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EVALUATE KNOWLEDGE MANAGEMENT TOOLS BY USING FUZZY LINEAR PROGRAMMING TECHNIQUE FOR MULTIATTRIBUTE GROUP DECISION MAKING*
EVALUATE KNOWLEDGE MANAGEMENT TOOLS BY USING FUZZY LINEAR PROGRAMMING TECHNIQUE FOR MULTIATTRIBUTE GROUP DECISION MAKING* Yıldız Esra ALBAYRAK 1 Yasemin Claire ERENSAL 2 1
Galatasaray University, Industrial Engineering Dept, Çiragan Cad. No: 36, 34357 Ortaköy, Istanbul Turkey Turkey [email protected] 2 Doğuş University, Industrial Engineering Dept, Acıbadem Zeamet Sokak 34722 Kadıköy, Istanbul Turkey [email protected]
Abstract: The concept of knowledge management is a tried and tested management science that has been implemented by numerous organizations, some with more success than others. The aim of this paper is to develop a framework to aid in the evaluation and selection of KM tools. In this paper, we investigate the fuzzy linear programming technique (FLP) for multiple attribute group decision making (MAGDM) problems with preference information on alternatives. Copyright © 2006 IFAC Keywords: Knowledge management tools, MCDM, Fuzzy multiattribute group decision making; Fuzzy numbers; Linear Programming technique for multidimensional analysis of preference; Linguistic variable; Linear Programming
1. INTRODUCTION In analyzing the reasons why organizations want to manage knowledge, investigating only objectives is not enough, as this will only provide a superficial understanding of what drives knowledge management. The activities of knowledge management (KM) should enable the creation, communication, and application of knowledge; and they should drive the capability of creating and adding a greater value to the core business competencies. For years, companies have strived to manage knowledge more effectively, the primary motivation being improved corporate performance (Choi & Lee, 2002). However, despite the growing body of theory, there are relatively few KM texts that make an explicit connection between KM activities and corporate performance (Kalling, 2003). As organizations realizing the importance of KM, many are developing knowledge management systems (KMS) that offer various benefits to facilitate KM * 1
activities. KMS are the IT-based systems developed to support and enhance the organizational processes of knowledge creation, storage/retrieval, transfer, and application (Alavi and Leidner, 2001). As a matter of fact KMS are largely governed around how information flows within and around an organization to provide sophisticated document management rather than actual KM. Despite this, some researchers cite (Malhotra 2002) examples where it was found that there is no direct correlation between information technology investments and knowledge management or business performance. Another research on KM also found that while many organizations have the necessary technological infrastructure in place to support knowledge management its application has not been entirely focused (Parlby, 1997). Furthermore, many of the KMS today seem to provide elaborate document management rather than actual knowledge management. Knowledge focused organizations
This research has been financially supported by Galatasaray University Research Fund. Corresponding Author 264
require information systems that maximize knowledge, not just manage data (Mellor, 1997). To this end, systems of knowledge management have proven to be ‘‘ineffective’’ or ‘‘a waste of money’’—thereby resulting in failures to meet company objectives and customer demands, challenges to internal and interface integration, extreme cost overruns, and resistance to change. Organizations operate in different business contexts and drivers of KM are often unique. Therefore if organizations do not fully comprehend what drives the need for KM and how to select the necessary technological infrastructure, they may fall into the trap of creating an inefficient knowledge management strategy and operational plans which are often based on experiences of other organizations. In absence of this understanding, KM will just be another cliché concept. Before embarking on a knowledge management journey, organizations therefore has to understand what it is that they would like to achieve with KMS and what value each alternative KM tool will add to the organization with respect to KM. For this particular reason, there is no blueprint for implementing KM in organizations. This suggests that organizations need to focus of a well-defined business strategy in order to establish the appropriate priorities. With this in mind, it is important to consider a number of critical issues when selecting a set of technologies for KM. Therefore, it is valuable to investigate how managers can eliminate vast numbers of tools to support KM. However, no framework currently exists to aid in the evaluation and selection of KM tools and to avoid performance gaps concerning technological infrastructure right in the beginning of the selection phase. KM decision-making problems are often associated with evaluation of alternative KM tools under multiple objectives and multiple criteria. Because organizations operate in different business contexts and drivers of KM are often unique for each company. Most multiattribute decision making problems include both quantitative and qualitative attributes which are using imprecise data and human judgments. We proposed a linear programming technique for multidimensional analysis of preferences under fuzzy environment (fuzzy LINMAP) in evaluating KM tools. (Sirinivasan and Shocker, 1973). Under many conditions, crisp data are inadequate to model real life situations. Fuzzy set theory is well suited to dealing with such decision problems. Finally, the developed model is applied to a real case of assisting decision-makers in a leading logistics company in Turkey to illustrate the use of the proposed method.
knowledge management is to arrange, orchestrate and organize an environment in which people are invited and facilitated to apply, develop, share, combine and consolidate knowledge. Knowledge management is, in a nutshell, aimed at achieving business value (Gartner Group, 2000). In summary, the basic objective of knowledge management lies in create, share, harvest and leverage knowledge in order to improve work efficiency, i.e. increased organizational capacity through: • • • • •
Improved decision making. Improved customer service. Improved solution of business problems. Increased productivity. Improved leveraging of corporate and individual knowledge. 3. EVALUATION CRITERIA FOR THE KM TOOLS AND ALTERNATIVES
In order to formulate the multiattribute evaluation model, it is necessary to identify the factors that influence KM practitioners’ choice of KM tools. After discussions with four KM consultants and the operations manager, we studied the features of the KM tools provided by vendors, reviewed the literature for selecting software, and identified three essential evaluation criteria to use in selecting the best KM tools: cost, functionality and vendors with sub-criteria and their attributes. The identified criteria were validated by the KM responsible for the firm’s KM program. 3.1 Cost Cost is a common factor influencing the purchaser to choose the software (Davis & Williams, 1994). It is simply the expenditure associated with KMS and includes product, license, training, maintenance and software subscription costs. Technically, these costs can be grouped under two major criteria, namely, capital expenditures and operating expenditures. 3.2. Functionality Functionality refers to those features that the KM tool performs and, generally, to how well the software can meet the user’s needs and requirements. Based on a review of the literature and on consultations with KM practitioners, we identified six key functional elements of a KM tool: document management, collaboration, communication, measurement, workflow management and scalability. Document management, which mainly involves searching for and organizing knowledge, consists of the following six basic features: storage, publishing, subscription, reuse, collaboration and communication (Conway & Sligar, 2002). Collaboration is one of the key aspects of KM, since collaborative problem solving, conversation and
2. KNOWLEDGE MANAGEMENT OBJECTIVES Many knowledge management objectives have been identified in the literature. Havens and Knapp (1999) is of the opinion that knowledge management is aimed at getting people to innovate, to collaborate, and to make good decisions efficiently. Van der Spek and Kingma (2000) state that the main objective of 265
teamwork generate a significant proportion of knowledge assets. The communication function provided in a KM tool helps users to work together and share knowledge. Measurement is the keeping of records on activities and changes in managed knowledge. Workflow management allows the movement of documents in information processes among individuals and applications to be specified according to a predefined process (Wensley, 2000).
and aggregating content from multiple sources into a single location. 4. METHODOLOGY In multiple attribute decision making (MADM) problems, the decision maker’s preference information is used to rank alternatives. This paper offers a methodology for analyzing individual and multidimensional preferences with linear programming technique in multiattribute group decision making under fuzzy environments (Hwang and Chen, 1992). The LINMAP method is based on pairwise comparisons of alternatives given by decision makers and generates the best compromise alternative as the solution that has the shortest distance to the positive ideal solution (Srinivasan and Shocker, 1973). The use of fuzzy linear programming (FLP) to knowledge management will be discussed and this approach to KM problems has not been appeared in the literature. Decision making problem is the process of finding the best option from all of the feasible alternatives. A MADM problem can be expressed in matrix format as
3.3. Vendor The quality of vendor support and its characteristics are of major importance in the selection of software, such as in (Byun & Suh, 1996; Min, 1992). It is also critical for the successful installation and maintenance of the software. The important factors affecting the decision to select a KM tool are vendor reputation, the training provided, the implementation vendor, KM consulting services and support, maintenance, upgrades and integration. 3.4 Alternatives Alternative 1. Knowledger: Knowledge Associates Ltd is a technology and consulting organization that provides KM solutions consisting of KM education, KM consulting, KM software systems (e.g. Knowledger) the use of the Internet and groupware technologies. Knowledger consists of components that support personal KM, team KM, and organizational KM. The benefit of these components is that, through the knowledge portal, it is possible to manage, collaborate, capture and convey information and so forth to the teams or organization. It integrates KM solutions with a high-level framework, methodologies, systems and tools to optimize working with knowledge at all levels.
X1 A1 ⎡ x11 ⎢ A2 ⎢ x21 . ⎢ . ⎢ D= . ⎢ . . ⎢ . ⎢ An ⎢ xn1 ⎣
X2 . . . X m x12 . . . x1n ⎤ ⎥ x22 . . . x2 n ⎥ . . . . . ⎥ ⎥ . . . . . ⎥ . . . . . ⎥ ⎥ x . . . x ⎥ n2 nm ⎦
w = ( w1, w2 , ..., wn )T , where
Ai , A2 ,..., Am
are possible
alternatives among which decision makers have to choose, X 1 , X 2 ,..., X m are with which alternative performance are measured,
Alternative 2. eRoom; eRoom technology focuses exclusively on providing Internet collaboration solutions to the extended enterprise. The eRoom software is a digital workplace that allows organizations to quickly assemble a project team, wherever people are located and to manage the collaborative activities that drive the design, development and delivery of their products and services. In addition, it is a secure extranet or Intranet which, by enabling teams to discuss ideas, share information and make decisions all within a central location, also provides a valuable KM solution.
alternative
Ai
xij
is the rating of
with respect to the criterion
the weight of criterion
X j.
Xj
,
wi
is
(Wang and Parkan, 2005;
Chen, 2000).
4.1 Basic Concepts Linguistic Variable: The MADM problem contains a mixture of crisp, fuzzy and/or linguistic data. In this methodology, linguistic variables are used to model human judgments. These linguistic variables can be described by triangular fuzzy numbers, ~ xij = ⎛⎜ aij ,bij ,cij ⎞⎟ (Laarhoven and Pedrycz, 1983; Zadeh, ⎝ ⎠ 1965). A linguistic variable is a variable whose values
Alternative 3. Microsoft SharePoint Portal Server; Microsoft offers a wide range of products and services designed to empower people through software at any time, any place and on any device. It is currently the worldwide leader in software, services and Internet technologies for personal and business computing. SharePoint Portal Server software is a KM tool that is an end-to-end solution for managing documents, developing custom portals
are linguistic terms. (Zadeh, 1975). The concept of linguistic variable is very useful in dealing with situations which are too complex not well-defined to be reasonably described in conventional quantitative expressions (Zimmermann, 1991). For example, “functonality” is a linguistic variable; its values are very poor, poor, fair, good and very good. These 266
where B and C are the sets of benefit criteria and cost criteria, respectively. We can obtain the normalized fuzzy decision matrix denoted by
linguistic values can also be represented by fuzzy numbers. (Chen, 2000) Distance between two triangular fuzzy number; Let ~ = ( m , m , m ) and n~ = (n , n , n ) be two triangular m 1 2 3 1 2 3
~p p p = 1,2 ,.., P; R = ⎛⎜ ~ r ⎞⎟ ⎝ ij ⎠ n×m
fuzzy numbers, then the vertex method is defined to calculate the distance between them as (Chen, 2000) ~ , n~ ) = d( m
1⎡ ( m − n )2 + ( m − n )2 + ( m − n )2 ⎤ 1 2 2 3 3 ⎥⎦ 3 ⎢⎣ 1
where
(1)
~ , n~ ) = d( m =
4.2 Fuzzy Group LINMAP Model
fuzzy numbers, the square of the weighted Euclidean ~ distance between Rip and a~* can be calculated as S
Normalization; Suppose the rating of alternative Ai ( i = 1,2 ,...n ) on attribute X j ( j = 1,2 ,...m ) given by DM
,
~p D
max min max max b j ,b j ,c j ,c j
j∈B
{ = min {a
k
p Sl =
p p ~p p p p ij ; aij ∈ xij = ( aij , bij , cij
alternatives by where ρ p is a
⎡ p * ⎤ ∑ w j ⎢d ⎛⎜⎝ ~rkj , a~ j ⎞⎟⎠⎥ ⎣ ⎦
m
2
j =1 m
⎡ p * ⎤ ∑ w j ⎢d ⎛⎜⎝ ~rlj , a~ j ⎞⎟⎠⎥ ⎣ ⎦
2
(6)
j =1
2 di )
are squared ( si = weighted Euclidean distances between each pair of alternative (k , l ) and the fuzzy
( )
positive ideal solution a~* . For every ordered pair p
(k , l ) ∈ Ω , the solution would be consistent with the Sp ≥Sp
weighted distance model if p
p
1973). If Sl < S k , If we define
(2)
p −
(S
p l
⎛⎜ S p − S p ⎞⎟ l ⎠ ⎝ k
l
k
(Sirinivasan,
gives the error.
p − p p ) = 0 if S ≥ S , k l k
− S
and
( S − S ) = S − S if S < S , (S lp - S kp ) = max ⎧⎨ 0 , S kp − S lp ⎫⎬ l k k l l k ⎩ ⎭ p
for j ∈ C
then
(3)
p
p
( S p − S p )− l
k
p
p
denotes the error of the pair (k , l ) . p
For all the pairs in Ω , the total inconsistency is p p − ∑ ( Sl − S k ) and the total poorness of fit for (k ,l )∈Ω the group (B ) is p
B =
} ), i = 1,2,...n; p = 1,2,..., P}
a max = max aijp ; aijp ∈ ~ xijp = (aijp , bijp , cijp ), i = 1,2,.., n; p = 1,2,.., P j a min j
}
Sp =
and ⎛ a min b min c min ⎞ ij ⎟ j p ⎜ j ~ rij = ⎜ , , p ⎟ p p b a ⎟ ⎜ c ij ⎠ ij ⎝ ij
{
between
the
preference relation given by the DM Pp .
the linear scale transformation, the various criteria scales are transformed into a comparable scale. Te set of criteria can be divided into benefit criteria (the larger the rating, the greater the preference) and cost criteria (the smaller the rating, the greater the preference). for
relations
Pp ( p = 1,2 ,..., P ) gives
Ω = (k ,l ) ; Ak ρ p Al , k ,l = 1,2 ,..., n ) p
have also same meaning. Using
⎞ ⎟ ⎟ ⎟ ⎠
1 m ∗ 2 ∗ ∗ 2 2 ∑ w ⎡( a − a jL ) + ( aijM − a jM ) + ( aijR − a jR ) ⎤⎥⎦ 3 j =1 j ⎢⎣ ijL
preference
is decision matrix for DM p .
p p ⎛ ap bij cij ⎜ ij ~ rijp = ⎜ , , max max max bj aj ⎜ cj ⎝
(5)
as (Li and Yang, 2004).
Suppose that the DM
X1 X 2 . . . X m p ~p ⎡~ . ~ xp ⎤ A1 ⎢ x11 x12 1n ⎥ A ⎢~ xp ~ xp . ~ xp ⎥ 2 21 22 2 n ⎥ p = 1,2,..., P ⎢ ~p p . . . D = ⎛⎜ ~ x ⎞⎟ = . ⎢. ⎥ ij ⎝ ⎠ n× m . ⎢ . ⎥ . ⎢. . . ⎥ A ⎢~ p ~ p p ⎥ ~ n x x . . . x mn ⎦ ⎣ m1 m 2
2
∗ a~ j
p
multiattribute group decision making problem can be expressed in matrix format as follows:
~ ~ ,w ~ ~ W =(w 1 2 ,..., wm )
⎡ p * ⎤ w ⎢d ⎛⎜ ~ r , a~ ⎞⎟⎥ j ⎣ ⎝ ij j ⎠⎦ j =1
∑
can be rewritten using triangular fuzzy numbers
Si =
. A fuzzy
m
p = i
Sp i
~x p = ⎛ a p , b p , c p ⎞ ⎜ ij ij ij ij ⎟⎠ ⎝
the fuzzy positive ideal
a~*j = ( a~*jL , a~*jM , a~*jR ) are triangular
solution, where
measurement
= ( m − n )2 = m-n
is
* * * * a~ = ⎛⎜ a~ , a~ ,...........a~ ⎞⎟ is m⎠ ⎝ 1 2
Let
1⎡ ( m − n )2 + ( m − n )2 + ( m − n )2 ⎤ 2 2 3 3 ⎥⎦ 3 ⎢⎣ 1 1 1⎡ 2 2 2⎤ (m − n) +(m − n) +(m − n) ⎥⎦ 3 ⎢⎣
P p ( p = 1 ,2 ,... P )
are normalized triangular
fuzzy numbers.
~ and n~ are real numbers, then the distance If both m ~ , n~ ) is identical to the Euclidean measurement d (m distance (Ross, 1995). Suppose that both ~ = (m , m , m ) and n~ = (n , n , n ) are two real m 1 2 3 1 2 3 numbers, then let and m1 = m2 = m3 = m
n1 = n2 = n3 = n . The distance ~ ~ (d (m, n )) can be calculated as
p p p p ~ r = ⎛⎜ a , a , a ⎞⎟ ij ⎝ ijL ijM ijR ⎠
(4)
B=
P
∑B
p =1
267
p
=
P
∑ ∑
p =1 (k ,l )∈Ω
p
p −
( Sl − S k )
(7)
5. APPLICATION
Our objective is to minimize the sum of errors for all p
pairs in Ω . Similarly, if p ( Sl
p − Sk )
p
l
k
l
Step1: The experts
goodness of fit for pair
k
k
the group is G=
P
∑G
p
=
p =1
By
definition
p
p
∑ ∑
p +
p
p =1 (k ,l )∈Ω
p −
p
∑ ( k ,l )∈Ω
∑ ( k ,l )∈Ω
( Sl − S k )
.
( Sl − S k ) = ( Sl − S k ) − ( Sl − S k ) ( S p − S p )+ − k p l
p _
p
and
to 3, etc.
(8)
( Sl − S k )
( Slp − S kp ) +
p +
p
( S p − S p )− = k p l
(Sp − Sp )=h ∑ k p l ( k ,l )∈Ω
Step2: The experts use the linguistic rating variables (shown in Table 1) to evaluate the rating of alternatives with respect to each attribute. The data and ratings of all alternatives on every attribute are given by the three experts P1 , P2 , P3 as in Table 2. Table 1 Linguistic variable for the ratings
Substituting for B and G from (7) and (8);
Very Poor (VP) Poor (P) Fair (F) Good (G) Very Good (VG)
(9)
G−B =h
The problem of finding the best solution ( w, a~* ) reduces to finding the solution ( w, v) (Fan and Xiao, 2004) which maximizes Equation (10) subject to the constraints (Li and Yang, 2004).
{
s .t .
}
Z klp
{
Z p = max 0 , S p − S p kl
l
k
≥ 0 , we have
Z klp
(10)
C2 C3
} for each (k , l ) ∈ Ω ≥
Slp
− S kp
p
and with
, Equation (10) can
A1 ~1 R = A 2 A3
maximize
p
l
k
( k ,l )∈Ω p p p Z + S − S ≥0 kl k l p Z ≥0 kl m
∑
( k ,l )∈Ω
l
p
{ }
∗
∗
∗
p
and
∗ a~ j
1
X
X
2
3
(0.6,0.77, 1.0) (0.8,1.0,1 .0) ⎤ ⎡ (0.5,0.5,0 .5) ⎢ (0.71,0.71 ,0.71) (0.2,0.33, 0.5) (0.6,0.77, 1.0) ⎥ ⎢ (1.0,1.0,1 .0) (0.8,1.0,1 .0) (0.6,0.77, 1.0) ⎥⎦ ⎣
To obtain the best weights and ideal point, taking ~p h = 1.0 and using R and Ω p we solve linear programming problem (Eq.(10)). can ∗
v jL = w j a jL , v jM = w j a jM and v jR = w j a jR
this linear programming,
P3
50,000 35,000 25,000 Fair Poor Good Good Very G Good
We can obtain the normalized decision matrices R 2 ~ and R 3 of the experts P2 and P3 (Eqs. (2) and (3)).
( k ,l ) ∈ Ω ; p = 1,2,..., P
we
50,000 35,000 25,000 Very G Fair Good Fair Good Fair
~
k
j = 1,2 ,..., m
V = v j = ( w j a~ j )
Using
( S p − S p )− ≥ h
∑
wj = 1
w j ≥ 0,
50,000 35,000 25,000 Good Poor Very G Very G Good Good
A1 A2 A3 A1 A2 A3 A1 A2 A3
X
⎧ P ⎫ ⎪ p⎪ ∑ max Z kl ⎬ ⎨∑ ⎪⎩ p =1 (k ,l )∈Ω p ⎪⎭ p p + subject to ( S − S ) − ∑
Decision Makers P1 P2
Step3: Constructing the normalized fuzzy decision ~ matrix R1 for expert (1) (using Eqs.(2 ) and (3))
be rewritten as
j =1
Alternatives
C1 ($x103)
where h is strictly positive. Let
(0, 0.1, 0.3) (0.2, 0.3, 0,4) (0.4, 0.5, 0.6) (0.6, 0.7, 0.8) (0.8, 0.9, 1.0)
Table 2 Decision informations and ratings of the three alternatives Criteria
⎧ P ⎫ ⎪ p p⎪ ∑ max 0 , Sl − S k ⎬ ⎨∑ ⎪⎩ p =1 (k ,l )∈Ω p ⎪⎭ ⎧ ⎪G - B ≥ h ⎪m ⎨ ∑ wj = 1 ⎪ j =1 ⎪w ≥ 0 , j = 1,2 ,..............., m ⎩ j
max
give their preference
Ω3 = {(2,1), (3,2)} i.e., 1 is preferred to 2, 2 is preferred
P
of
Pp ( p = 1,2 ,3 )
judgments between alternatives with paired comparisons as Ω1 = {(1,2), (2,3)} , Ω2 = {(1,2), (1,3)} ,
. The total goodness (G ) of fit for
( S p − S p )+ l
p
p p + p p ( S − S ) = S − S if Sl ≥ Sk l k l k
( S p − S p )+ = 0 if S p < S p ,
(k, l ) is
The proposed method is currently applied to solve KM tools selection problem and the computational procedure is summarized as follows:
may be designated as the goodness of fit
for this pair. Defining and
for the pair, (k, l ) ,
Sp ≥ Sp l k
w j , v jL , v jM , v jR
write
as
w1 = 0.284 w2 = 0 .398 w3 = 0 .318
and
. By solving
a~ ∗ = (( 0.27 , 0.27, 0.27), (0.19, 0.20, 0.22), (0.23, 24, 0.25 ))
are obtained
Using Eq. (6), the distances between
is computed.
∗ a~ can
~ Rip
and the
positive ideal be obtained. According these distances, the ranking orders of the three alternatives for the three experts are as follows: 268
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For P1 : A2 ρ A3 ρA1 For P2 : A3 ρ A1 ρ A2 For P3 : A3 ρ A2 ρ A1 The group ranking order of all alternatives can be obtained using social choice functions such as Copeland’s function (Hwang and Lin, 1987). Copeland’s function ranks the alternatives in the order of the value of f cp ( x ) , Copeland score. Table 3 Copeland’s scores Alternatives A1 A2 A3
Decision Makers P1 P2 P3
-1,-1 1, 1 1,-1
-1, 1 -1,-1 -1, 1
-1, -1 -1, 1 1, 1
Copeland’s scores -4 0 2
According to the Copeland’s scores, the ranking order of the three alternatives is A3, A2, A1. The best alternative is A3. 6. CONCLUSION AND IMPLICATIONS Through the proposed methodology in this research, enterprises can reduce the mismatch between the capability and implementation of the KM system, and greatly enhance the effectiveness of implementation of the KMS. The development of a KMS is still relatively new to many organizations. With the rise of the organization came a strong interest in KM, and KM tools assumed an important role in supporting KM. KM tools can capture, organize, share and leverage knowledge elements, along with the necessary support and training to insure a successful launch of KM solutions within an organization. In this paper, a systemic approach is proposed using fuzzy linear programming to evaluate an appropriate KM tool for the organization. The usefulness of the model was examined through observing its effect on the decision-making process in selecting an appropriate KM tool. To reflect the DM’s subjective preference information, a fuzzy LINMAP model is constructed to determine the weight vector of attributes and then to rank the alternatives. This study has several implications for KM practitioners who intend to evaluate KM tools to build a KMS. REFERENCES Alavi,M.,&Leidner,D.E. (2001). Review: Knowledge management and knowledge management: Conceptual foundations and research issues. MIS Quarterly, 25(1), 107–136. Byun,D.H.,&Suh,E.H.(1996). A methodology for evaluation EIS software packages. Journal of End User Computing, 8(21), 31. Chen, C.T., (2000). Extensions of the TOPSIS for Group Decision-Making under Fuzzy Environment, Fuzzy Sets and Systems, 114, 1-9. Choi,B.,&Lee,H.(2002).Knowledge management strategy and its link to knowledge creation process. Expert Systems with Applications, 23(3), 173–187.
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Galatasaray University, Industrial Engineering Dept, Çiragan Cad. No: 36, 34357 Ortaköy, Istanbul Turkey Turkey [email protected] 2 Doğuş University, Industrial Engineering Dept, Acıbadem Zeamet Sokak 34722 Kadıköy, Istanbul Turkey [email protected]
Abstract: The concept of knowledge management is a tried and tested management science that has been implemented by numerous organizations, some with more success than others. The aim of this paper is to develop a framework to aid in the evaluation and selection of KM tools. In this paper, we investigate the fuzzy linear programming technique (FLP) for multiple attribute group decision making (MAGDM) problems with preference information on alternatives. Copyright © 2006 IFAC Keywords: Knowledge management tools, MCDM, Fuzzy multiattribute group decision making; Fuzzy numbers; Linear Programming technique for multidimensional analysis of preference; Linguistic variable; Linear Programming
1. INTRODUCTION In analyzing the reasons why organizations want to manage knowledge, investigating only objectives is not enough, as this will only provide a superficial understanding of what drives knowledge management. The activities of knowledge management (KM) should enable the creation, communication, and application of knowledge; and they should drive the capability of creating and adding a greater value to the core business competencies. For years, companies have strived to manage knowledge more effectively, the primary motivation being improved corporate performance (Choi & Lee, 2002). However, despite the growing body of theory, there are relatively few KM texts that make an explicit connection between KM activities and corporate performance (Kalling, 2003). As organizations realizing the importance of KM, many are developing knowledge management systems (KMS) that offer various benefits to facilitate KM * 1
activities. KMS are the IT-based systems developed to support and enhance the organizational processes of knowledge creation, storage/retrieval, transfer, and application (Alavi and Leidner, 2001). As a matter of fact KMS are largely governed around how information flows within and around an organization to provide sophisticated document management rather than actual KM. Despite this, some researchers cite (Malhotra 2002) examples where it was found that there is no direct correlation between information technology investments and knowledge management or business performance. Another research on KM also found that while many organizations have the necessary technological infrastructure in place to support knowledge management its application has not been entirely focused (Parlby, 1997). Furthermore, many of the KMS today seem to provide elaborate document management rather than actual knowledge management. Knowledge focused organizations
This research has been financially supported by Galatasaray University Research Fund. Corresponding Author 264
require information systems that maximize knowledge, not just manage data (Mellor, 1997). To this end, systems of knowledge management have proven to be ‘‘ineffective’’ or ‘‘a waste of money’’—thereby resulting in failures to meet company objectives and customer demands, challenges to internal and interface integration, extreme cost overruns, and resistance to change. Organizations operate in different business contexts and drivers of KM are often unique. Therefore if organizations do not fully comprehend what drives the need for KM and how to select the necessary technological infrastructure, they may fall into the trap of creating an inefficient knowledge management strategy and operational plans which are often based on experiences of other organizations. In absence of this understanding, KM will just be another cliché concept. Before embarking on a knowledge management journey, organizations therefore has to understand what it is that they would like to achieve with KMS and what value each alternative KM tool will add to the organization with respect to KM. For this particular reason, there is no blueprint for implementing KM in organizations. This suggests that organizations need to focus of a well-defined business strategy in order to establish the appropriate priorities. With this in mind, it is important to consider a number of critical issues when selecting a set of technologies for KM. Therefore, it is valuable to investigate how managers can eliminate vast numbers of tools to support KM. However, no framework currently exists to aid in the evaluation and selection of KM tools and to avoid performance gaps concerning technological infrastructure right in the beginning of the selection phase. KM decision-making problems are often associated with evaluation of alternative KM tools under multiple objectives and multiple criteria. Because organizations operate in different business contexts and drivers of KM are often unique for each company. Most multiattribute decision making problems include both quantitative and qualitative attributes which are using imprecise data and human judgments. We proposed a linear programming technique for multidimensional analysis of preferences under fuzzy environment (fuzzy LINMAP) in evaluating KM tools. (Sirinivasan and Shocker, 1973). Under many conditions, crisp data are inadequate to model real life situations. Fuzzy set theory is well suited to dealing with such decision problems. Finally, the developed model is applied to a real case of assisting decision-makers in a leading logistics company in Turkey to illustrate the use of the proposed method.
knowledge management is to arrange, orchestrate and organize an environment in which people are invited and facilitated to apply, develop, share, combine and consolidate knowledge. Knowledge management is, in a nutshell, aimed at achieving business value (Gartner Group, 2000). In summary, the basic objective of knowledge management lies in create, share, harvest and leverage knowledge in order to improve work efficiency, i.e. increased organizational capacity through: • • • • •
Improved decision making. Improved customer service. Improved solution of business problems. Increased productivity. Improved leveraging of corporate and individual knowledge. 3. EVALUATION CRITERIA FOR THE KM TOOLS AND ALTERNATIVES
In order to formulate the multiattribute evaluation model, it is necessary to identify the factors that influence KM practitioners’ choice of KM tools. After discussions with four KM consultants and the operations manager, we studied the features of the KM tools provided by vendors, reviewed the literature for selecting software, and identified three essential evaluation criteria to use in selecting the best KM tools: cost, functionality and vendors with sub-criteria and their attributes. The identified criteria were validated by the KM responsible for the firm’s KM program. 3.1 Cost Cost is a common factor influencing the purchaser to choose the software (Davis & Williams, 1994). It is simply the expenditure associated with KMS and includes product, license, training, maintenance and software subscription costs. Technically, these costs can be grouped under two major criteria, namely, capital expenditures and operating expenditures. 3.2. Functionality Functionality refers to those features that the KM tool performs and, generally, to how well the software can meet the user’s needs and requirements. Based on a review of the literature and on consultations with KM practitioners, we identified six key functional elements of a KM tool: document management, collaboration, communication, measurement, workflow management and scalability. Document management, which mainly involves searching for and organizing knowledge, consists of the following six basic features: storage, publishing, subscription, reuse, collaboration and communication (Conway & Sligar, 2002). Collaboration is one of the key aspects of KM, since collaborative problem solving, conversation and
2. KNOWLEDGE MANAGEMENT OBJECTIVES Many knowledge management objectives have been identified in the literature. Havens and Knapp (1999) is of the opinion that knowledge management is aimed at getting people to innovate, to collaborate, and to make good decisions efficiently. Van der Spek and Kingma (2000) state that the main objective of 265
teamwork generate a significant proportion of knowledge assets. The communication function provided in a KM tool helps users to work together and share knowledge. Measurement is the keeping of records on activities and changes in managed knowledge. Workflow management allows the movement of documents in information processes among individuals and applications to be specified according to a predefined process (Wensley, 2000).
and aggregating content from multiple sources into a single location. 4. METHODOLOGY In multiple attribute decision making (MADM) problems, the decision maker’s preference information is used to rank alternatives. This paper offers a methodology for analyzing individual and multidimensional preferences with linear programming technique in multiattribute group decision making under fuzzy environments (Hwang and Chen, 1992). The LINMAP method is based on pairwise comparisons of alternatives given by decision makers and generates the best compromise alternative as the solution that has the shortest distance to the positive ideal solution (Srinivasan and Shocker, 1973). The use of fuzzy linear programming (FLP) to knowledge management will be discussed and this approach to KM problems has not been appeared in the literature. Decision making problem is the process of finding the best option from all of the feasible alternatives. A MADM problem can be expressed in matrix format as
3.3. Vendor The quality of vendor support and its characteristics are of major importance in the selection of software, such as in (Byun & Suh, 1996; Min, 1992). It is also critical for the successful installation and maintenance of the software. The important factors affecting the decision to select a KM tool are vendor reputation, the training provided, the implementation vendor, KM consulting services and support, maintenance, upgrades and integration. 3.4 Alternatives Alternative 1. Knowledger: Knowledge Associates Ltd is a technology and consulting organization that provides KM solutions consisting of KM education, KM consulting, KM software systems (e.g. Knowledger) the use of the Internet and groupware technologies. Knowledger consists of components that support personal KM, team KM, and organizational KM. The benefit of these components is that, through the knowledge portal, it is possible to manage, collaborate, capture and convey information and so forth to the teams or organization. It integrates KM solutions with a high-level framework, methodologies, systems and tools to optimize working with knowledge at all levels.
X1 A1 ⎡ x11 ⎢ A2 ⎢ x21 . ⎢ . ⎢ D= . ⎢ . . ⎢ . ⎢ An ⎢ xn1 ⎣
X2 . . . X m x12 . . . x1n ⎤ ⎥ x22 . . . x2 n ⎥ . . . . . ⎥ ⎥ . . . . . ⎥ . . . . . ⎥ ⎥ x . . . x ⎥ n2 nm ⎦
w = ( w1, w2 , ..., wn )T , where
Ai , A2 ,..., Am
are possible
alternatives among which decision makers have to choose, X 1 , X 2 ,..., X m are with which alternative performance are measured,
Alternative 2. eRoom; eRoom technology focuses exclusively on providing Internet collaboration solutions to the extended enterprise. The eRoom software is a digital workplace that allows organizations to quickly assemble a project team, wherever people are located and to manage the collaborative activities that drive the design, development and delivery of their products and services. In addition, it is a secure extranet or Intranet which, by enabling teams to discuss ideas, share information and make decisions all within a central location, also provides a valuable KM solution.
alternative
Ai
xij
is the rating of
with respect to the criterion
the weight of criterion
X j.
Xj
,
wi
is
(Wang and Parkan, 2005;
Chen, 2000).
4.1 Basic Concepts Linguistic Variable: The MADM problem contains a mixture of crisp, fuzzy and/or linguistic data. In this methodology, linguistic variables are used to model human judgments. These linguistic variables can be described by triangular fuzzy numbers, ~ xij = ⎛⎜ aij ,bij ,cij ⎞⎟ (Laarhoven and Pedrycz, 1983; Zadeh, ⎝ ⎠ 1965). A linguistic variable is a variable whose values
Alternative 3. Microsoft SharePoint Portal Server; Microsoft offers a wide range of products and services designed to empower people through software at any time, any place and on any device. It is currently the worldwide leader in software, services and Internet technologies for personal and business computing. SharePoint Portal Server software is a KM tool that is an end-to-end solution for managing documents, developing custom portals
are linguistic terms. (Zadeh, 1975). The concept of linguistic variable is very useful in dealing with situations which are too complex not well-defined to be reasonably described in conventional quantitative expressions (Zimmermann, 1991). For example, “functonality” is a linguistic variable; its values are very poor, poor, fair, good and very good. These 266
where B and C are the sets of benefit criteria and cost criteria, respectively. We can obtain the normalized fuzzy decision matrix denoted by
linguistic values can also be represented by fuzzy numbers. (Chen, 2000) Distance between two triangular fuzzy number; Let ~ = ( m , m , m ) and n~ = (n , n , n ) be two triangular m 1 2 3 1 2 3
~p p p = 1,2 ,.., P; R = ⎛⎜ ~ r ⎞⎟ ⎝ ij ⎠ n×m
fuzzy numbers, then the vertex method is defined to calculate the distance between them as (Chen, 2000) ~ , n~ ) = d( m
1⎡ ( m − n )2 + ( m − n )2 + ( m − n )2 ⎤ 1 2 2 3 3 ⎥⎦ 3 ⎢⎣ 1
where
(1)
~ , n~ ) = d( m =
4.2 Fuzzy Group LINMAP Model
fuzzy numbers, the square of the weighted Euclidean ~ distance between Rip and a~* can be calculated as S
Normalization; Suppose the rating of alternative Ai ( i = 1,2 ,...n ) on attribute X j ( j = 1,2 ,...m ) given by DM
,
~p D
max min max max b j ,b j ,c j ,c j
j∈B
{ = min {a
k
p Sl =
p p ~p p p p ij ; aij ∈ xij = ( aij , bij , cij
alternatives by where ρ p is a
⎡ p * ⎤ ∑ w j ⎢d ⎛⎜⎝ ~rkj , a~ j ⎞⎟⎠⎥ ⎣ ⎦
m
2
j =1 m
⎡ p * ⎤ ∑ w j ⎢d ⎛⎜⎝ ~rlj , a~ j ⎞⎟⎠⎥ ⎣ ⎦
2
(6)
j =1
2 di )
are squared ( si = weighted Euclidean distances between each pair of alternative (k , l ) and the fuzzy
( )
positive ideal solution a~* . For every ordered pair p
(k , l ) ∈ Ω , the solution would be consistent with the Sp ≥Sp
weighted distance model if p
p
1973). If Sl < S k , If we define
(2)
p −
(S
p l
⎛⎜ S p − S p ⎞⎟ l ⎠ ⎝ k
l
k
(Sirinivasan,
gives the error.
p − p p ) = 0 if S ≥ S , k l k
− S
and
( S − S ) = S − S if S < S , (S lp - S kp ) = max ⎧⎨ 0 , S kp − S lp ⎫⎬ l k k l l k ⎩ ⎭ p
for j ∈ C
then
(3)
p
p
( S p − S p )− l
k
p
p
denotes the error of the pair (k , l ) . p
For all the pairs in Ω , the total inconsistency is p p − ∑ ( Sl − S k ) and the total poorness of fit for (k ,l )∈Ω the group (B ) is p
B =
} ), i = 1,2,...n; p = 1,2,..., P}
a max = max aijp ; aijp ∈ ~ xijp = (aijp , bijp , cijp ), i = 1,2,.., n; p = 1,2,.., P j a min j
}
Sp =
and ⎛ a min b min c min ⎞ ij ⎟ j p ⎜ j ~ rij = ⎜ , , p ⎟ p p b a ⎟ ⎜ c ij ⎠ ij ⎝ ij
{
between
the
preference relation given by the DM Pp .
the linear scale transformation, the various criteria scales are transformed into a comparable scale. Te set of criteria can be divided into benefit criteria (the larger the rating, the greater the preference) and cost criteria (the smaller the rating, the greater the preference). for
relations
Pp ( p = 1,2 ,..., P ) gives
Ω = (k ,l ) ; Ak ρ p Al , k ,l = 1,2 ,..., n ) p
have also same meaning. Using
⎞ ⎟ ⎟ ⎟ ⎠
1 m ∗ 2 ∗ ∗ 2 2 ∑ w ⎡( a − a jL ) + ( aijM − a jM ) + ( aijR − a jR ) ⎤⎥⎦ 3 j =1 j ⎢⎣ ijL
preference
is decision matrix for DM p .
p p ⎛ ap bij cij ⎜ ij ~ rijp = ⎜ , , max max max bj aj ⎜ cj ⎝
(5)
as (Li and Yang, 2004).
Suppose that the DM
X1 X 2 . . . X m p ~p ⎡~ . ~ xp ⎤ A1 ⎢ x11 x12 1n ⎥ A ⎢~ xp ~ xp . ~ xp ⎥ 2 21 22 2 n ⎥ p = 1,2,..., P ⎢ ~p p . . . D = ⎛⎜ ~ x ⎞⎟ = . ⎢. ⎥ ij ⎝ ⎠ n× m . ⎢ . ⎥ . ⎢. . . ⎥ A ⎢~ p ~ p p ⎥ ~ n x x . . . x mn ⎦ ⎣ m1 m 2
2
∗ a~ j
p
multiattribute group decision making problem can be expressed in matrix format as follows:
~ ~ ,w ~ ~ W =(w 1 2 ,..., wm )
⎡ p * ⎤ w ⎢d ⎛⎜ ~ r , a~ ⎞⎟⎥ j ⎣ ⎝ ij j ⎠⎦ j =1
∑
can be rewritten using triangular fuzzy numbers
Si =
. A fuzzy
m
p = i
Sp i
~x p = ⎛ a p , b p , c p ⎞ ⎜ ij ij ij ij ⎟⎠ ⎝
the fuzzy positive ideal
a~*j = ( a~*jL , a~*jM , a~*jR ) are triangular
solution, where
measurement
= ( m − n )2 = m-n
is
* * * * a~ = ⎛⎜ a~ , a~ ,...........a~ ⎞⎟ is m⎠ ⎝ 1 2
Let
1⎡ ( m − n )2 + ( m − n )2 + ( m − n )2 ⎤ 2 2 3 3 ⎥⎦ 3 ⎢⎣ 1 1 1⎡ 2 2 2⎤ (m − n) +(m − n) +(m − n) ⎥⎦ 3 ⎢⎣
P p ( p = 1 ,2 ,... P )
are normalized triangular
fuzzy numbers.
~ and n~ are real numbers, then the distance If both m ~ , n~ ) is identical to the Euclidean measurement d (m distance (Ross, 1995). Suppose that both ~ = (m , m , m ) and n~ = (n , n , n ) are two real m 1 2 3 1 2 3 numbers, then let and m1 = m2 = m3 = m
n1 = n2 = n3 = n . The distance ~ ~ (d (m, n )) can be calculated as
p p p p ~ r = ⎛⎜ a , a , a ⎞⎟ ij ⎝ ijL ijM ijR ⎠
(4)
B=
P
∑B
p =1
267
p
=
P
∑ ∑
p =1 (k ,l )∈Ω
p
p −
( Sl − S k )
(7)
5. APPLICATION
Our objective is to minimize the sum of errors for all p
pairs in Ω . Similarly, if p ( Sl
p − Sk )
p
l
k
l
Step1: The experts
goodness of fit for pair
k
k
the group is G=
P
∑G
p
=
p =1
By
definition
p
p
∑ ∑
p +
p
p =1 (k ,l )∈Ω
p −
p
∑ ( k ,l )∈Ω
∑ ( k ,l )∈Ω
( Sl − S k )
.
( Sl − S k ) = ( Sl − S k ) − ( Sl − S k ) ( S p − S p )+ − k p l
p _
p
and
to 3, etc.
(8)
( Sl − S k )
( Slp − S kp ) +
p +
p
( S p − S p )− = k p l
(Sp − Sp )=h ∑ k p l ( k ,l )∈Ω
Step2: The experts use the linguistic rating variables (shown in Table 1) to evaluate the rating of alternatives with respect to each attribute. The data and ratings of all alternatives on every attribute are given by the three experts P1 , P2 , P3 as in Table 2. Table 1 Linguistic variable for the ratings
Substituting for B and G from (7) and (8);
Very Poor (VP) Poor (P) Fair (F) Good (G) Very Good (VG)
(9)
G−B =h
The problem of finding the best solution ( w, a~* ) reduces to finding the solution ( w, v) (Fan and Xiao, 2004) which maximizes Equation (10) subject to the constraints (Li and Yang, 2004).
{
s .t .
}
Z klp
{
Z p = max 0 , S p − S p kl
l
k
≥ 0 , we have
Z klp
(10)
C2 C3
} for each (k , l ) ∈ Ω ≥
Slp
− S kp
p
and with
, Equation (10) can
A1 ~1 R = A 2 A3
maximize
p
l
k
( k ,l )∈Ω p p p Z + S − S ≥0 kl k l p Z ≥0 kl m
∑
( k ,l )∈Ω
l
p
{ }
∗
∗
∗
p
and
∗ a~ j
1
X
X
2
3
(0.6,0.77, 1.0) (0.8,1.0,1 .0) ⎤ ⎡ (0.5,0.5,0 .5) ⎢ (0.71,0.71 ,0.71) (0.2,0.33, 0.5) (0.6,0.77, 1.0) ⎥ ⎢ (1.0,1.0,1 .0) (0.8,1.0,1 .0) (0.6,0.77, 1.0) ⎥⎦ ⎣
To obtain the best weights and ideal point, taking ~p h = 1.0 and using R and Ω p we solve linear programming problem (Eq.(10)). can ∗
v jL = w j a jL , v jM = w j a jM and v jR = w j a jR
this linear programming,
P3
50,000 35,000 25,000 Fair Poor Good Good Very G Good
We can obtain the normalized decision matrices R 2 ~ and R 3 of the experts P2 and P3 (Eqs. (2) and (3)).
( k ,l ) ∈ Ω ; p = 1,2,..., P
we
50,000 35,000 25,000 Very G Fair Good Fair Good Fair
~
k
j = 1,2 ,..., m
V = v j = ( w j a~ j )
Using
( S p − S p )− ≥ h
∑
wj = 1
w j ≥ 0,
50,000 35,000 25,000 Good Poor Very G Very G Good Good
A1 A2 A3 A1 A2 A3 A1 A2 A3
X
⎧ P ⎫ ⎪ p⎪ ∑ max Z kl ⎬ ⎨∑ ⎪⎩ p =1 (k ,l )∈Ω p ⎪⎭ p p + subject to ( S − S ) − ∑
Decision Makers P1 P2
Step3: Constructing the normalized fuzzy decision ~ matrix R1 for expert (1) (using Eqs.(2 ) and (3))
be rewritten as
j =1
Alternatives
C1 ($x103)
where h is strictly positive. Let
(0, 0.1, 0.3) (0.2, 0.3, 0,4) (0.4, 0.5, 0.6) (0.6, 0.7, 0.8) (0.8, 0.9, 1.0)
Table 2 Decision informations and ratings of the three alternatives Criteria
⎧ P ⎫ ⎪ p p⎪ ∑ max 0 , Sl − S k ⎬ ⎨∑ ⎪⎩ p =1 (k ,l )∈Ω p ⎪⎭ ⎧ ⎪G - B ≥ h ⎪m ⎨ ∑ wj = 1 ⎪ j =1 ⎪w ≥ 0 , j = 1,2 ,..............., m ⎩ j
max
give their preference
Ω3 = {(2,1), (3,2)} i.e., 1 is preferred to 2, 2 is preferred
P
of
Pp ( p = 1,2 ,3 )
judgments between alternatives with paired comparisons as Ω1 = {(1,2), (2,3)} , Ω2 = {(1,2), (1,3)} ,
. The total goodness (G ) of fit for
( S p − S p )+ l
p
p p + p p ( S − S ) = S − S if Sl ≥ Sk l k l k
( S p − S p )+ = 0 if S p < S p ,
(k, l ) is
The proposed method is currently applied to solve KM tools selection problem and the computational procedure is summarized as follows:
may be designated as the goodness of fit
for this pair. Defining and
for the pair, (k, l ) ,
Sp ≥ Sp l k
w j , v jL , v jM , v jR
write
as
w1 = 0.284 w2 = 0 .398 w3 = 0 .318
and
. By solving
a~ ∗ = (( 0.27 , 0.27, 0.27), (0.19, 0.20, 0.22), (0.23, 24, 0.25 ))
are obtained
Using Eq. (6), the distances between
is computed.
∗ a~ can
~ Rip
and the
positive ideal be obtained. According these distances, the ranking orders of the three alternatives for the three experts are as follows: 268
Conway,S.,&Sligar,C.(2002). Unlocking knowledge assets: Knowledge management solutions from Microsoft. Redmond: Microsoft Press. Davis,L.,&Williams,G.(1994). Evaluating and selecting simulation software using the analytic hierarchy process. Integrated Manufacture Systems, 5(1), 23–32. Fan, Z.PHu, G.F., Xiao, S.H., (2004). A Method for Multiple Attribute Decision-Making with the Fuzzy Preference Relation on Alternatives, Computers&Industrial Engineering, 46, 321-327. Gartner Group. (1998). Knowledge Management Scenario. Conference presentation. Havens, C. and Knapp, E. (1999) “Easing Into Knowledge Management”, Strategy & Leadership; Chicago, Vol. 27, No. 2; pp. 4 – 9 Hwang, C.,L., Lin, M., J., (1987). Group Decision Making under Multiple Criteria, Springer-Verlag, Berlin. Hwang, C.-L., and S.-J. Chen, in collaboration with F.P. Hwang (1992). Fuzzy Attribute Decision Making: Methods and Applications. Springer-Verlag, Berlin. Kalling,T.(2003).Knowledge management and the occasional links with performance. Journal of Knowledge Management, 7(3), 67–81. Li, D.,F., Yang, J.,B., (2004). Fuzzy Linear Programming Technique for Multiattribute Group Decision Making in Fuzzy Environments. Information Sciences, 158, 263-275. Malhotra, Y. (2002). Why knowledge management Systems fail? Enablers and constraints of knowledge management in human enterprises. Handbook on knowledge management Knowledge Matters. Heidelberg, Germany: Springer-Verlag, 577–599. Mellor G. F., 1997, Getting to Real Time Knowledge Management: From Knowledge Management to Knowledge Generation, Online, 21, 5, 99-102. Parlby, D. (1997). The power of knowledge: A business guide to knowledge management. KPMG Management Consulting, internal report. Ross, T.J. (1995). Fuzzy Logic with Engineering Applications. (International Edition). McGraw-Hill, NY. Sirinivasan, V., Shocker, A.D., (1973). Linear Programming Techniques for Multidimensional Analysis of Preferences, Psychometrica, 38 (3), 337369. Van der Spek, R., & Kingma, J. (c2000). Achieving successful knowledge management initiatives. In S. Rock (Ed.), Liberating knowledge. London: IBM/CBI. Van Laarhoven, P.J.M., and W. Pedrycz (1983). A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems, 11 (3), 229-241. Wang, Y., M., Parkan, C., (2005). Multiple Attribute Decision Making Based on Fuzzy Preference Information on Alternatives: Ranking and Weighting, Fuzzy Sets and Systems, 153, 331-346. Wensley,A.K.P.(2000).Toolsforknowledgemanagement,htt p://www.icasit.org/km/resources/toolsforkm.htm. Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8 (3), 338-353. Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8, 199-249(I), 301-357(II). Zimmermann,H.J., (1991). Fuzzy Sets Theory and its Applications, Kluwer Academic Publishers, Third Edition, Boston/Dordrecht/London.
For P1 : A2 ρ A3 ρA1 For P2 : A3 ρ A1 ρ A2 For P3 : A3 ρ A2 ρ A1 The group ranking order of all alternatives can be obtained using social choice functions such as Copeland’s function (Hwang and Lin, 1987). Copeland’s function ranks the alternatives in the order of the value of f cp ( x ) , Copeland score. Table 3 Copeland’s scores Alternatives A1 A2 A3
Decision Makers P1 P2 P3
-1,-1 1, 1 1,-1
-1, 1 -1,-1 -1, 1
-1, -1 -1, 1 1, 1
Copeland’s scores -4 0 2
According to the Copeland’s scores, the ranking order of the three alternatives is A3, A2, A1. The best alternative is A3. 6. CONCLUSION AND IMPLICATIONS Through the proposed methodology in this research, enterprises can reduce the mismatch between the capability and implementation of the KM system, and greatly enhance the effectiveness of implementation of the KMS. The development of a KMS is still relatively new to many organizations. With the rise of the organization came a strong interest in KM, and KM tools assumed an important role in supporting KM. KM tools can capture, organize, share and leverage knowledge elements, along with the necessary support and training to insure a successful launch of KM solutions within an organization. In this paper, a systemic approach is proposed using fuzzy linear programming to evaluate an appropriate KM tool for the organization. The usefulness of the model was examined through observing its effect on the decision-making process in selecting an appropriate KM tool. To reflect the DM’s subjective preference information, a fuzzy LINMAP model is constructed to determine the weight vector of attributes and then to rank the alternatives. This study has several implications for KM practitioners who intend to evaluate KM tools to build a KMS. REFERENCES Alavi,M.,&Leidner,D.E. (2001). Review: Knowledge management and knowledge management: Conceptual foundations and research issues. MIS Quarterly, 25(1), 107–136. Byun,D.H.,&Suh,E.H.(1996). A methodology for evaluation EIS software packages. Journal of End User Computing, 8(21), 31. Chen, C.T., (2000). Extensions of the TOPSIS for Group Decision-Making under Fuzzy Environment, Fuzzy Sets and Systems, 114, 1-9. Choi,B.,&Lee,H.(2002).Knowledge management strategy and its link to knowledge creation process. Expert Systems with Applications, 23(3), 173–187.
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