An Enterprise Competitive Capability Evaluation Based on Rough Sets

Transcription

1 An Enterprse Compettve Capablty Evaluaton Based on Rough Sets 59 An Enterprse Compettve Capablty Evaluaton Based on Rough Sets Mng-Chang Lee Department of Informaton Management Fooyn Unversty, Kaohsung, Tawan, R.O.C. Emal: ABSTRACT Rough sets are an effectve mathematcal analyss tool to deal wth vagueness and uncertanty n the area of decson analyss and synthess evaluaton. Informaton Entropy, as a measurement of the average amount of nformaton contaned n an nformaton system, s used n the classfcaton of objectves and the analyss of nformaton systems. The weght of synthess evaluaton s determned by expert, lendng to subjectvty and wthout consderng the redundancy of attrbutes exsts n tradtonal synthetc evaluaton. Therefore, n ths paper we apply the mportance measure of attrbute based on nformaton entropy to create weght of each attrbute. The procedure ndcates that the approach s practcal and effectve. Keywords: Enterprse compettve capablty, Attrbute Reducton, Rough set theory, Informaton entropy Acknowledgement: I would lke to thank the anonymous revewers for ther constructve comments on ths paper.

2 60 Mng-Chang Lee INTRODUCTION Enterprse compettve capablty advantage evaluaton s one of busness management major drecton. Many studes have demonstrated that data mnng such as Analytc Herarchy Process (AHP), Fuzzy synthess evaluaton, neural networks, Data Envelopment Analyss (DEA) and Grey Relaton Analyss (GRA) (Ahn,et al. 2000; Hawley et al. 2000; Ln and pesse, 2004; Lu and Shn, 2005; Ln, et al. 2007; Xu and Ln 200; Zhang and L 2006; Road et al. 20; Zhang et al. 2006). Rough set s a mathematcs method that can be used to deal wth ncomplete and mprecse knowledge. The result s that the connecton of data s dscovered and useful feature s extracted and concse knowledge expresson s ganed. The rough set theory has been successfully appled n a varety of felds, ncludng: fnancal dstress classfcaton (Lee, 2007), busness falure predcton (Beynon and peel, 200), travel demand analyss (Goh and Law, 2003), mnng stock prces (Wang, 2003), nsurance market (Shyng et al. 2007), accdent preventon (Wong and chung, 2007), customer relatonshp management (Lou, 2009) etc. Recently, the rough set theory has become a popular evaluaton technque for classfcaton problems because of ther strength of handng vague and mprecse data (Jang and Ruan, 200). It can extract knowledge from the data tself by mean of ndscernble relatons, and generally needs fewer calculatons than that of other soft computng technques. The theory of rough set deals wth the approxmaton of arbtrary subsets of a unverse by two defnable or observable subsets called lower and upper approxmatons. By usng the concept of lower and upper approxmaton n rough set theory, the attrbutes n an nformaton system may be redundant and thus can be elmnated wthout losng essental classfcatory nformaton (Knodo, 2006; Lu and Hu, 2007). In ths paper, we defne the mportant measure of attrbute and nformaton entropy. Usng ths defnton, we can easly calculate the weght acquston of attrbutes. The purpose of ths research s to apply the mportance measure of attrbute based on nformaton entropy to create weght of each attrbute and create enterprse compettve capablty evaluaton functon. The proposed approaches are: () The establshment of related objects of a knowledge system n enterprse compettve capablty. (2) Attrbute reducton for the knowledge system, and fnd the attrbute core value. (3) Calculaton the mportant measure of attrbutes and calculaton of the weght of attrbutes. (4) Create enterprse compettve capablty evaluaton functon. The rest of ths paper s organzed as follows. In secton 2 we dscussed the concept of rough set theory. The algorthm of weght acquston of attrbutes and nformaton gan are dscussed n secton 3. Secton 4 gves an llustraton. It help n understandng of ths procedure, a demonstratve llustraton s gven to show the key stages nvolvng the use of the ntroduced concepts. Secton 5 s concluson.

3 An Enterprse Compettve Capablty Evaluaton Based on Rough Sets 6 THE CONCEPT OF ROUGH SET THEORY In ths secton, we dscussed the concept of ndscernble relatons. More ntroductons the man concepts of the theory can be found n Jng and Yanzh (2007) and through theoretcal foundaton are llustrated n (Jang and Ruan, (200). The basc concepts of rough set theory are as follows: Concept : Knowledge systems Gven an nformaton system (a data set), S = {U, A, V, f}, where U and A are fnte and nonempty sets called the unverse, and the sets of attrbutes, respectvely. In nformaton system, there exsts a functon, such that f: U A V. A s the unon of C and D, the ntersecton of C and D s empty. C s called as condtonal attrbutes, and D s called as decson attrbutes. The nformaton system s also called decson system, or knowledge system. Concept 2: Indscernble relaton Indscernble relaton s equvalence relaton n U, and P s a subset of C (P C ). IND (P), called the ndscernble relaton s defned as follows: IND (P) = {(x, y) U U:f (x, a) = f (y, a), for all a P}. Concept 3: Equvalence classes Let U / IND (P) be the famly of all Equvalence classes of the relaton IND (P). For smplcty of notaton U/P wll be wrtten nstead of U/ IND (P). U/ IND (C) and U/ IND (D) wll be called condton and decson classes, respectvely. Concept 4: Attrbute reducton and classfcaton Attrbute reducton s one of the central of rough set theory. It s well-known that attrbute s not same mportant n repostory, even some attrbutes are redundant. Some attrbutes n an nformaton system can be elmnated wthout losng essental classfcatory nformaton. The process of fndng a smaller set of attrbutes wth the same or close classfcatory power as the orgnal set s called attrbute reducton Through the process of attrbute reducton, redundant attrbutes, called superfluous attrbutes are removed wthout losng the classfed power of a reduced nformaton system. Let R be an equvalence relaton (r R). If IND(R) = IND(R- {r}), then r s thought unnecessary for C, otherwse r s thought necessary for C. Concept 5: Upper approxmaton and lower approxmaton (Jang and Yanzh, 2007) Let U be a non-empty set of fnte objects (the unverse), R be a subset of A, and X be a sunset of U. The lower approxmaton of set X, denoted by R( X ) s a unon of all elementary sets; objects n ths lower approxmaton unambguously belong to set X. R( X) = { Y U / R Y X} () The upper approxmaton of set X, denoted by R( X ) s a unon of all elementary sets each of whch has no-empty ntersecton wth X.; objects n ths upper approxmaton possble belong to set X.

4 62 Mng-Chang Lee R( X) = { Y U / R Y X φ} (2) The R-lower approxmaton of X s the set of all objects, whch can be certanty classfed to X usng attrbutes from R. The set U - R( X ) s the R-outsde regon of X and conssts of those objects, whch can be wth certanty classfed as not belongng to X usng attrbutes from R. The set BN R (X) = R( X )- R( X ) s the R- boundary regon of X. If R( X )) = R( X ), X s exact set, otherwse X s rough set. Concept 6: Dspensable and Indspensable Features Gven an nformaton system, S = {U, A, V, f}, A =C D. The postve regon n D defnte as: Pos ( ) ( ) C D = R X (3) x U / D If Pos ( C D ) Pos ( ) C { a} D, the condton attrbutes a s ndspensable attrbute n C; otherwse the condton attrbutes a s dspensable attrbute n C. A s an ndependent, f all c C are ndspensable. Concept 7: Concepts of attrbute reducton and core Supposng R C, f R s ndependent and IND(R) = IND(C), then R s thought as reducton of C. The set that s composed by all necessary relaton of C s called core of C and marked CORE (C). There s relaton between CORE and relaton as follows. CORE( C) = RED( C) (4) RED( C) means all the reducton of C. THE ALGORITHM OF WEIGHT ACQUISITION Ths secton presents the weght acquston method based on rough set theory and Informaton gan. The result of the lower approxmaton can descrbe the credtable knowledge n nformaton system and the weght of an attrbute can be estmated by the varety ratng of the lower approxmaton when the attrbute s deleted. One measure to descrbe the nexactness of approxmaton classfcaton s called qualty of approxmaton of D by means of the attrbutes from C. Defnton : Qualty of approxmaton andσ - mportant ratng Gven an nformaton system, S = {U, A, V, f}, the qualty of approxmaton of D by means of the attrbutes from C s denoted γ ( D) = n card( R( X )/ card( U ) (5) C = Where card( U ) denotes the cardnalty of set U The σ - mportant ratng of attrbute a s defned as σ ( a ) = γ ( D) - γ ( ) (6) { } CD C C a D

5 An Enterprse Compettve Capablty Evaluaton Based on Rough Sets 63 Defnton 2: Informaton entropy Gven an nformaton system, S = {U, A, V, f}, If P A, U / IND (P) = {X, X 2,, X n } s a n equvalence relaton on U. I (P) s called as Informaton entropy. n X X I(X)= - (-log 2 ) (7) U U Where, X / U s card n X = Defnton 3: Concepts of attrbute mportance Gven knowledge system S = (U, A, V, f), C s called a set of condtonal attrbute, D s called a set of decson attrbute and C D =φ and A = C D. f: U U = V s an nformaton functon. The mportant measure of attrbute a s defned: SGF (a) = I(C) - I(C- {a}) (8) Where a C When SGF (a) > 0, t s denoted that attrbute a s need. When S (a) = 0, a s redundant attrbuton, that s, a can leave out from the attrbuton s set. If SGF (a) > SGF (b), the attrbute a s more mportant than attrbute b n condton C. Defnton 4: The weghts based on nformaton entropy Gven nformaton system S = (U, A, V, f), C s called a set of condtonal attrbute, D s called a set of decson attrbute and C D =φ and A = C D. f: U U = V s an nformaton functon. a A= { a, a,..., a } 2 n. The attrbute weght of a denoted: n w SGF( a )/ SGF( a ) (9) = = Defnton 5: Create enterprse compettve capablty evaluaton functon After constructed the weghts of each attrbute, we create enterprse compettve capablty evaluaton functon. k py ( ) = w y (0) Where = y denotes the value of the th compettve capablty evaluaton ndex. ILLUSTRATION- ENTERPRISE COMPETITIVE CAPABILITY EVALUATION Step : Enterprse Compettve Capablty Evaluaton Index. The emprcal research whch s based on the data Tawan s lsted company (food stocks). 9 expermental samples are select n Therefore, U= {, 2,, 9}. In ths study, we use 2 enterprse compettve capablty evaluated ndexes are: Return on total assets (x ), proft rato of sales (x 2 ), Proft rato of total captal (x 3 ), Workng captal to sales rato (x 4 ), Inventory turnover rato (x 5 ), Account recevable turnover rato (x 6 ), Current rato (x 7 ), Asset-lablty current rato (x 8 ), Current Labltes rato (x 9 ), Asset-lablty rato (x 0 ), Equty rato (x ), pretax proft current debt rato (x 2 ).

6 64 Mng-Chang Lee Therefore, C= {x, x 2,., x 2 }, D= {0, }, where 0 denotes the stock prce > 0, and denotes the stock prce >= 0. Set each compettve capablty evaluated ndex threshold value, whch s the average value of 20 enterprses on lately 0 years fnancal ndex. The compettve capablty evaluated ndex threshold values are 25.0, 34.0, 330, 0.75, 635.0, 78.0, 30., 24.0, 28.0, 24.8, 256.0, For example, the threshold value of attrbute Return on total assets s 25% (see Table ). If (x ) > 25%, we set (x ) equal to ; otherwse set (x ) equal to 0. Accordng to the threshold value, we obtan the enterprse compettve capablty evaluated dscrete decson table (see Table 2). Table : Enterprse compettve capablty evaluated ndexes U X X 2 X 3 X 4 X 5 X 6 X Table : Enterprse compettve capablty evaluated ndexes (contnue) U X 8 X 9 X 0 X X 2 D : Threshold value

7 An Enterprse Compettve Capablty Evaluaton Based on Rough Sets 65 Table 2: The Enterprse Compettve Capablty Evaluated Dscrete Decson Table U X X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 0 X X 2 D Step 2: Reducton of Attrbutes We fnd out that the attrbutes X 3, X 4, X 8, X 0 have the same value n table 2, and therefore we remove attrbutes X 4, X 8, X 0 ; the attrbutes X 2, X 7, X 2 have the same value n table 2, and therefore we remove attrbutes X 7, X 2 ; the attrbutes X 6, X have the same value n table 2, and therefore we remove attrbutes X 6. Based algorthm of reducton, the reduce attrbutes are {X, X 2, X 3, X 5, X 9,X }. We calculate the mnmum attrbutes set by usng concept 2 and 3. IND (C) = {, 2, 3, 4, 5, 6, 7, 8, 9} IND (D) = {(, 3, 5, 6, 9), (2, 4, 7, 8)} IND ( C-(x ))= {, 2, 3, 4, 5, (6, 7), 8, 9} IND ( C) IND ( C-(x 2 ))= {, 2, (4, 5), 3, 6, 7, 8, 9 } IND ( C) IND ( C-(x 3 ))= {, 2, 3, 4, (5, 9}, 6, 7, 8 } IND ( C) IND ( C-(x 5 ))= {, 2, 3, 4, 5, 6, 7, 8, 9}= IND ( C) IND ( C-(x 9 ))= {, 3, 5, 6,( 2, 4),7, 8, 9} IND ( C) IND ( C-(x ))= { ( 4), 2, 3, 5, 6, 7, 8, 9} IND ( C) Under concept 5, we calculate the postve regon n D. POS C (D) = {, 2, 3, 4, 5, 6, 7, 8, 9} POS C-(x) (D) = {, 2, 3, 4, 5, 8, 9} POS C (D) POS C-(x2) (D) = {, 2, 3, 6, 7, 8, 9} POS C (D) POS C-(x3) (D) = {, 2, 3, 4, 6, 7, 8, 9} POS C (D) POS C-(x5) (D) = {,2, 3, 4, 5, 6, 7, 8, 9} = POS C (D) POS C-(x9) (D) = {, 3, 5, 6, 7, 8, 9} POS C (D) POS C-(x) (D) = {2, 3, 5, 6, 7, 8, 9} POS C (D) The attrbutes X 5 s dspensable n C by usng concept 6 and the mnmum attrbutes set s {X, X 2, X 3, X 9, X }. The enterprse compettve capablty evaluated reducton decson table s showed as Table 3.

8 66 Mng-Chang Lee Table 3: The Enterprse Compettve Capablty Evaluated Reducton Decson Table U X X 2 X 3 X 9 X D Step 3: Calculaton the Importance Measure of Attrbutes and Calculaton of the Weght of Attrbutes We calculate the mportant measure of attrbute by usng defnton 2 and 3 SGF( x ) = I(C) - I(C- { x }) = = SGF( x ) = SGF( x ) = SGF( x ) = SGF( x ) = We calculate the weght of attrbutes x by usng defnton 4: n w = SGF( a )/ SGF( a ) = 0.2 (I =,2,, 5) = Table 4: The Enterprse Compettve Capablty Evaluaton Functon Company X X 2 X 3 X 9 X Evaluaton Rank functon of Weght w

9 An Enterprse Compettve Capablty Evaluaton Based on Rough Sets 67 Step 4: Create Enterprse Compettve Capablty Evaluaton Functon We calculate the enterprse compettve capablty evaluaton functon by usng eq. 0. Where w s called mportant measure of attrbute, n ths example w = 0.2 (=,2,, 5). Therefore, we obtan the order sequence of company (see Table 4). In addton, the process of the weght acquston s based on the data from the nformaton system and don t add any expert s preference. CONCLUSIONS The weght of synthess evaluaton s determned by expert, lendng to subjectvty and wthout consderng the redundancy of attrbutes exsts n tradtonal synthetc evaluaton. The advantage of ths method s that t elmnates the personal subjectvty as and deals wth the redundancy of attrbutes properly. Ths study presents an approach based on rough set theores, whch can fnd out evaluaton to enterprse compettve capablty. The expermental above can prove that the approach s practcal and effectve. We thnk that rough set theory wll do more achevement n ths doman. Our future research wll work more effectve method for weght generaton such as fuzzy rough set theory. REFERENCES Ahn, B. S., Cho, S. & Smkm, C. Y. (2000). The ntegrated methodology of rough sets and artfcal neural network for busness falure predcton. Expert system wth applcaton, 8(4), Beynon, M. J. & peel, M. J. (200). Varable precson rough set theory and data dscretzaton: an applcaton to corporate falure predcton. Omega, 29(6), Goh, C. & Law, R. (2003). Incorporatng the rough sets theory nto travel demand analyss. Toursm Management, 24(5), Hawley, D. D., Johnson, J. D., & Rsna, D., (2000). Artfcal Neural Network Systems: A Network tool for fnancal Decson Makng. Fnancal Analyss Journal, Nov/Dec, 63-72, Jang, H. & Ruan, H. (200). Applyng rough set theory to evaluate network marketng performance of chna s agrcultural products. Journal of Computers, 5(8), Jang, H. & Yanzh, D. (2007). Applcaton of assocaton rules based on rough set n human resource management. The sxth Wuhan Internatonal Conference on E-busness Innovaton Management Track, Knodo, M. (2006). On the structure of generalzed rough sets. Informaton Scence, 76, Kusak, A. (200). Rough set Theory: A Data Mnng Tool for Semconductor Manufacturng. IEEE Transactons on Electronc Packagng Manufacturng, 24(), January Lee, M. C. (2007). Developng fnancal dstress evaluaton based on fuzzy-rough

10 68 Mng-Chang Lee approach. Proceedng of Second Internatonal Conference on Innovatve Computng, Informaton and Control (ICICIC 2007), 00, Ln, L. & Pesse, J., (2004). Identfcaton of corporate dstress n UK ndustrals: A condtonal probablty analyss approach. Appled Fnancal Economcs, 4, 73-82, Ln, S. J., Lu, I. J. & Lews, C. (2007). Grey relaton performance correlatons among economcs, energy use and carbon doxde emsson n Tawan, Energy Polcy, 33, Lou, James J. H. (2009). A novel decson rules approach for customer relatonshp management of the arlne market. Expect System wth Applcatons, 36(3), Lu, D. & Hu, P., (2007). Herarchcal cluster analyss methodology based on rough sets Theory and ts applcaton. Statc and Decson, 236, Lu, D. R. & Shn, Y. Y., (2005). Integratng AHP and Data mnng for product recommendaton based on customer lfetme value. Informaton &management, 42, Pal, S. K., (2004). Soft data mnng computatonal theory of perceptons and rough fuzzy approach. Informaton Scence, 63, 5-2. Road, A., Nader, B. & Soltan, M. (20). Clusterng and rankng unversty majors usng data mnng and AHP algorthm: A case study n Iran. Expert System wth Applcaton, 38(), Shyng, J. Y., Wang, F. K., Tzeng, G. H., & Wu, K. (2007). Rough set theory n analyzng the attrbutes of combnaton values for nsurance market. Expert System wth Applcatons, 32(), Wang, Y. F. (2003). Mnng stock prce usng fuzzy rough set system. Expect System wth applcaton, 24(), Wong, J. C. & chung, Y. S. (2007). Rough set approach for accdent chans exploraton. Accdent Analyss and Preventon, 39(3), Xu, X. & Ln, J. (200). Strategc suppler network for suppler selecton. Journal of Computers, 5(6), Zhang, L. J. & L, Z. J. (2006). Gene selecton for classfyng mcroarray data usng Grey relaton Analyss. Lecture Notes n Computer Scence, 4265, Zhang, L. j., L, Z. j., Chen, H. W., & Wen, J. (2006). Mnmum redundancy gene selecton based on grey relatonal analyss IEEE Internatonal Conference on Data mnng workshops, Mng-Chang Lee s Assstant Professor of Department of Informaton Management at Fooyn Unversty and Natonal Kaohsung Unversty of Appled Scences. Hs qualfcatons nclude a Master degree n appled Mathematcs from Natonal Tsng Hua Unversty and a PhD degree n Industral Management from Naton Cheng Kung Unversty. Hs research nterests nclude knowledge management, parallel computng, and data analyss. Hs publcatons nclude artcles n the journal of Computer & Mathematcs wth Applcatons, Internatonal Journal of Operaton Research, Computers & Engneerng, Amercan Journal of Appled Scence and Computers, Industral Engneerng, Internatonal Journal nnovaton and Learnng, Int. J. Servces and Standards, Lecture Notes n computer Scence (LNCS), Internatonal Journal of Computer Scence and Network Securty, Journal of Convergence Informaton Technology and Internatonal Journal of Advancements n computng Technology.