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1 - 21 > / 89 / 92 / @> > @ >@ - @ > @ @ @ >@ > D mahdiyeh_akhbari@yahoo.com SI >< > farimah@cc.iut.ac.ir 89/3/5 : 87/7/28 : > of > @ @ @ . @ @ . >@ ive > @ @ >@ @ > > > @ .> > > > @ > @ <@ @ > @ < >. @ @ >. > @ >< > @ ch @ @ - @ > @ @ < @> @ . > <@ > Ar @ @ >> . @ > 69/36 > <1385-1380 @ . G52 : JEL @ < @ > <@ @ < @ - : @ > www.SID.ir 89 / 92 / @> > @ 2 -1 > @ > > . @ <> @ @ @ @ < @ @ > <> > < . <> > @ . @ @ <@ > @ > D . > > @ @ > @ @ >< > >< > < > > @ <@ @ @ @ SI @ < @ > > . of @ @ @ > > < > @ >@ @ @ @ @ @ > ive @ > @ > > >@ > <@ .[6 5 <4] @ @ @ > > > @ @ <@ > <> @ @ ch @ - @ @ <@ @ @ > > < >. @ >> > > Ar .> > @ > @ >@ < .> @ > @ @ > @ -2 @ @ >@ @ @ > > @ > > @ > < www.SID.ir 3 …@ @ >@ - @ > >@ @ @ .[5 <4]> < @ < > > > @ @ >@ @ @ <> [6] . > > > > @ @ <[7] @ @ [8] . > @ @ > <> @ @ - D @ @ – @ >> . @ > > < > < . > ١ @ . > @ @ > SI <[9] @ (ANN) of ٢ @ - @ > . > @ > > > @ <(ANFIS) @ ANN >> > > ( / >) > >@ @ @ > >@ ive ) @ > ANN >> . > @ > <> > @ @ @ ( > . @ @ ( > ) ch (ANFIS) @ - @ <[10] > @ > . > (MDA) ٣ @ ( @ 250 @ 250) 500 @ > > @ Ar > > ( ) ( )@ > @ > > < > > @ @ > > . > .> MDA ANFIS 1- Artificial neural networks. 2- adaptive network based fuzzy inference system or adaptive neuro-fuzzy inference system. 3- Multiple Discriminate Analysis. www.SID.ir 89 / 92 / @> > @ 4 <@ @ > @ > > ١ @ @ .> @ < >. > @ @ @ > (FAN) @ > < @ @ @ @ @ > @ > . @ > < >@ . > D > > . < @ > . > > @ > @ > .> @ @ > > < @> > @ > @ < SI @ @ > .[11] of @ <@ @ @ > > > <> @ @ @ < @ .[12] %80 > ive @ - > @ @ ch .> - @ @ A < B A > @ > - @ >. @ @ Ar B > > > >@ @ @ > @ @ < @ > : > @ .[3 1<2] . < @ > 1- fuzzy adaptive network. www.SID.ir 5 …@ @ >@ - @ > < @ <@ > > @ . (1983) @ - @ > > .> @ @ > < > < @ - :> D *@ > +β * +γ < @ > . =α > @ ( ) > > @ @ > @ @ >@ > @ > @ > SI @ > - . > of @ .> > . > @ > (@ - > > )@ @ : > @ ive > <( ) > @> @ @ -1 @ @ (@ ) @ @ .(> @ @ < ) > ch > ( @ < -T > ) -2 > ( ) @ <( ) > . Ar @ ( @ > ) -3 . @ @ @ < ) > > -4 .(> www.SID.ir 89 / 92 / @> > @ 6 ) - > < > > .> > > <(> . > < @ @ > > .[13<14] >@ @ < > > > > >. @ > @ @ D < @ > > @ @ < . < > @ > > @ > @ . < < SI ١ > @ @ > of > @ > @ . .> > @ ٢ > @ @ ive . > (1974) ٣ < [16 <15 <13] <> @ @ > .> ch > X1 > Y1 @> Ar X2 Y2 @ 1- adaptive networks. 2- gradient descent. 3- chain rule. www.SID.ir 7 …@ @ >@ - @ > < (1 ) @ . @> @ @ ( ١ ) -@> < >@ . <> > @ > < > < @ > > @ >< @ > (٢ ) .> > < @ @ @ .> @ ( ٣ )@ > D . @ @ @ @ -1-2-3 @ < -@> > > > >. < > < nk @ > SI ( . < )@ > @ >> <>> @ of k L >> O ik ( ) (k,i) k > i : @ @> @ Oi . k Oi = Oi (O1 −1,...Ok −1, a , b, c,...), (1) ive k k k n @ c <b <a k −1 k Oi . . < >> P ( ) @ > @ >> @ ch > @ > @ > > @> (1 ≤ p ≤ P ) p@ (٤@ ) :> > ∑ (Tm, p − OL ,p )2 , nL (2) Ar Ep = m m =1 m < OL ,p m > p m <Tm,p 1- node function. 2- adaptive node. 3- fixed node. 4- energy function. www.SID.ir 89 / 92 / @> > @ 8 @ . @> > p@ > .E = ∑ Ep : P p =1 ∂E p @ > @ >> p@ < < > < > @ > ∂O > (L , i) @ > .> O@ @ :> D ∂E p = −2(Ti, p − Oi, p ). L (3) ∂O i , p L : ∂E p ∂Oik p = @ ∑ n k +1 m =1 ∂O m, p ∂Oi, p k +1 ∂E p ∂O k +p k @ m, 1 > , SI > <(k,i) @ (4) of .1 ≤ k ≤ L − 1 , @ @ > > @ > < 1 ≤ i ≤ nk 1 ≤ k ≤ L @ .> @ @ ive ∂E p .> > (4) (3) > > > ∂O i , p k : > < @ @ α ch ∂E p ∂E p ∂O* ∂α = ∑ ∂O* ∂α , (5) O * ∈S . α @ Ar S : α E @ ∂E P ∂E p =∑ . (6) ∂α p =1 ∂α : > α @ < ∂E ∆α = − η (7) ∂α www.SID.ir 9 …@ @ >@ - @ > :> > @ > > η η= (8) k , ∑α ( ∂α )2 ∂E <@ . @ @ > <١ @ k . > <k > @ ٢ > .> > > @ @ > D > (6) > α > <٣ ٤ > @ > @ >> @ >< >@ .> @ > ٧ -@ ٦ < SI < -@> > .[15< 14] ٥ @ (5) of @ - @ @ -1-2-3 ANFIS > <[20] < @ (y x) @> > @ > (2 ) >< .> (z) ive > > <> > @ ANFIS : > > if x is A1 and y is B1 , then f1 = p1x + q1y + r1 1@ ch if x is A 2 and y is B 2 , then f 2 = p2 x + q2 y + r2 2@ ( <4) > @ : >> ( <4) > Ar ANFIS 1- step size. 2- batch learning. 3- off-line. 4- epoch. 5- sweep. 6- pattern learning. 7- on- line. www.SID.ir 89 / 92 / @> > @ 10 D SI of @ - -1 ive (@> @ ) @ : ( ) < @ >i O1, i = µ A i (x ), i = 1,2, or (9) ch O1, i = µ Bi −2 (x ), i = 3,4. @ > Ol,i ( ) @ B A @ > @ > >. l@ > i . > @ Ar @ > @> @ > > > > @ @ (1 0 @> ) @ < < < @ > . . @> @ @ > > > .> > @ @ www.SID.ir 11 …@ @ >@ - @ > (@ @ @ ) >@ > (@ >) @ : > @ O2, i = w i = µ A i (x ) * µ Bi (x ), i = 1,2. (10) @ and T-norm > < @ > @ >. > @ > < > . > @ ( ) D (@ @ ) @ @ > @ > > > O 3,i = w i = wi w1 + w 2 : , i = 1,2. > SI(@ @ @ @ ) (11) @ of @ . @ @ > @ > @ : > ive O4, i = w i f i = w i ( p i x + q i y + ri ), for i = 1,2 (12) wi @ @ <ri qi <pi .> > @ @ ( >@ ) @ ch > @ @ > > @ : > @> @ >> @ @ ∑ w i fi Ar Z = O 5, i = ∑ w i f i = i (13) ∑ wi , for i = 1,2. i www.SID.ir 89 / 92 / @> > @ 12 (ANFIS) ١ @ – @ < <ANFIS : > . (r2 q2 <p2 <r1 <q1 <p1) w1 w2 Z= f1 + f2 w1 + w 2 w1 + w 2 = w1f1 + w 2f 2 (14) = ( w1x ) p1 + ( w1y)q1 + ( w1)r1 + ( w 2 x ) p2 + ( w 2 y)q 2 + ( w 2 )r2 . D > .> > >@ > @ @ < @ > .[20] > > @ > < > @ @ > SI @ ( > < >. ) > ANFIS @ > of @ @ > ANFIS > >< > .> > :> > @ @ ive Y=F(X1,X2,…,Xn) @ @ < Xi @ > Y ch > > @ < > <" ": : . > > @ >> > <" "< > Ar @ Y > >. > . @ i@ Pi <Y <(Yi=1) > >> > > > (xi) > 1- Adaptive network based fuzzy inference system or adaptive neuro-fuzzy inference system. www.SID.ir 13 …@ @ >@ - @ > > (Yi=0) > > > i@ 1-Pi : (15) @ <> E ( Yi / x i ) = 0 * P ( Yi = 0 / x i ) + 1 * P ( Yi = 1 / x i ) = P ( Yi = 1 / x i ) = Pi (15) Yi @ @ >> > < < Pi i @ .> @ > > <ANFIS > @> > D @ > > . > < @ SI > @ @ > @ @ -1-4 of . > >@ > >@ 85 80 @ < > . 272 > @ > > @ > @ 235 > < ive > @ 37 > . > @ < 235 @ . > > @ >> . > > 70 > 165 ch < <@ @ @ @ > <> @ > < <@ < <> @ < > > < >@> < @> Ar @ < > @> > > > @ < > . < @ > > @> @ @ > > @ < >@ . < > < > @ > @ > @ www.SID.ir 89 / 92 / @> > @ 14 @> < > > >> > @ . @ > @> @ . > < < @ > . >< @ . @ @ @ < D < > @ > < > < . > @ . > > ( @ )> > @ @ SI :(x1) of > <> > > .> > > .> > > @ < @ > :(x2) ive > > @ > @ > > < . > > @ .@ @ @ <@ @ > ch @ < > . > > @ : (x3) > Ar . @ @ > <> @ > @ < > . > @> @ -2-4 :> > @ < > www.SID.ir 15 …@ @ >@ - @ > R1: If (x1 is Low and x2 is Low and x3 is Low, then ( Y1 = c1 + c1x1 + c1 x1 + c1 x 3 ) o 1 2 3 2 R2: If (x1 is Low and x2 is Low and x3 is Medium, then ( Y 2 = c 2 + c1 x1 + c 2 x 2 + c2 x 3 ) o 2 3 M 27 R27:If(x 1is High and x2 is High and x3 is High then ( Y 27 = c 27 + c1 x1 + c 27 x 2 + c 27 x 3 ) 2 3 ) x3 ( ) x 2 <( ) x1 @> @ < > o (Medium ) <(Low) > ( > i@ <Yi . @ @ @ (High) > >> >< D cij . > ٣ > < ٢ > < ١ @ @ @ < . @ @ > @ > > @ > SI @ @ < 200 <1,1 <0,9 <0,01 > < > < < > @ > > of . < <@ @ > <(8) @ > > <k < @ (1-2-3) > < > ive k @ <> > > > @> > > > <> > <> k@ > >@ <> . > @ > < ch @ @ >k <[20] <> : > %10 <k < > 4 > -1 Ar .( 1,1 > ) < 2 > -2 .( 0,9 > ) %10 <k 1- initial step size. 2- step size decrease rate. 3- step size increase rate. www.SID.ir 89 / 92 / @> > @ 16 < >> 2 4 <%10 > < @ > . . > @ k@ < @ > < @ > > @ > > RMSE 200 > RMSE > > > D @ <200 > < > > >@ >> .> > @ > < @ < @ > > . ( . > :> SI @ِ @ ) 108 < ci < > @ of 27 ∑ w l Yl Y = l =1 ˆ 27 (16) ∑ ive wl l =1 :> > wl wl = ∏ µ (x i ) = µ (x i ) * µ (x i ) * µ (x i ) (17) ch Fil Fil Fil Fil Fil . > @ > Yl < > >. > xi @ @ (@ ) @ >@ @ < @ @ Ar @ > (17) @ > > > . < <@> . @ @ wl . > @ > (@> @ ) @ @ > 135 > > 27 >< < .> > www.SID.ir 17 …@ @ >@ - @ > < > MATLAB ANFIS @ @ .> > 27 > <1,6GHz > Pentium IV > @ @ - 3- 4 :> > @ @ @ <(Y=1) @ > ," @ >"(1 . > > @ D @ > =" @ >" (2 . > > @ <(Y=0) > @ > SI > < > > @ -4-4 > of > > [0<1] @ >@ .> @ @ @ > @ >< . ive .> @ @ @ >. @ > > @ <[22] @ > > @ @ < .> @ > ch > < @> > @ < > @ > > >@ @ <(3) > >. Ar > > @ > @ > > @ . >> < @ @ > < . @ > < ANFIS > @ <> (3) > . 0,32 www.SID.ir 89 / 92 / @> > @ 18 D @ @ SI -2 of ANFIS > -5-4 <0,32 <(C) @ > <> @ <(1) > Y@ @ @ > @ >> > @ > >< ive . @ < @ > > > ANFIS @ > @ > . 0,70 0,67 ch ANFIS > -1 ( ) Y=1 ( ) Y =o > > Ar 138 23 116 P(Y)≤C 97 47 49 P(Y)>C 235 70 165 163 47 116 > 69,36 67,14 70,30 (%) > 30,64 32,86 29,70 (%) > www.SID.ir 19 …@ @ >@ - @ > @ < @ <(1) > > )@ < > @ ( @ >@ > ) . 0,30 0,33 > <( @ >@ @ >> > -6-4 > @ >> @ > < @ > > 272 > > 37 > .> > @ >> D > > > > > @ < @ < > > >> >. > @ @ ANFIS <> SI (@ . @ ) > > of ( Y =o ) >@ < (@ ) >@ < > (2) > .> @ ( Y =1 ) . ive ANFIS @ > <> . 0,69 0,625 > ch ANFIS -2 ( ) Y =1 ( ) Y =o > > 23 3 20 P(Y)≤C 14 5 9 Ar P(Y) >C 37 8 29 25 5 20 > 67,57 62,5 68,97 (%) > 32,43 37,5 31,03 (%) > www.SID.ir 89 / 92 / @> > @ 20 @ @ .> @ < > @ > > > @ > @ > <> @ > > .> > > @ @ . @ >. @ @ < @ @ < @ - D <> > < . @ @ @ > > < > . @ <> <@ . SI > @ > <> @ @ @ of <@ @ @ ” (1381) < . . . .>. -1 > <@ >: <“ > . ive : <" @ > @ @ @ "(1383) < -2 > >> < > > > . ch > > @ " (1381) < < > > < > -3 .< C < > < @ <" @ @ (1382) < < < / < -4 Ar . >> < 5- Wilson, R. and Sharda, R. (1997) “Business Failure Prediction Using Neural Networks.”, Encyclopedia of Computer Science and Technology, Vol.37, No.22, pp.193-204. 6- Generation Approach for Managing Credit Scoring Problems. (2001)” In Fuzzy Sets in Management, Economics and Marketing.(ed.), pp.223- 228. 7- Syau, Y., Hsieh, H. and Lee, E. S., (2001) “Fuzzy Numbers in the Credit Rating of Enterprise Financial Condition.” Review of Qunatitative Finance and Accounting, Vol.17, pp. 351-360. www.SID.ir 21 …@ @ >@ - @ > 8- Cheng, C. B. and Lee, E. S., (1999) “Applying Adaptive Network to Fuzzy Regression Analysis.”, Computers and Mathematics with Applications, Vol.38, pp.123-140. 9- Boussabaine, A. H. and Wanoous, M.” (2000) A Neurofuzzy Model for Predicting Business Bankruptcy.” In Business Applications of Neural Networks: The State-of-the-Art of Real-World Applications(ed.), pp.55- 69. 10- Castillo, O. and Melin, P., (2002) ”Hybrid Intelligent Systems for Time Series Prediction Using Neural Networks, Fuzzy Logic and Fractal Theory.” IEEE Transactions on Neural Networks, Vol.13, No. 16. D 11- Malhotra, R and Malhotra, D. K., (2002) ”Differentiating between Good Credits and Bad Credits Using Neural-fuzzy Systems.” European Journal of Operational Research, Vol. 136, pp.190-211. 12- 13- Vol.45, pp.717–731. SI Jiao,Y., Syau,Y. and Lee, E. S., (2007) ”Modelling credit rating by fuzzy adaptive network”, Mathematical and Computer Modelling Hoffmann, F. Baesens, C. and Mues, T., (2007) "Inferring descriptive and approximate fuzzy rules for credit scoring using evolutionary algorithms" in European Journal of Operational Research, Vol.177, pp. of 540–555. 14- Jang, J.S.R, (1993) “ANFIS: Adaptive – network based fuzzy inference systems.”, IEEE transactions on systems Man. and Cybernetics, Vol.23, No.3, pp.665-685. 15- Douligeris, C., and Palazzo, S., (1999) “Fuzzy Expert Systems in ATM ive Networks”,Fusion of Neural Networka, Fuzzy Sets, and Genetic Algorithms: Industrial Application (ed.). 16- Jang, J.S.R, (1992) “Neuro fuzzy modeling: Architectures, Analysis and Applications”, Department of Electrical Engineering and Computer Science, University of California, Berkeley. ch 17- Jang, J.S.R, (1995) “Neuro fuzzy modeling and Control.”, Proceedings of IEEE, Vol.83, No.3, pp.378-406. 18- Rumelhart, D.E, Hinton, G.E. and Williams, R.J. (1986) "Learning internal representations by error propagation," D. Rumelhart and J. McClelland, editors. Parallel Data Processing, Vol.1, pp. 318-362. Ar 19- Hagan, M.T., Demuth, H.B. and Beale, M.H. “Neural Network Design”, PWS Publishing Company, Boston, MA 1996. 20- Jang, J.S.R, (1993) ANFIS: Adaptive – network based fuzzy inference systems, Department of Electrical Engineering and Computer Science, University of California, Berkeley. 21- Korsholm, L. (2004) ”Analysis of Diagnostic Studies, Sensitivity and specificity positive predicted values ROC curves tests based on logistic regression”, Departmant of statistics and demography, University of Southern Denmark. www.SID.ir

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posted: | 10/26/2011 |

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