Ｐｅｒｆｏｒｍａｎｃｅ Ｅｖａｌｕａｔｉｏｎ ｏｆ Ｅｎｔｅｒｐｒｉｓｅ Ｋｎｏｗｌｅｄｇｅ Ｍａｎａｇｅｍｅｎｔ ｂａｓｅｄ ｏｎ Ｍｕｌｔｉｐｌｅ Ａｔｔｒｉｂｕｔｅ Ｇｒｏｕｐ Ｄｅｃｉｓｉｏｎ

Abstract: Given that the classical performance evaluation models can not deal with the group decision making problems since they simply average the index， we propose an enterprise knowledge management evaluation model based on multiple attribute group decision making (MAGDM). Find the differences between Ordered Weighted Averaging (OWA) and methods for uncertain decision making. Also， analyze the multiple attribute group decision making process and implement the algorithm. Finally， apply the method on performance evaluation of four enterprises and make sensitivity analysis towards the evaluation results.

Key words: Knowledge Management; OWA; Multiple Attribute Group Decision Making

doi:10.3969/j.issn.1673-0194.2009.15.026

CLC number: F272Article character:AArticle ID:1673-0194（2009）15-0084-04

1 Introduction

Knowledge management performance is the direct economic performance， the development driving force of staff， the improvement of work process and the value to customersbrought by knowledge management after the implementation of the knowledge management strategy. Knowledge management performance evaluation makes analysis on these areas through vertical or horizontal comparative， using measured indicators， with reference to the original or leader.

Researches aboard related to knowledge management performance mainly are: assessment method of intellectual assets by Verna Allee［1］， Skandian model designed by Edvinsson， KMAT-the knowledge management evaluation tool， which uses leadership， culture， assessment， technology and learning to evaluate the effectiveness of enterpriseknowledge management by Arthur Andersen［2］. Current researches on knowledge management performance evaluation in China are still in the initial stage. Wei Jiang［3］ proposes an enterprise core competence fuzzy comprehensive evaluation model. Jin Bei［4］ evaluate enterprise core competitiveness using statistics method.

2 Multi Attribute Group Decision Making based on OWA Operators

Decision-making， which is a basic human activity， is one way to make choice in political， economic， technical and daily life. It’s a highly frequent activity of management. However， there are a large number of multi attribute group decision making problems in actual decision making due to the complexity. The problem contains both quantitative indicators and qualitative indicators and its attribute values are various， such as precise number， interval number and fuzzy number. And the aggregation of preferences of group experts is needed to reduce the irrational factors in decision making. Multi attribute group decision making based on OWA is more in line with the ambiguity and uncertainties of human thinking and can take full advantages of the wisdom of the expert group.

OWA operator which is a method of information fusion is proposed by Yager. It can eliminate some anomalies through the sort and aggregation of the data. In addition， some extended OWA operators can integrate uncertain decision making information of interval number， and convert it to information in the form of precise real numbers.

Definition 1.1［5］ An OWA operator of dimension n is a mapping f∶Rn→R， that has an associated n vector w=(w1，w2，…，wn)T such as wj∈［0，1］，∑nj=1wj=1，1≤j≤n， furthermore f(a₁，a₂，…，an)=∑nj=1wjbj， where bj is the j-t h largest element of the bag (a₁，a₂，…，an).

Definition 1.2［6］An Continuous Ordered Weighted Averaging (COWA) operator is a mapping fQ(［a，b］)=∫10dQ(y)dy(b-y(b-a))dy， that has an function Q∶［0，1］→［0，1］ with properties as follows: ① Q(0)=0， ② Q(1)=1， ③ if x≥y， then Q(x)≥Q(y).

3 OWA Decision Making and Uncertain Decision Making Method

Decision makers often make choices based on subjective preferences in uncertain decision making， such as Pessimism (Maxmin) Criterion， Optimism (Maxmax) Criterion and Laplace Criterion.

However， the accuracy of these criteria is not enough to describe real preferences of decision maker. The OWA operator can be a unified interpretation of these criteria， and the subjective preferences of decision makers can be accurately described with it.

A typical uncertain decision making problem can be described as matrix X:

θ1θ2… θn

X=x11 x12 … x1n

x21 x22 …x2n

   

xm1 xm2 … xmn

A1A2Am

Ai(i=1，2，…，m) stands for m decision alternatives， which has n attributes θj with uncertain distribution situation. xij means the revenue function of alternative Ai inθj.

3.1 Pessimism (Maxmin) criterion

Decision makers just take the worst result of every alternative Ai . Then the earning value of Aiis Val(Ai)=minj{xij} with a matching OWA operator asf=minj{xij}=∑nj=1wj xij， where w=(0，0，…，1)T， and xij is the j-th largest element of the bag (xi1，xi2，…，xin). The optimistic level is orness(w)=1n-1∑nj=1(n-j)wj=0.

3.2 Optimism (Maxmax) criterion

Decision makers just take the best result of every alternative Ai. Then the earning value of Ai is Val(Ai)=maxj{xij} with a matching OWA operator as f=minj{xij}=∑nj=1wj x′ij， where w=(0，0，…，1)T， and xij is the j-th largest element of the bag (xi1，xi2，…，xin). And the optimistic level is orness(w)=1n-1∑nj=1(n-j)wj=1.

3.3 Laplace criterion

Each result of every alternative Ai is equally likely to decision maker. Then the earning value of Ai is Val(Ai)=1n∑nj=1xijwith a matching OWA operator as f=1n∑nj=1xij=∑nj=1wj x′ij， where w=(1/n，1/n，…，1/n)T， and x′ij is the j-the largest element of the bag (xi1，xi2，…，xin). The optimistic level is orness(w)=1n-1∑nj=1(n-j)wj=1/2.

4 Process of Multi Attribute Group Decision Making Evaluation

The process of multi attribute group decision making evaluation based on OWA operator and extended OWA operators is as follows:

Step 1: Set up an evaluate method of fuzzy language and COWA operator， and get the weight of group experts fixed.

Step 1.1: Set up the expert evaluation indicator system C=(cj|j=1，2，…，s) with weight vector R=(r1，r2，…，rs) for indicator set C.

Step 1.2: Judgment matrix P=(pij)mxn in language form is given by decision makers.

Step 1.3: Aggregate the evaluate information to integrate evaluation value Zi=1n∑nj=1(rjpij) through OWA operator.

Step 1.4: Convert fuzzy number Zi to precise real number Rn(Zi) with Rn(Zi)=((1-λ)(a₁+2a₂)+λ(2a3+a4))/6 ， and the weight ν1 of expertdican be obtained by normalizing Rn(Zi)， where ν1=Rn(Zi)∑nj=1Rn(Zi)，i=1，2，…，s.

Step 1.5: Get the weight vector of expert group ν=(ν1，ν2，…，νs).

Step 2: Get the evaluation value of each alternative.

Step 2.1: Convert the interval number to precise real number， the interval fuzzy decision matrix B′ to precise real number decision matrix B＾′ by using COWA operator.

Step 2.2: According to the expert weight vector v and attribute weight vector w， decision matrix B′ can be obtained due to aggregation and standardization of decision matrixB＾′ using OWA operator.

Step 2.3: After the positive and negative ideal alternatives are obtained， the distances from each alternative to them are d+i=∑nj=1(wj)2(B*ij-A+)2， d-i=∑nj=1(wj)2(B*ij-A-)2.

Step 2.4: Calculate the relatively approach degree of each alternative and positive alternative Dei=d-id-i+d+i .

Step 2.5: Choose the optimal alternative through the ranking of alternatives.

5 Application

There were 6 experts to finish questionnaires of 4 enterprises. Then the scores of 5 indicators can be obtained through calculation. Also， the enterprise indicator weights are w=(0.32，0.19，0.25，0.15，0.09).

5.1 Obtain the expert weights

(1) First of all 8 indicators for evaluation of 6 experts are formulated: academic status c1， academic level c2， ability to access to information c3， fairness c4， self-confidence c5， familiarity with the project c6， innovation c7， degree of experience c8.

Weight vector in the form of language as R = (important， very important， most important， most important， normal， very important， normal， very important) for indicator set C is given.

(2) Calculate integrate evaluation value Zi:

Z1=(0.338，0.613，0.642，0.85);

Z2=(0.218，0.451，0.487，0.685);

Z3=(0.238，0.478，0.506，0.711);

Z4=(0.39，0.675，0.731，0.898);

Z5=(0.276，0.526，0.555，0.76);

Z6=(0.0.271，0.518，0.555，0.76).

(3) Set λ， convert Zi to Rn(Zi):

Rn(Z1)=0.2926; Rn(Z2)=0.2168; Rn(Z3)=0.2287;

Rn(Z4)=0.3245; Rn(Z4)=0.2515; Rn(Z6)=0.2493.

(4) Get the expert weight vector:

ν=(0.1872，0.1387，0.1463，0.2076，0.1609，0.1595).

5.2 Calculate the optimistic weight

The weights in different optimistic levels can be calculated［7］， as shown in Table 1. Optimistic level α=0.6 will be taken for example in 5.3 and 5.4.

Table 1 Optimistic weight in different optimistic levels

000.06660.26660.51

000.16670.16670.16670

00.16660.16670.16670.16670

00.16670.16670.16670.16670

00.16670.16670.166700

10.50.26660.066600

5.3 Aggregation

The standard aggregation matrix can be obtained according to expert weights v and optimistic weights w:

0.90 0.84 0.96 0.92 0.99

0.94 1.00 0.93 1.00 1.00

1.00 0.97 1.00 0.87 0.90

0.92 0.91 0.89 0.83 0.66

The positive ideal alternative is （1.00，1.00，1.00，1.00，1.00）.

The negative ideal alternative is （0.90，0.84，0.89，0.83，0.66）.

5.4 Ranking of the alternatives

(1) Calculate the distances from each alternative to positive and negative ideal alternatives:

d+=(0.05，0.03，0.02，0.06)，d-=(0.04，0.05，0.05，0.01)

(2) Calculate the relatively approach degree of each alternative and positive alternative: De=(0.44，0.68，0.71，0.21).

(3) Get the result according to De: C>B>A>D.

5.5 Results of different optimistic weights

Above is the result when optimistic weight α is 0.6， and follow the steps above， the results in different optimistic weights can be calculated， as shown in Table 2.

Table 2 Results of different optimistic weights

optimistic weight αresult

0B>C>D>A

0.2B>C>A>D

0.4B>C>A>D

0.6C>B>A>D

0.8C>B>A>D

1C>B>A>D

5.6 Sensitivity analysis of enterprise knowledge management performance evaluate

Sensitivity analysis is to analyses the effect of optimistic weight to the result of evaluation， as shown in Fig.1 and Fig.2.

Fig.1 Influence of α on relatively approach degree

Fig.2 Influence of α on sort order

As can be seen from Fig.1， relatively approach degree changes as the change of optimistic weight α. So in the performance evaluation of enterprise knowledge management， the ranking of enterprises have also changed. As shown in Fig.2， with the changes of optimistic level， A and B， C and D are exchanged in the sort order. Thus， the results of performance evaluation will be different when the optimistic level changes.

6 Conclusion

Given that the classical performance evaluation models can not deal with the group decision making problems since they simply average the index， an enterprise knowledge management evaluation model based on multiple attribute group decision making is proposed. It deals with interval fuzzy judgment matrix， interval fuzzy decision matrix， and takes expert preference into consideration， aggregate the decision information of single expert to group decision information， finally sort the group decision information and the rank of different enterprises can be obtained.

References

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［2］ Andersen A. The Knowledge Management Assessment Tool (KMAT)［M］. London: Arthur Andersen KMAT Study， 1996.

［3］ Jiang W. MA Strategy for New Thinking［M］. Beijing: Science Press， 2002.

［4］ Bei J. Theory and Methodology of Measuring Enterprise Competitiveness［J］. China Industrial Economy， 2003(3):5-13.

［5］ R R Yager On Ordered Weighted Averaging Aggregation Operators in Multi-criteria Decision Making［J］. IEEE Transactions on Systems， Man and Cybernetics， 1988， 18(1): 183-190.

［6］ R R Yager. OWA Aggregation Over a Continuous Interval Argument with Applications to Decision Making［J］. IEEE Transactions on Systems， Man and Cybernetics， 2004， 34(5):1952-1963.

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