 0.633 0.367 0.500 ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

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(1)-(2) stated above can calculate the preference relation matrices of the other ten evaluators; therefore, using Eq.(4a) , the averaged pairwise comparison matrix of eleven

evaluators can be obtained as listed below.

1 2 3 4 5 6 7 1 2 3 4 5 6 7 0.500 0.478 0.443 0.398 0.440 0.405 0.465 0.522 0.500 0.465 0.420 0.462 0.427 0.487 0.557 0.535 0.500 0.45 k k ij C C C C C C C C C C C C p C C C × ⎡ ⎤ =_{⎣ ⎦} = 4 0.496 0.461 0.521 0.602 0.580 0.546 0.500 0.542 0.507 0.567 0.560 0.538 0.504 0.458 0.500 0.465 0.525 0.595 0.573 0.539 0.493 0.553 0.500 0.573 0.535 0.513 0.479 0.433 0.475 0.427 0.500 ⎡ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣ ⎦7 7x ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

4)

Eq.(5a) is used to normalize the aggregated pairwise

comparison matrix. 1 2 3 4 5 6 7 1 2 3 4 5 6 7 0.129 0.129 0.119 0.126 0.127 0.127 0.128 0.135 0.135 0.125 0.133 0.133 0.134 0.134 0.144 0.144 0.135 0.14 k k ij C C C C C C C C C C C C h C C C × ⎡ ⎤ =_{⎣ ⎦} = 4 0.143 0.145 0.143 0.156 0.156 0.147 0.158 0.156 0.159 0.156 0.145 0.145 0.135 0.145 0.144 0.146 0.144 0.154 0.154 0.145 0.156 0.159 0.157 0.157 0.138 0.138 0.129 0.137 0.137 0.134 0.137 ⎡ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣ ⎦7 7x ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

5)

The priority weight of each influential factor can the be obtained by Eq.(6). The priority weight and rank of each influential factor assessed by eleven evaluators are listed in Table 3 The rank of the influential factor importance weight is substituted as:

Table 3 The rank of the influential factor importance weight

C1 C2 C3 C4 C5 C6 C7 Total Rank Weight C1 0.129 0.129 0.119 0.126 0.127 0.127 0.128 0.884 7 0.128 C2 0.135 0.135 0.125 0.133 0.133 0.134 0.134 0.928 6 0.134 C3 0.144 0.144 0.135 0.144 0.143 0.145 0.143 0.997 4 0.144 C4 0.156 0.156 0.147 0.158 0.156 0.159 0.156 1.088 1 0.157 C5 0.145 0.145 0.135 0.145 0.144 0.146 0.144 1.004 3 0.145 C6 0.154 0.154 0.145 0.156 0.159 0.157 0.157 1.083 2 0.156 C7 0.138 0.138 0.129 0.137 0.137 0.134 0.137 0.951 5 0.137 Total 6.935 1.000 (0.157) (0.156) (0.145) (0.144) (0.137) (0.134) (0.128) C4 C6 C5 C3 C7 C2 C1 f f f f f f

B. Calculation of the weights for possible outcomes with respect to influential factors

If every influential factor has a strong presence in the company, then implement ERP system is more likely to be successful. To determine the priority weight matrix for possible outcomes with respect to each influential factor, the linguistic variables for evaluators are listed in Table 2. The priority weights of two possible outcomes are calculated as follow.

1) The eleven evaluators are interviewed to assess which is more likely to occur according to each influential factors. All the opinions of these eleven evaluators regarding the preference intensity for the chance of success and failure with respect to each influential factor are described in Table 4.

2) Transform the values in the scale [-4,4] into the interval [0,1]. Inverse comparison for failure and success.

3) Using Eq.(8a) average value to integrate the judgment values of n evaluators.

4) Using Eq.(9a) and Using Eq.(10) the can be used to normalize and synthesize the preference ratings of two possible outcomes based on seven in influential factors. 5) The normalized values and priority ratings are listed in

Table 5.

Table 4 Linguistic variables given to the priority ratings of two possible outcomes

(1)

D

( )2

D

( )3

D

( )4

D

( )5

D

( )6

D

( )7

D

( )8

D

( )9

D

(10)

D

(11)

F

1

C

S

H LHF VH VH F VHG VHG HF VHG VHG H 2

C

S

LVH VHG VHG LH HF HF H VHG H H HF 3

C

S

VHG VH HF HF LHF H LHF HF LHF LVHG F 4

C

S

VH H VHG H H VHG VH H H VHG H 5

C

S

HF H H LHF H F H HF H LVHG VH 6

C

S

VH H H F VH H VH VH VHG VHG VH 7

C

S

H HF VH VHG VHG H F HF VH VHG H Not:

S

,

F

denoting the abbreviation of success and failure respectively.

( )n

(8)

Table 5 Normalize priority ratings of possible outcomes based on seven factors

Success Failure Total Priority

Rating Success Failure Total Priority Rating 1

C

Success 0.688 0.607 1.295 0.647

C

₅ Success 0.579 0.560 1.139 0.569 Failure 0.313 0.393 0.705 0.353 Failure 0.421 0.440 0.861 0.431 2

C

Success 0.579 0.560 1.139 0.569

C

₆ Success 0.786 0.633 1.419 0.710 Failure 0.421 0.440 0.861 0.431 Failure 0.214 0.367 0.581 0.290 3

C

Success 0.537 0.532 1.069 0.534

C

₇ Success 0.698 0.611 1.309 0.655 Failure 0.463 0.468 0.931 0.466 Failure 0.302 0.389 0.691 0.345 4

C

Success 0.746 0.624 1.370 0.685 Failure 0.254 0.376 0.630 0.315

Table 6 Prediction successful and failure ERP implementation

1

C

₂

C

₃

C

₄

C

₅

C

₆

C

₇ Prediction probability

Factor weight 0.128 0.134 0.144 0.157 0.145 0.156 0.137

Success _{0.647 0.569 0.534 0.685 0.569 0.710 0.655}

_0.626

Failure 0.353 0.431 0.466 0.315 0.431 0.290 0.345

0.374

C. Determining the prediction possibilities of successful and failure ERP implementation

Using Eq.(11), the prediction successful and failure ERP implementation are listed in Table 6. The prediction successful and failure ERP implementation as below: (0.353* 0.128) (0.431* 0.134) (0.466 * 0.144) (0.315* 0.157) (0.431* 0.145) (0.290 * 0.156) (0.345* 0.137) 0.374 failure Z = + + + + + + = (0.647 * 0.128) (0.569 * 0.134) (0.534 * 0.144) (0.685* 0.157) (0.569 * 0.145) (0.710 * 0.156) (0.655* 0.137) 0.626 success Z = + + + + + + = V. ACKNOWLEDGMENT

The study is the research results of the 2008

funding research project of the National Science

Council of the Republic of China (Number of the

project :NSC 97-2410-H-151-017). The authors

appreciate for financial supporting from the

Council sincerely.

VI. CONCLUSIONS

In order enterprises and organizations, growing revenues, increasing profits, improving customer services, shortening product-manufacturing cycle and enhancing competitive competency are cited ERP systems. Then predicted success/failure values are obtained to enable organizations to decide whether to initiate ERP, inhibit adoption or take remedial actions to increase the possibility of successful ERP. A successfully implemented ERP can offer organizations many major benefits, including automating business process, timely access to management information

and improving supply chain management through the use of e-commerce. The empirical results not only demonstrate the senior manager support degree, organizational and coordination are the three most important influential factors in the ERP initiative process, but also reveal the applicability and feasibility of reciprocal Incomplete Linguistic Preference Relation for solving complicated hierarchical multiple attribute prediction problems. Subsequently, organizations or enterprises planning to initiate ERP system can apply the proposed prediction model to enhance their decision-making process and take proper actions to avoid wasting time and money before ERP Implementation.

VII. REFERENCES

[1] Holland, C. P. and B. Light, “A Critical Success Factors Model for ERP Implementation”, IEEE Software ,vol. 16, no.3, pp. 30-36, 1999. [2] Hunter, Richard, “The Big Bad ERP, Executive Edge”, 7-8 (1999) [3] Illa, X. B., X. Franch and J. A. Pastor, “Formalising ERP Selection

Criteria”, IEEE Computer Society, pp. 115-122, (2000.

[4] Herrera-Viedma, E., Herrera, E., Chiclana, F., Luque, M. , “Some issues on consistency of fuzzy preference relations”, European

Journal of Operational Research, vol. 154, 2004, pp 98-109, 2004.

[5] Wang, T.C., Chen, Y.H., ”Applying consistent fuzzy preference relations to partnership selection”, Omega, vol. 35. no.4, pp. 384—388, 2007.

[6] Xu, Z.S., “Deviation measures of linguistic preference relations in group decision making”, Omega, vol. 33, pp. 249-25, 2005. [7] Xu, Z.S., “Incomplete linguistic preference relations and their

fusion”, Information Fusion, vol. 7, no.3, pp. 331-337, 2006. [8] Wang, T.C., Chiang Y.C., Hsu, S.C., “Applying Incomplete

Linguistic Preference Relations to a Selection of ERP System Suppliers”, The 3th IEEE International conference on Wireless

Communications, Networking and Mobile Computing, pp. 119-123,

2007.

[9] Wang, T.C., Hsu, S.C., Chiang Y.C., “Multi-criteria Decision Making with Expansion of Incomplete Linguistic Preference Relations, WSEAS Transaction on Mathematics”, vol.6, no. 9, pp. 817-823, 2007.

(9)

(10)

表 Y04

出席國際學術會議心得報告

計畫編號

NSC 98-2410-H-151-006

計畫名稱