Research Article New Combined Weighting Model Based on Maximizing the Difference in Evaluation Results and Its Application

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1 Hdaw Publshg Corporato Mathematcal Problems Egeerg Volume 2015, Artcle ID , 9 pages Research Artcle New Combed Weghtg Model Based o Maxmzg the Dfferece Evaluato Results ad Its Applcato B Meg ad Guota Ch Faculty of Maagemet ad Ecoomcs, Dala Uversty of Techology, Dala , Cha Correspodece should be addressed to Guota Ch; chgt@dluteduc Receved 17 May 2015; Revsed 2 August 2015; Accepted 18 August 2015 Academc Edtor: Davde La Torre Copyrght 2015 B Meg ad G Ch Ths s a ope access artcle dstrbuted uder the Creatve Commos Attrbuto Lcese, whch permts urestrcted use, dstrbuto, ad reproducto ay medum, provded the orgal work s properly cted Ths paper presets a approach for weghtg dces the comprehesve evaluato I accordace wth the prcple that the etre dfferece of varous evaluato obects s to be maxmally dfferetated, a adusted weghtg coeffcet s troduced Based o the dea of maxmzg the dfferece betwee the adusted evaluato scores of each evaluato obect ad ther mea, a obectve programmg model s establshed wth more obvous dfferetato betwee evaluato scores ad the combed weght coeffcet determed, thereby avodg cotradctory ad less dstgushable evaluato results of sgle weghtg methods The proposed model s demostrated usg 2,044 observatos The emprcal results show that the combed weghtg method has the least msudgmet probablty, as well as the least error probablty, whe compared wth four sgle weghtg methods, amely, G1, G2, varato coeffcet, ad devato methods 1 Itroducto I the process of comprehesve evaluato, a complete set of evaluato dces must be determed, wth the correspodg weght of each evaluato dex The dex weght reflects the relatve mportace of each dex, that s, the status adfuctoofeachfactortheevaluatoaddecsomakg process Hece, the determato of dex weght relates to the relablty ad valdty of rakg results of the proect For example, a eterprse credt rsk evaluato s related to ts facal factors, ofacal factors, ad macro factors I terms of large eterprses, facal codto ca reflect the repaymet ablty ad wllgess to remburse well; for ths reaso, there must be substatal weghts for the facal factors a large eterprse credt rsk evaluato Whe the facal system of small eterprses s ot stadard ad soud, facal formato caot fully reflect ther operatg codto, ad ofacal ad macro factors have greater fluece As a result, f we caot allocate the weghts of facal, ofacal, ad macro factors, the rratoal pheomeo that small eterprses wth poor credt mght have a hgh rakg ca result losses to the bak Therefore, weght determato methods have bee a maor focus comprehesve evaluato research Weghtg methods for comprehesve evaluato ca be dvded to three categores: subectve, obectve, ad combed A subectve weghtg method s a meas whereby decso makers obta dex weghts o the bass of ther ow experece ad the emphass that they subectvely place o each dex For ths reaso, the dex weght obtaed usg subectve weghtg depeds o experts kowledge, experece, ad persoal prefereces, wth o cosderato for the characterstcs ad regulartes of actual sample data [1] Subectve weghtg models clude, for example, the aalytc herarchy process (AHP) [2, 3], aalytc etwork process (ANP) [4, 5], ad Delph method [6] I cotrast, a obectve weghtg method s a meas whereby the dex weght s determed usg obectve formato regardg each dex Hece, the dex weght obtaed usg ths method does ot volve subectve opos of decso makers Obectve weghtg models clude, for example, themeaweght[7],goalprogrammg[8,9],etropy[10] stadard devato (SD) [11], crtera mportace through tercrtera correlato (CRITIC) [12], ad preferece selecto dex (PSI) [13] methods Though a obectve weghtg method provdes weghts accordg to the actual sample data, t s easly subect to the fluece of sample data Moreover, dfferet obectve

2 2 Mathematcal Problems Egeerg weghtg methods ted to yeld dfferet results Therefore, may scholars have proposed combed weghtg methods that cosder the advatages ad dsadvatages of both subectve ad obectve weghtg A combed weghtg model has the advatage of tegratg the beefts from both subectve ad obectve weghtg models ad mtgatg lmtatos of sgle weghtg models [14, 15] Su ad Bao tegrated the rough set weghtg method ad AHP model based o varace maxmzato theory to mprove the tradtoal combato weghts determato method ad made the weghts determed more reasoably ad more helpful supportg decso makg [16] L ad Ch proposed a combed weghtg model that tegrates the evaluato values from sgle evaluato methods by maxmzg the devato of sgle evaluato values [17] Although exstg research has made great progress, there are stll drawbacks Frst, there s usually radomess the method selecto for the determato of obectve ad subectveweghtsmeawhle,themethodforthecoeffcet ofobectveadsubectveweghtssotappropratesecod, a reasoable test s lackg to verfy the ratoalty of a combed weghtg method Ths paper proposes a combed weghtg method based o dfferece maxmzato Dfferet evaluato scores for the same obect are obtaed usg dfferet weghtg methods Accordg to the prcple that the etre dfferece of dfferet evaluato obects must be maxmally dfferetated, a adusted weghtg coeffcet s troduced Based o the dea of maxmzg the dfferece betwee the adusted evaluato scores of each evaluato obect ad ther mea, a obectve programmg model s establshed wth more obvous dfferetato betwee evaluato scores guarateed ad the combed weght coeffcet determed At the same tme, wth 2,044 small prvate busesses from a Chese govermet-owed commercal bak as emprcal samples, a hgher dfferetato accuracy of the combed weghtg method compared wth four kds of sgle weghtg methods, amely, G1, G2, varato coeffcet, ad devato methods, s esured by usg msudgmet probablty (MP) ad error probablty (EP) to test evaluato results from the use of dfferet weghtg methods The rest of the paper s structured as follows Secto 2 troduces the prelmary models Secto 3 dscusses the proposed model Secto 4 presets the data ad the emprcal results Coclusos are gve Secto 5 2 Prelmary Models 21 Data Stadardzato The purpose of dex data stadardzato s to trasform the dex data to [0, 1] to elmate the cosstecy of uts ad dmesos There are four types of dexes: postve, egatve, terval, ad qualtatve Postve dces are those for whch greater values are better, such as X 4,1 Net come, egatve dces are those for whch smaller values are better, such as X 3,1 Lqudty rato, ad terval dces are those for whch the values are reasoable oly whe they le partcular tervals, such as X 1,2 Age Let x deotethestadardscoreoftheth sample o the th dex Let V deote the orgal data of the th sample o the th dex s the total umber of dces ad m s the total umber of samples The stadardzato equatos of the postve ad egatve dces are show as (1) ad (2), respectvely [18] Cosder the followg: x = x = V m 1 (V ) max 1 (V ) m 1 (V ), (1) max 1 (V ) V max 1 (V ) m 1 (V ) (2) Equato (1) s the rato of the devato betwee the dex orgal data V ad the mmum value m(v ) to the rage max(v ) m(v ) It dcates that the closer the dex of the orgal data V stothemaxmumvaluemax(v ),the greater the stadardzed value x wll be The two equatos have smlar meags Equato (2) dcates that the closer the dex of the orgal data V s to the mmum value m(v ), the greater the stadardzed value x wll be Let q 1 ad q 2 be the left ad rght boudares of the deal terval, respectvely The stadardzato of the terval factorssshowasfollows[18]equato(3)dcatesthata dex value wll be gve oe pot f t falls the optmal rage [q 1,q 2 ] Greater devato from ths terval leads to lower x : q 1 V 1 max (q 1 m 1 (V ),max 1 (V ) q 2 ), V <q 1 (a) { x = V q 2 1 max (q 1 m 1 (V ),max 1 (V ) q 2 ), V >q 2 (b) { { 1, q 1 V q 2 (c) (3) For all qualtatve dces, we establsh a gradg stadard sutable for small prvate busesses Note that the data of qualtatve dces fall [0, 1] after stadardzato, dcatg that we eed ot ormalze them through (1) (3) 22 Sgle Weghtg Models 221 Subectve Weghtg Model: G1 G1 reflects the mportace of dces by ther sequetal order After the order s

3 Mathematcal Problems Egeerg 3 determed, ratoal weghts are assged based o comparg the adacet dces Therefore, the relatve mportace of ay two adacet dces s certa, assurg that the mportace correspods to the weght The steps of G1 are as follows Step 1 Experts specfy the sequece order of dces Step 2 Defe as the G1 weght of the th dex ad as the total umber of dex Experts specfy the ratoal rato r of dces ext to each other, that s, specfyg the relatve rato of mportace betwee adacet dex x 1 ad x [19]: r = w(1) 1 (4) Step 3 Based o the ratoal rato r of (4), the weght of the th dex the etre dex system s calculated usg (5), as follows [19] also deotes the total umber of dex: =(1+ =2 k= r k ) 1 (5) Step 4 Equato (4) ca be trasformed to (6) Based o weght of (5), the ( 1)th,( 2)th,,3th,2th,1st dex s weghts are calculated usg the followg: 1 =r (6) Note that =1 w(1) =1; hece the ormalzato of s ot ecessary =1 w(1) =1sproved as follows The symbolc meags (7) (10) are the same as (4) (6) Equato (6) ca be terated to obta the followg: =r (7) Equato (7) s substtuted to (6) to obta the followg: 1 =r r (8) Smlarly, terato cotues utl 1 cabeexpressed by, show as follows: 1 =r =r r =r r +1 r = I (9), each 1 that =r r +1 r +2 r w(1) = k=2 = k= r k (9) ca be expressed by w(1),wththeresult r k + k=3 r k + + k= r k + 1 = ( k=2 r k + = ( =2 k= k=3 r k +1) r k + + k= r k +1) (10) As a result of (5), (10) clearly equals oe; hece =1 w(1) = 222 Subectve Weghtg Model: G2 The essetal role of G2 s to reflect dex mportace by dex order; a more mportat dex correspods to a greater weght We frst specfy dex order by expert experece ad fd the least mportat dex labelg x p The, experts specfy the relatve rato of mportace betwee x p ad every other dex x Let w (2) be the G2 weght of the th dex, p the relatve rato of mportace betwee all other dces x ad x p,ad the total umber of dex, wth w (2) calculated usg the followg [20]: w (2) = p =1 p (11) Equato (11) dcates that a greater weght comes wth a greater relatve rato p 223 Obectve Weghtg Model: Varato Coeffcet Let w (3) be the varato coeffcet weght of the th dex, c the varato coeffcet of the th dex, δ the stadard devato of the th dex, the total umber of dex, ad x the mea value of all samples of the th dex Thus, the varato coeffcet weght γ of the th dex s calculated usg the followg [21]: w (3) = c =1 c, (12) c = δ x (13) The, x = (1/m) m =1 x, δ = (1/m) m =1 (x x ) 2, where x s the stadard score of the th sample o the th dex, ad m s the total umber of samples Equatos (12) ad (13) dcate that a greater varato coeffcet correspods to a greater dstrbuto varato comprehesve evaluato Furthermore, the formato dscrmato capacty of the dex s stroger ad ts weght w (3) s greater 224 Obectve Weghtg Model: Devato Let w (4), x, x q,,adm be the devato weght of the th dex, the stadard score of the th sample o the th dex, the stadard score of the qth sample o the th dex, the total umber of dces, ad the total umber of samples, respectvely The,

4 4 Mathematcal Problems Egeerg the devato weght of the th dex s calculated usg the followg [22]: m w (4) =1 = m q=1 x x q =1 m =1 m q=1 x (14) x q m =1 m q=1 x x q (14) reflects the dfferece of ay two samples Greater m =1 m q=1 x x q dcates greater dfferece betwee ay two samples; hece the formato dscrmato capacty of the dex s stroger, ad ts weght s greater w (4) 3 Proposed Model 31 Stadardzato of Multple Evaluato Models Dfferet sgle weghtg models lead to varyg evaluato results Stadardzato s ecessary to establsh the comparablty of weghtg models Let y (h), w (h),adx be the score of the th obect of the hth weghtg model, the weght of the th dex of the hth weghtg model, ad the stadard score of the th dex ad the th evaluato obect, respectvely Let m be the total umber of samples ad H the total umber of weghtg models The symbolc meags of m ad H (16) (19) are the same as (15) The, the score of the hth model ad the th evaluato obect s show as y (h) = w (h) =1 x (15) Let z (h) be the stadardzed score of the hth weghtg model ad the th evaluato obect The, the stadardzed process s show as z (h) = y(h) y (h), (16) s (h) where y (h) s the mea of all evaluato scores of the hth weghtg model ad s (h) s the stadard devato of the evaluato scores of the hth weghtg model For coveece, the ormalzed evaluato result matrx s deoted as Z = [z (h) ] m H 32 Combed Weghtg Model to Maxmze the Evaluato Score Dfferece The H colum vectors z (1),z (2),,z (H) of the stadardzed matrx Z have postve dces We troduce a adusted weght coeffcet λ=(λ 1,λ 2,,λ H ) T to reflect the etre dfferece of varous evaluato obects most fully The adusted evaluato score s show as Z =λ T Z=λ 1 z (1) +λ 2 z (2) + +λ H z (H) (17) Based o the prcple of reflectg the etre dfferece of dfferet evaluato obects most fully, the varace of the evaluato scores adusted by (17) must be as large as possble The adusted varace of the evaluato scores s show as m s 2 z = 1 (z m 1 z ) 2 =1 = (λt (Z) T Zλ) m 1 m m 1 (z ) 2 (18) Amog these, s 2 z s the adusted varace of the evaluato scores, whle z s the th adusted evaluato score, ad z s the mea of the adusted evaluato scores z (1),z (2),,z (H) are stadardzed values Combed wth the rght sde of (18) z =0, ths leads to the followg: (m 1) s 2 z =λt (Z) T Zλ (19) Matrx (Z) T Z s the covarace matrx Accordg to the prcple of reflectg the etre dfferece of dfferet evaluato obects to the maxmum, solvg for λ trasforms the problem to a programmg problem, as show max st λ T (Z) T Zλ λ T λ=1 (20) The ecoomc sgfcace of (17) (20) les the troducto of the adusted weghtg coeffcet λ = (λ 1,λ 2,,λ H ) T to satsfy the prcple of reflectg the etre dfferece of dfferet evaluato obects to be the maxmum A obectve programmg model s establshed to calculate the combed weght coeffcets of the dces based o the dea of maxmzg the dfferece betwee the adusted evaluato scores of each evaluato obect ad ther mea Accordg to [23], the optmum soluto of (20) s the characterstc vector correspodg to the largest characterstc root of the covarace matrx (Z) T Z The ormalzed characterstc vector ca lead to weght vector λ = (λ 1,λ 2,,λ H ) T The calculato process s to calculate the (Z) T Z characterstc roots of equato λe (Z) T Z = 0 to obta the greatest characterstc root λ max,toestablsh equato (λ max E (Z) T Z)X = 0, adtosolvethsequato to obta the characterstc vector correspodg to the greater characterstc root of the covarace matrx (Z) T Z Adusted weght vector λ=(λ 1,λ 2,,λ H ) T s obtaed by ormalzg the characterstc vector Note that ths paper lets H have the value of four as a result of the fact that there are four sgle weghtg models Secto 22 Let w,, w (2), w (3),adw (4) be the combed, G1, G2, varace coeffcet, ad devato weghts, respectvely The, the combed weght w ca be expressed as w =λ 1 +λ 2 w (2) +λ 3 w (3) +λ 4 w (4) (21) 33 The Accuracy Test The accuracy of the evaluato results for each weghtg model s tested usg the recever operatg characterstc (ROC) curve ROC requres two dces, MP (msudgmet probablty), the probablty of reectg a good sample as a bad sample by msudgmet, ad EP (error probablty), the probablty of acceptg a bad sample as a good sample by msudgmet I the case

5 Mathematcal Problems Egeerg 5 of measurg a credt evaluato model, there are default samples ad odefault samples the sample set; hece each weghtg model ca dscrmate a sample as ether default or odefault Greater MP ad EP dcate that the model has less dscrmato accuracy, whle lower MP ad EP dcate that the model has greater dscrmato accuracy 4 Emprcal Study 41 Samples ad Data Source Based o avalable dces from a Chese govermet-owed commercal bak, ths paper selects 21 dces of small prvate busesses, cludg sx feature layers, X 1 Basc formato, X 2 Guaratee ad ot guaratee, X 3 Capacty of repaymet, X 4 Capacty of proftablty, X 5 Capacty of operato, ad X 6 Macro evromet, as show Table 1 Data are collected from a Chese govermet-owed commercal bak that deals wth 2,044 small prvate busesses from 30 provces [24] The 2,044 small prvate busesses cosst of 348 default small prvate busesses ad 1,696 odefault small prvate busesses Moreover, we ca compute that the default small prvate busesses accout for oly 1703% of the total sample, wth the odefault small prvate busesses accoutg for 8297% of the total sample The samples are dvded to two groups, expermetal ad test Each group has 1,022 small prvate busesses, cosstg of 174 default ad 848 odefault samples Accordg to the type Colum 4 of Table 1, substtute the orgal data of postve dces V, egatve dces V, ad terval dces V to (1), (2), ad (3), respectvely, to obta the stadard scores of dces x Thescorgstadard of qualtatve dces ca be obtaed usg ratoal aalyss, as show Colums 2 through 6 of Table 2 Accordg to the dex type Colum 4 of Table 1, the stadard scores of qualtatve dces ca be obtaed based o the scorg crtera of the qualtatve dces Table 2 42 Calculato of Fve Types of Weght 421 Calculato of G1 Weght Through tervews wth may customer maagers from a Chese govermetowed commercal bak, the order ratoal rato r betwee two adacet dces was determed, as show Colum 4 of Table 3 Substtutg the order ratoal rato r from Colum 4 of Table 3 to (5), the G1 weght of the last dex X 6,3 Idustry cycle dex = s obtaed, as show the last row of Colum 5 of Table 3 Through (6), the other 20 dces G1 weghts are obtaed, as show Colum 5 of Table Calculato of G2 Weght w (2) Through tervews wth may customer maagers from a Chese govermetowed commercal bak, we ca determe the least mportat dex of 21 dces X 6,2 GDP growth rate ad, at the same tme, the mportat degree rato p of the other 20 dces to the dex X 6,2 GDPgrowthrate, asshow Colum 6 of Table 3 The, substtutg the mportace degree rato p to (11), the G2 weght w (2) s obtaed, as showcolum7oftable X 1 X 3 X 5 X 7 X 9 X 11 X 13 X 15 X 17 X 19 X 21 G1 model G2 model Varato coeffcet Devato model Combed weghtg model Fgure 1: Results of fve kds of weghtg method 423 Calculato of Varato Coeffcet Weght w (3) The mea x ad the stadard devato δ of each dex ca be obtaed from the stadardzed score x of all samples of each dex The varato coeffcet of each dex c,show Colum 8 of Table 3, s obtaed by substtutg x ad δ to (13) The, thevarato coeffcet weght w (3),show Colum 9 of Table 3, s obtaed by substtutg the varato coeffcet c to (12) 424 Calculato of Devato Weght w (4) The devato weghts, show Table 3, Colum 10, are obtaed by substtutg the stadardzed score x of all samples of each dex to (14) 425 Calculato of Combed Weght w The evaluato scores of the four kds of sgle weghtg methods are obtaed by substtutg the G1 weght from Colum 5, G2 weght w (2) from Colum 7, varato coeffcet weght w (3) from Colum 9, devato weght w (4) from Colum 10 of Table 3, ad the stadard score x of all samples of each dex to (15) separately The stadard matrx Z s obtaed by puttg the evaluato scores of four kds of sgle weghtg methods to (16) The, we calculate covarace matrx (Z) T Z The maxmum egevalue of (Z) T Z s λ max = , ad the correspodg egevector s ( 03682, 04068, 06332, 05458) Last, weobtathe weght coeffcets λ 1 = 0201, λ 2 = 0105, λ 3 = 0327, ad λ 4 = 0367 from egevector ormalzato The combed weght w, show Table 3, Colum 11, s obtaed by substtutg λ 1 = 0201, λ 2 = 0105, λ 3 = 0327, λ 4 = 0367,G1weght from Colum 5, G2 weght w (2) from Colum 7, varato coeffcet weght w (3) from Colum 9, ad devato weght w (4) from Colum 10 of Table 3 to (21) Results of the fve kds of weghtg method are show Fgure 1 The results of combg weghts demostrate that the weght of X 4,2 Operatg come s greatest, exceedg 01 The weghts of X 2,2 Stregth of the guarator ad X 1,5 Number of labor force are ad 00701, rakg umber 2 ad umber 3, respectvely These three dces have a more mportat fluece o the credt evaluato of

6 6 Mathematcal Problems Egeerg Table 1: Idex system for small prvate busesses (1) Number (2) Feature layer (3) Idces (4) Type of dex 1 X 1,1 Educatoal backgroud Qualtatve 2 X 1,2 Age Iterval 3 X X 1 Basc formato 1,3 Years for a busess lcese Qualtatve 4 X 1,4 Owed place of busess or ot Qualtatve 5 X 1,5 Number of labor force Postve 6 X 1,6 Famly expedture Negatve 7 X 2,1 Geder of guarator Qualtatve 8 X X 2 Guaratee ad ot guaratee 2,2 Stregth of the guarator Postve 9 X 2,3 Martal status of guarator Qualtatve 10 X 2,4 Credt status of ot guarator Qualtatve 11 X X 3 Capacty of repaymet 3,1 Lqudty rato Postve 12 X 3,2 Asset-lablty rato Negatve 13 X 4,1 Net come Postve 14 X 4 Capacty of proftablty X 4,2 Operatg come Postve 15 X 4,3 Average tax each moth Postve 16 X 5,1 Accouts recevable turover Postve 17 X 5 Capacty of operato X 5,2 Ivetory turover Postve 18 X 5,3 Operato tme Qualtatve 19 X 6,1 Per capta savgs balace Postve 20 X 6 Macro evromet X 6,2 GDP growth rate Postve 21 X 6,3 Idustry cycle dex Iterval (1) Number (2) Feature layer (3) Idces Table 2: The scorg crtera of qualtatve dces (4) Optos umber (5) Optos (6) Scorg 1 1 Udergraduate ad above Juor college 08 3 X 1 Basc formato X 1,1 Educatoal backgroud 3 Hgh school ad techcal secodary school Juor hgh school Prmary school Other Eght years or more Fve years or more ad less tha eght years X 5 Capacty of operato X 5,3 Operato tme 3 Two years or more ad less tha fve years Less tha two years Mssg Data 0 small prvate busesses I cotrast, the three dces X 1,1 Educatoal backgroud, X 2,1 Geder of guarator, ad X 3,1 Lqudty rato have weghts smaller tha 003, ad they have less mportat fluece o credt evaluato of small prvate busesses 43 Accuracy Test of the Fve Kds of Weghtg Method To test the accuracy of the fve kds of weghtg method, we used the remag 1,022 small prvate busesses as the test sample There are 174 default samples ad 848 odefault samples The results of MP ad EP ca be obtaed usg the ROC curve The accuracy of weghtg results ca be estmatedbycompargthempadepofthedfferet kds of weghtg method I ths way, we ca evaluate the advatages ad dsadvatages of the dfferet weghtg methods as well The results of MP ad EP based o the dfferet kds of weghtg method are show Fgure 2

7 Mathematcal Problems Egeerg 7 Table 3: Weghts of dfferet types of weghtg method 1 (4) Order (6) Importace (8) (9) Varato (10) (11) (5) G1 (7) G2 (1) Number (2) Feature layer (3) Idces ratoal weght degree rato p weght w (2) Varato coeffcet Devato Combed rato r of G1 of G2 coeffcet c weght w (3) weght w (4) weght w X 1,1 Educato backgroud X 1,2 Age X 1 Basc X 1,3 Years for a busess lcese formato X 1,4 Owed place of busess or ot X 1,5 Number of labor force X 1,6 Famly expedture X 2,1 Geder of guarator X 2 Guaratee ad X 2,2 Stregth of the guarator ot guaratee X 2,3 Martal status of guarator X 2,4 Credt status of ot guarator X 3 Capacty of X 3,1 Lqudty rato repaymet X 3,2 Asset-lablty rato X X Capacty of 4,1 Net come X proftablty 4,2 Operatg come X 4,3 Average tax each moth X X Capacty of 5,1 Accouts recevable turover X operato 5,2 Ivetory turover X 5,3 Operato tme X X Macro 6,1 Per capta savgs balace X evromet 6,2 GDP growth rate X 6,3 Idustry cycle dex

8 8 Mathematcal Problems Egeerg G1 model G2 model Varato coeffcet model Devato model Combed weghtg model MP EP Fgure 2: MP ad EP of the dfferet kds of weghtg models Fgure 2 demostrates that of the fve kds of weghtg method, the combed weghtg method has the smallest msudgmet probablty as well as the smallest error probablty, wth G2 havg the hghest MP ad EP The obectve weghtg models, varato coeffcet ad devato, have smaller MP ad EP tha the subectve weghtg models G1 ad G2 5 Coclusos I a comprehesve evaluato, the dex weght reflects the relatve mportace of each dex I other words, t reflects the status ad fucto of each factor the evaluato ad decso-makg process Hece, the determato of dex weght relates to the relablty ad valdty of rakg results of the proect It s for ths reaso that weght determato methods have bee a maor focus comprehesve evaluato research To ths ed, may mathematcal models have bee explored as decso support methods Ths paper proposed a combed weghtg method based o dfferece maxmzato Dfferet evaluato scores for the same obect are obtaed usg dfferet weghtg methods A adusted weghtg coeffcet was troduced accordace wth the prcple that the etre dfferece of dfferetevaluatoobectsstobemaxmallydfferetated A obectve programmg model was establshed wth more obvous dfferetato betwee evaluato scores guarateed ad the combed weght coeffcet determed Our model s based o the dea of maxmzg the dfferece betwee the adusted evaluato scores of each evaluato obect ad ther mea The proposed model s demostrated usg 2,044 observatos The emprcal results show that the combed weghtg method has the smallest msudgmet probablty, as well as the smallest error probablty, whe compared wth four kds of sgle weghtg methods, G1, G2, varato coeffcet, ad devato methods The research cotrbuto theory was as follows A adusted weghtg coeffcet was troduced accordace wth the prcple of reflectg the etre dfferece of dfferet evaluato obects to the maxmum A obectve programmg model was establshed to calculate the combed weght coeffcets of the dces, based o the dea of maxmzg the dfferece betwee the adusted evaluato scores of each evaluato obect ad ther mea Therefore, our model avods the cotradctory ad less dstgushable evaluato results that are typcal sgle weghtg methods Coflct of Iterests The authors declare that there s o coflct of terests regardg the publcato of the paper Ackowledgmets ThsresearchssupportedbytheNatoalNaturalScece Foudato of Cha (os , , ad ), Bakg Iformato Techology Rsk Maagemet Proect of Cha Bakg Regulatory Commsso (CBRC) (o ), Scece ad Techology Research Proect of Mstry of Educato of Cha (o ), the Bak of Dala as credt ratg ad loa prcg systems for Small busess (o ), ad Credt Rsks Evaluato ad Loa PrcgForPettyLoaFudedfortheHeadOffceofPost Savgs Bak of Cha (o ) The authors thak the orgazatos metoed above Refereces [1] T L Saaty, Measurg the fuzzess of sets, Joural of Cyberetcs,vol4,o4,pp53 61,1974 [2] W N P, Suppler evaluato usg AHP ad TOPSIS, Joural of Scece ad Egeerg Techology,vol1,pp75 83,2005 [3] W-N P ad C Low, Suppler evaluato ad selecto va Taguch loss fuctos ad a AHP, Iteratoal Joural of Advaced Maufacturg Techology, vol27,o5-6,pp , 2006 [4]RVRao, Machabltyevaluatoofworkmateralsusg a combed multple attrbute decso-makg method, The Iteratoal Joural of Advaced Maufacturg Techology, vol 28, o 3-4, pp , 2006 [5] H-J Shyur, COTS evaluato usg modfed TOPSIS ad ANP, Appled Mathematcs ad Computato, vol 177, o1,pp , 2006 [6] B Brow, Delph Process: A Methodology Usg for the Elctato of Opos of Experts, o 9, RAND Corporato, Sata Moca, Calf, USA, 1987 [7] H Deg, C-H Yeh, ad R J Wlls, Iter-compay comparso usg modfed TOPSIS wth obectve weghts, Computers ad Operatos Research,vol27,o10,pp ,2000 [8] F García, F Guarro, ad I Moya, A goal programmg approach to estmatg performace weghts for rakg frms, Computers & Operatos Research,vol37,o9,pp , 2010 [9] F García, V Gméez, ad F Guarro, Credt rsk maagemet: a multcrtera approach to assess credtworthess, Mathematcal ad Computer Modellg, vol57,o7-8,pp , 2013 [10] A Shaa ad O Savadogo, A methodologcal cocept for materal selecto of hghly sestve compoets based o multple crtera decso aalyss, Expert Systems wth Applcatos,vol36,o2,pp ,2009 [11] D Dakoulak, G Mavrotsa, ad L Papayaaks, Determg obectve weghts multple crtera problems: the crtc method, Computers ad Operatos Research,vol22,o7,pp , 1995 [12] K Maya ad M G Bhatt, A selecto of materal usg a ovel type decso-makg method: preferece selecto dex

9 Mathematcal Problems Egeerg 9 method, Materals ad Desg, vol 31, o 4, pp , 2010 [13] CLHwagadKYoo,Multple Attrbute Decso Makg Methods ad Applcatos, Sprger, Berl, Germay, 1981 [14] K Zbkowsk, Usg volume weghted support vector maches wth walk forward testg ad feature selecto for the purpose of creatg stock tradg strategy, Expert Systems wth Applcatos,vol42,o4,pp ,2015 [15] B Aou, C Colapto, ad D La Torre, Facal portfolo maagemet through the goal programmg model: curret state-of-the-art, Europea Joural of Operatoal Research,vol 234, o 2, pp , 2014 [16] Y Su ad X Z Bao, A ew combato weghtg method ad ts applcato based o maxmzg devatos, Chese Joural of Maagemet Scece, vol 6, pp , 2011 [17] G L ad G T Ch, The comprehesve evaluato of all-roud huma developmet based o level dfferet maxmzato, Cha Soft Scece Magaze,vol9,pp ,2009 [18] ZL,GCh,adZXu, Measuremetmodelofproectrsksof commercal baks based o combato weghtg, Idustral Egeerg ad Egeerg Maagemet, vol6,pp , 2013 [19] C Qa, M Zhag, Y Che, ad R Wag, A quattatve udgmet method for safety admttace of facltes chemcal dustral parks based o g1-varato coeffcet method, Proceda Egeerg,vol84,pp ,2014 [20] K Khall-Damgha ad S Sad-Nezhad, A decso support system for fuzzy mult-obectve mult-perod sustaable proect selecto, Computers & Idustral Egeerg, vol64, o 4, pp , 2013 [21] Y Gao, Z Da, ad W Lu, Modelg dyamc trust ad rsk evaluato based o hgh-order momets, Mathematcal Problems Egeerg, vol2015,artcleid789820,9pages, 2015 [22] PWag,YL,Y-HWag,adZ-QZhu, Aewmethodbased o topss ad respose surface method for MCDM problems wth terval umbers, Mathematcal Problems Egeerg, vol 2015, Artcle ID , 11 pages, 2015 [23] M-RGhasem,JIgatus,adAEmrouzead, Ab-obectve weghted model for mprovg the dscrmato power MCDEA, Europea Joural of Operatoal Research, vol 233, o 3, pp , 2014 [24] Postal Savgs Bak of Cha, The Busess Credt Ratg Table of Postal Savgs Bak of Cha, The busess credt ratg table of Postal Savgs Bak of Cha, 2009

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