logic mo va cac ung dung trong linh vuc tai chinh

TP SAN TIN HC QUN L Tp 03, s 1&2, 2014, 27-44.

LOGIC M V CC BI TON

NG DNG TRONG LNH VC TI CHNH

Phan Hin1

Thi Kim Phng1

1 T VN

Logic m (Fuzzy logic) c bit n ln u tin trong nghin cu v tp m (fuzzy set) ca Zadeh (1965) v nhanh chng c ng dng rng ri trong hu ht cc lnh vc khoa hc k thut. n nay, vic ng dng logic m dn chuyn sang cc lnh vc kinh t, c bit l trong ti chnh v t c nhng kt qu

kh quan (Korol, 2012). Ti Vit Nam, vic ng dng logic m cn nhiu hn ch, nht l trong lnh vc kinh t (Duc & Thien, 2013). Vi nhng ng dng rng ri

v hiu qu ca logic m trn phm vi ton th gii, trong bi vit ny chng ti mun gii thiu i nt v logic m v mt s bng chng thc nghim ca vic ng dng logic m trong lnh vc ti chnh. Qua y, chng ti nhn thy rng

logic m c xem nh mt phng php tip cn mi gii quyt cc bi ton trong lnh vc ti chnh.

2 LOGIC M

2.1 Gii thiu v tp m

Trong thc t, khi nh ngha mt tp cc s ln hn 10 v k hiu l A, ta c nh ngha nh sau:

Khi , rt d xc nh c cc phn t chc chn thuc v khng thuc khi nim A. Tuy nhin, nu a ra mt khi nim v tp nh giu (vi nhng ngi c thu nhp hn hay bng 10 triu mt thng) v k hiu l B

Khi ta bo mt ngi c thu nhp l 10 triu/thng l thuc nh giu, tuy nhin bng trc gic bnh thng n s khng hp l nu gi ngi c thu nhp 9999999/thng khng phi l nh giu.

V vy, khi nim tp m xut hin gii quyt nhng nim nhm ti cc tp khng c ranh gii r rng. Thng th tp m biu din cho mt th hin ngn ng, ly v d: tri rt nng, anh ta rt hin,

1 Khoa H Thng Thng Tin Kinh Doanh H Kinh T HCM

Logic m v cc bi ton ng dng trong lnh vc ti chnh

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Gi X l khng gian cc i tng v x l cc phn t tng qut thuc X. Khi , theo Zadeh (1965), mt tp m A trong X c nh ngha l tp cc cp nh sau:

trong , c gi l hm thnh vin ca tp m A. Hm thnh vin ny ch mc thuc ca x trong khng gian X v c gi tr t 0 n 1. Hay k hiu khc khi X l khng gian lin tc: (k hiu ny khng phi ch hm tch phn m ch s hi cc phn t lin tc)

D dng nhn thy, nu nh tp m A ch ton nhng hm thnh vin c gi tr 0

hoc 1 th A tr thnh mt tp r.

Ly v d: khi m t tp khi nim v tui l tr k hiu l:

Khi v hm thnh vin c dng nh sau:

Hnh 1: Hm thnh vin

y l dng s m hnh thang v thng c k hiu l b bn s tre: [15, 20, 27, 37]

2.2 Php m rng hnh tr trn tp m

Cho mt nh ngha tp m A vi hm thnh vin l trong khng gian X. Ta c php m rng hnh tr ca tp m A trn khng gian Y, ta c mt tp m mi nh ngha trong khng gian X x Y nh sau

Tp san Tin hc qun l, tp 03, s 1&2, 2014.

29

hay

Hnh 2: Php m rng hnh tr trn tp m

2.3 Php giao trn tp m

Cho tp m A v B cng trong khng gian X. Giao ca tp m A v tp m B l tp m mi C trong khng gian X c nh ngha nh sau:

Trong T c bit nh hm T-norm (triangular norm) [12]. Hm T ny thng c 4 dng

2.4 Php hi trn tp m

Cho tp m A v B cng trong khng gian X. Hi ca tp m A v tp m B l tp m mi C trong khng gian X c nh ngha nh sau:

Trong S c bit nh hm T-conorm (S-norm) [12]. Hm S ny thng c 4 dng


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2.5 Quan h m

Cho tp m A trong khng gian X, tp m B trong khng gian Y. Quan h R ca A

v B hay cn gi l quan h m 2 - ngi c nh ngha nh l mt tp m R trn

khng gian :

2.6 Php chiu

Cho tp m R trong khng gian X x Y, khi ta nh ngha php chiu ca R trn khng gian X v Y nh sau:

2.7 Lut m v suy din lut

Lut m c bit n nh dng lut nuth nhng c s dng cc khi nim tp m ch ng ngha. Cho 2 tp m A trong khng gian X v B trong khng gian Y. Ta pht biu mt lut nh sau:

Nu x l A th y l B

Vi lut nh vy, ta c th nh ngha lut m nh mt quan h m R ca A v B.

C th hiu lut m theo mt s cch khc :


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Trong bi ny, nhm tc gi la chn cch hiu lut m nh mt quan h m ca A v B.

Nh vy, nu ta c s tht l x l A v ta c lut Nu x l A th y l B th ta s c kt qu l y l B.

Hay trong trng hp s tht x l A v ta c lut Nu x l A th y l B th ta s c kt qu l y l B.

tnh ton c kt qu, ta thc hin vic suy lun trn nh sau: (phng php suy din v hm T-norm theo xut ca Mamdani [13])

B1: Giao gia tp hnh tr m rng ca A vi RAxB , ta c:

B2: Chiu trn khng gian Y, ta c tp m

B3: Ta c hm thnh vin

Tng t nu ta c lut vi 3 tp m A,B,C trong 3 khng gian X,Y,Z nh sau:

Nu x l A v y l B th z l C

V khi ta c s tht x l A v y l B th z l C, vi hm thnh vin ca C

nh sau:

Hnh 4: Suy din lut

w1

w2


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2.8 M hnh suy din m

Hnh 5: M hnh suy din m (tham kho Jang & Sun (1996))

u vo: Cc gi tr r hay m ca cc tnh cht

H thng: H suy lun da vo tp lut (tri thc)

u ra: Cc gi tr r m c suy lut da trn tp lut v phng php suy lun.

Theo nh h suy din th kt qu l mt tp m, chnh v vy m c thnh phn gii m lm kt qu tr thnh kt qu r.

Mt s phng php gii m theo Mamdani [13]:

Phng php phn i:

Phng php bnh qun hay ln nht hay nh nht ca gi tr ln nht:

Phng php trng tm vng:

2.9 V d minh ho

Cho tp lut m t chnh nhiu my lnh theo s ngi v nhit ngoi tri :

Nu phng nhiu ngi v tri nng th my iu ha ch lnh.

Nu phng nhiu ngi v tri bnh thng th my iu ha ch bnh thng.

Nu phng t ngi v tri nng th my iu ha ch bnh thng.

Nu phng t ngi v tri lnh th my iu ha ch nng. Vi cc khi nim m c biu din dng s m hnh thnh vi 4 chn nh sau:

Nhiu ngi: [10,15,18,22] t ngi [2,8,12,15]

Nng (nhit) [26,31,31,35] Bnh thng [20,22,25,29]

Lnh [14,16,20,24]

Tri thc (dng lut)

Gii m

H suy din

u vo r

u ra r

u vo m


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Vy nu phng c 20 ngi v nhit ngoi tri l 28 , th my iu ha phi ch th no ?

Ta thy c 20 ngi thuc khi nim nhiu ngi v 28 thuc khi nim nng, bnh thng. Ta s dng 2 lut u tin trong 4 lut.

Hnh 6: V d v suy din m

3 MT S NGHIN CU NG DNG LOGIC M TRONG LNH VC

TI CHNH

Vlachos & Tolias (2003) bo co nghin cu ti hi ngh Vn tr hc (Operational Research) ti Balkan v ng dng logic m trong d bo ph sn.

Nhm mc ch so snh kt qu vi m hnh ca Altman, nghin cu ch xem xt 5 ch s ti chnh m Altman (1968) a ra trc . D liu bao gm 129 cng ty xem xt giai on 1975 1982, trong c 65 cng ty ph sn. D liu s dng d bo l bo co ti chnh nm cui cng trc khi cng ty tuyn b ph sn. Kt qu thu c ngoi s mong i ca cc tc gi khi d bo chnh xc 100%,

tt hn hn so vi cc m hnh nh lng (ch t 85%). Mc d, nghin cu chn la trn cc cng ty ph sn, nn s ngu nhin khch quan trong nh gi cha tuyt i. Tuy nhin, kt qu cng cho thy nhng u im vt tri ca logic m.

w21

w22

Nhiu ngi Bnh thng

Bnh thng

w11

w12

Nhiu ngi Nng Lnh

49.203.4

125.88

6*25.07*4.0

5.144*25.0130*4.0

5.144)6/1264(*)4/1()2/47*3(128*)6/1(

)]3/())2/1(29[()4/1()2/(]10)3/[()2/1(

)29()4/1()20()2/1()(

1301024*)24/1(72)6/92(

)]3/())2/1(24[()4/1()2/(]7)3/[()2/1(

)24()4/1()14()2/1()(

3229

25

225

22

2322

20

29

25

25

22

22

20

3224

20

220

16

2316

14

24

20

20

16

16

14

COA

binhthuong

lanh

Z

zzzzz

zdzzzdzzdzzzdzz

zzzzz

zdzzzdzzdzzzdzz


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Malagoli & cng s (2009) xp hng v xp hng tn dng cng ty phn phi gas Camuzzi ca s dng kin chuyn gia kt hp logic m. Tc gi dng mnh hp thnh nu th. tng hp im v xp hng tn nhim da trn c tiu ch nh tnh v nh lng. Vi 21 ch tiu u vo, nghin cu tng hp li thnh cc bin trung gian thng qua cc lut m ra kt qu. Bin

gi tr doanh nghip s c gii m ra kt qu trong khong [0;1] th hin kh nng ti chnh ca doanh nghip. Tuy nghin cu ch tp trung vo mt cng ty c th nhng m hnh vn c th dng nh gi cho cc doanh nghip trong cng ngnh.

Yildiz & Akkoc (2010) thc hin nghin cu d bo ph sn ngn hng s dng logic m Th Nh K. Cuc khng hong ti chnh ton cu cun i kh nhiu doanh nghip yu km. Do vy, nh gi hiu qu hot ng ca cng ty v

ri ro ph sn, c bit h thng ngn hng tr nn cc k cn thit. Nghin cu xem xt d liu 55 ngn hng, chn lc 24 ch tiu t 36 ch tiu ti chnh, vi mc

ngha thng k l 5%. Thc nghim so snh da trn 2 phng php: (i) m hnh hi qui tuyn tnh; v (ii) hm phi tuyn da trn logic m, s dng lut hp thnh vi mnh nu . th.. Kt qu t c cho thy dng phng php s dng l thuyt m c kh nng d bo ng l 90,91% trong khi m hnh hi quy

ch t 81,82%.

Othman & Etienne (2010) s dng logic m kt hp tr tu nhn to thc hin nghin cu Ra quyt nh s dng logic m trong giao dch chng khon. Cc yu t u vo cho m hnh m cc tc gi quan tm l kin chuyn gia, li nhun trn tng c phiu v t l li nhun mong mun. Kt qu ca nghin cu

cho thy hiu qu u t khi s dng logic m tt hn so vi nhng phng php nghin cu trc y trong iu kin thiu thng tin.

Korol & Korodian (2011) tin hnh nghin cu, nh gi mc hiu qu ca

logic m trong vic d bo ph sn ca doanh nghip. Trong qu trnh nghin cu, tc gi s dng bo co ti chnh ca 132 cng ty trn th trng chng khon (trong c 25 cng ty ph sn). Cc tc gi s dng c d liu chc chn (nh lng) v khng chc chn (nh tnh) lm d liu u vo d bo kh

nng ph sn ca cng ty trong 1, 2 v 3 nm ti. Kt qu khi s dng d liu chc chn th kt qu khng khc bit nhiu so vi cc m hnh d bo ri ro, ph sn

khc nh Z-score. Nhng kt qu khi s dng d liu khng chc chn th kt qu t m hnh logic m c ci thin rt nhiu.

4 NG DNG LOGIC M CHO BI TON XP HNG TN DNG

Xp hng tn dng l nh gi kh nng tn dng ca bn phi thc hin ngha v ti chnh trong tng lai da trn nhng yu t hin ti v quan im ca ngi nh gi (Standard & Poors, 2012). Theo quan im ca Moodys (2013), xp hng tn dng nhm mc ch nh gi cc ri ro tn dng lin quan n ngha v

ti chnh ca mt i tng trong tng lai. Bi ton xp hng tn dng c th c m hnh ha di dng ton hc nh sau (Lahsasna & cng s, 2010):


35

Trong :

x1,x2,,xm : l m thuc tnh ca i tng c xp hng (hoc nh gi)

yi: l hn mc tn dng ca i tng th i (i = 1,2,n)

f l hm hoc m hnh xp hng tn dng, thc hin d bo gi tr yi khi bit gi tr ca cc thuc tnh x1,x2,,xm.

C rt nhiu m hnh xp hng tn dng c s dng nh: m hnh Z-score ca Altman (1968), m hnh hi quy logistic (Logistic Regression), mng thn kinh nhn to (Artificial Neural Network), SVM (Support Vector Machine),

Trong ni dung ca bi vit ny, chng ti mun gii thiu mt cch tip cn mi da trn logic m cho bi ton xp hng tn dng khch hng ca Korol (2012).

Tt c khch hng c m t bi 10 bin bao gm: nhm bin nhn khu hc (demographical variables) v nhm bin ti chnh (financial variables).

K hiu

bin

Tn bin

X1 Tui (Age)

X2 Trnh hc vn (Education)

X3 Tnh trng hn nhn (Marital status)

X4 S con (Number of children)

X5 Thu nhp hng thng (Monthly income)

X6 Thm nin cng tc (Length of employment)

X7 Loi hp ng lao ng (Type of employment contract)

X8 Gi tr ti sn xe hi (Value of owned car)

X9 Gi tr ti sn nh (Value of owned

apartment/house)

X10 Gi tr ti sn khc (Value of other assets)

Bng 1: Cc bin nhn khu hc v ti chnh ca khch hng

M hnh c chia ra lm 4 nhm lut (rule blocks). Nhm 1 Nhn khu hc, bao gm: Tui, Trnh hc vn, Tnh trng hn nhn v S con. Nhm 2 Ti chnh, nh gi iu kin ti chnh ca khch hng, bao gm: Thu nhp hng thng, Thm nim cng tc v Loi hp ng lao ng. Nhm 3 Ti sn m bo, bao gm: Gi tr ti sn xe, Gi tr ti sn nh v Gi tr ti sn khc.

Nhm 4 Xp hng, bao gm: Cc bin nhn khu hc, Cc bin ti chnh v cc bin ti sn m bo da bo kt qu u ra.


36

Hnh 6: Cu trc m hnh Logic m cho bi ton xp hng tn dng (Korol, 2012)

Tp m v ngng cho cc hm thnh vin c trnh by trong bng sau:

Tn bin Ngng cho tt c cc hm thnh vin

Tui (t 18 n 65 tui) Tr: nh hn 33

Trung nin: t 27 n 53

Gi: ln hn 48

Trnh hc vn (t 1 n 3: 0- ph thng, 1- cng nhn k thut, 2- cao ng, 3- i hc v sau i hc)

Thp: nh hn 1

Trung bnh: t 0.8 n 2.25

Cao: hn 1.5

Tnh trng hn nhn (t 0 n 1: 0 c thn, 1 c gi nh; t 0-1: l tnh nhn hoc ga ph,)

c thn: nh hn 0.7

C gia nh: ln hn 0.7

S con (t 1 n 5 con) t: nh hn 2

Va: t 1 n 3.7

Nhiu: ln hn 3

Thu nhp hng thng (t 800 n 5000)

Thp: nh hn 2900

Trung bnh: t 1850 n 3950

Cao: ln hn 2950


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Thm nin cng tc (t 0 n 15 nm) Ngn: nh hn 7.5 nm

Trung bnh: t 3.7 n 11.25 nm

Di: trn 7.5 nm

Loi hp ng lao ng (t 0 n 2: 0-thi v, 1- c thi hn, 2-khng thi hn)

Thi v: nh hn 1

C thi hn: t 0.5 n 1.5

Khng thi han: ln hn 1

Gi tr ti sn xe hi (t 10000 n 100000)

R: nh hn 55000

Va: t 33000 n 77500

t: ln hn 55000

Gi tr ti sn nh (t 0 n 500000) Thp: nh hn 325000

Trung bnh: t 237500 n 412500

Cao: ln hn 325000

Gi tr ti sn khc (t 1000 n 20000)

Thp: nh hn 4500

Trung bnh: t 2700 n 15250

Cao: ln hn 10500

Kt qu xp hng (t 0 n 1) Ri ro cao: nh hn 0.3

Ri ro trung bnh: t 0.3 n 0.7

Ri ro thp: ln hn 0.7

Bng 2: Xc nh ngng cho cc hm thnh vin

Nu Tui Nu Trnh hc vn Nu Tnh trng hn nhn Nu S con Th Nhn khu hc

Tr Thp c thn t Yu

Tr Trung bnh c thn t Trung bnh

Tr Cao c thn t Trung bnh

Trung nin Thp c thn t Yu

Trung nin Trung bnh c thn t Trung bnh

Trung nin Cao c thn t Trung bnh

Gi Thp c thn t Yu

Gi Trung bnh c thn t Trung bnh


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Gi Cao c thn t Trung bnh

Tr Thp C gia nh t Yu

Tr Trung bnh C gia nh t Trung bnh

Tr Cao C gia nh t Mnh

Trung nin Thp C gia nh t Yu

Trung nin Trung bnh C gia nh t Trung bnh

Trung nin Cao C gia nh t Mnh

Gi Thp C gia nh t Yu

Gi Trung bnh C gia nh t Trung bnh

Gi Cao C gia nh t Mnh

Tr Thp c thn Va Yu

Tr Trung bnh c thn Va Yu

Tr Cao c thn Va Trung bnh

Trung nin Thp c thn Va Yu

Trung nin Trung bnh c thn Va Trung bnh

Trung nin Cao c thn Va Trung bnh

Gi Thp c thn Va Yu

Gi Trung bnh c thn Va Trung bnh

Gi Cao c thn Va Trung bnh

Tr Thp C gia nh Va Yu

Tr Trung bnh C gia nh Va Trung bnh

Tr Cao C gia nh Va Mnh

Trung nin Thp C gia nh Va Yu

Trung nin Trung bnh C gia nh Va Trung bnh

Trung nin Cao C gia nh Va Mnh

Gi Thp C gia nh Va Yu

Gi Trung bnh C gia nh Va Trung bnh

Gi Cao C gia nh Va Mnh


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Tr Thp c thn Nhiu Yu

Tr Trung bnh c thn Nhiu Yu

Tr Cao c thn Nhiu Trung bnh

Trung nin Thp c thn Nhiu Yu

Trung nin Trung bnh c thn Nhiu Trung bnh

Trung nin Cao c thn Nhiu Trung bnh

Gi Thp c thn Nhiu Yu

Gi Trung bnh c thn Nhiu Yu

Gi Cao c thn Nhiu Trung bnh

Tr Thp C gia nh Nhiu Yu

Tr Trung bnh C gia nh Nhiu Trung bnh

Tr Cao C gia nh Nhiu Trung bnh

Trung nin Thp C gia nh Nhiu Yu

Trung nin Trung bnh C gia nh Nhiu Trung bnh

Trung nin Cao C gia nh Nhiu Trung bnh

Gi Thp C gia nh Nhiu Yu

Gi Trung bnh C gia nh Nhiu Trung bnh

Gi Cao C gia nh Nhiu Trung bnh

Bng 3: Lut cho nhm Nhn khu hc

Nu Thu nhp hng thng Nu Thm nin cng tc Nu Loi hp ng Th Ti chnh

Thp Ngn Thi v Yu

Thp Trung bnh Thi v Yu

Thp Di Thi v Trung bnh

Thp Ngn C thi hn Yu

Thp Trung bnh C thi hn Yu

Thp Di C thi hn Trung bnh

Thp Ngn Khng thi hn Yu

Thp Trung bnh Khng thi hn Trung bnh


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Thp Di Khng thi hn Trung bnh

Trung bnh Ngn Thi v Yu

Trung bnh Trung bnh Thi v Trung bnh

Trung bnh Di Thi v Trung bnh

Trung bnh Ngn C thi hn Yu

Trung bnh Trung bnh C thi hn Trung bnh

Trung bnh Di C thi hn Trung bnh

Trung bnh Ngn Khng thi hn Trung bnh

Trung bnh Trung bnh Khng thi hn Trung bnh

Trung bnh Di Khng thi hn Mnh

Cao Ngn Thi v Trung bnh

Cao Trung bnh Thi v Trung bnh

Cao Di Thi v Mnh

Cao Ngn C thi hn Trung bnh

Cao Trung bnh C thi hn Mnh

Cao Di C thi hn Mnh

Cao Ngn Khng thi hn Mnh

Cao Trung bnh Khng thi hn Mnh

Cao Di Khng thi hn Mnh

Bng 4: Lut cho nhm Ti chnh

Nu Gi tr ti sn xe Nu Gi tr ti sn nh Nu Gi tr ti sn khc Th Ti sn m bo

R Thp Thp Yu

R Trung bnh Thp Yu

R Cao Thp Trung bnh

R Thp Trung bnh Yu

R Trung bnh Trung bnh Yu

R Cao Trung bnh Mnh


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R Thp Cao Yu

R Trung bnh Cao Trung bnh

R Cao Cao Mnh

Va Thp Thp Yu

Va Trung bnh Thp Trung bnh

Va Cao Thp Mnh

Va Thp Trung bnh Trung bnh

Va Trung bnh Trung bnh Trung bnh

Va Cao Trung bnh Mnh

Va Thp Cao Trung bnh

Va Trung bnh Cao Trung bnh

Va Cao Cao Mnh

t Thp Thp Yu

t Trung bnh Thp Trung bnh

t Cao Thp Mnh

t Thp Trung bnh Trung bnh

t Trung bnh Trung bnh Trung bnh

t Cao Trung bnh Mnh

t Thp Cao Trung bnh

t Trung bnh Cao Mnh

t Cao Cao Mnh

Bng 5: Lut cho nhm Ti sn m bo

Nu Nhn khu hc Nu Ti chnh Nu Ti sn m bo Th Kt qu (Xp hng)

Yu Yu Yu Ri ro cao

Yu Yu Trung bnh Ri ro cao

Yu Yu Mnh Ri ro cao

Yu Trung bnh Yu Ri ro cao

Yu Trung bnh Trung bnh Ri ro trung bnh


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Yu Trung bnh Mnh Ri ro trung bnh

Yu Mnh Yu Ri ro trung bnh

Yu Mnh Trung bnh Ri ro trung bnh

Yu Mnh Mnh Ri ro thp

Trung bnh Yu Yu Ri ro cao

Trung bnh Yu Trung bnh Ri ro cao

Trung bnh Yu Mnh Ri ro trung bnh

Trung bnh Trung bnh Yu Ri ro trung bnh

Trung bnh Trung bnh Trung bnh Ri ro trung bnh

Trung bnh Trung bnh Mnh Ri ro trung bnh

Trung bnh Mnh Yu Ri ro trung bnh

Trung bnh Mnh Trung bnh Ri ro thp

Trung bnh Mnh Mnh Ri ro thp

Mnh Yu Yu Ri ro trung bnh

Mnh Yu Trung bnh Ri ro trung bnh

Mnh Yu Mnh Ri ro trung bnh

Mnh Trung bnh Yu Ri ro trung bnh

Mnh Trung bnh Trung bnh Ri ro trung bnh

Mnh Trung bnh Mnh Ri ro thp

Mnh Mnh Yu Ri ro thp

Mnh Mnh Trung bnh Ri ro thp

Mnh Mnh Mnh Ri ro thp

Bng 6: Lut cho Xp hng tn dng

Korol (2012) thc nghim m hnh logic m cho bi ton xp hng tn dng trn tp d liu 500 khch hng ti Ba Lan. Hiu qu ca phng php tip cn da trn logic m vt tri hn hn so vi cc m hnh thng k (88,75% so vi 72%).


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5 THO LUN V TRAO I

Cc bi ton ti chnh ni ring v lnh vc kinh t ni chung thng cha ng nhng yu t (bin) khng chc chn, kh lng ha mt cch r rng. Phng php logic m c th gii quyt tt nhng bi ton c tnh cht ny (t cc minh chng thc nghim gii thiu trn).

c im ca logic m l khng cn phi xc nh m hnh ton hc (hoc m hnh thng k) m t mi quan h gia cc bin trong bi ton m ch cn pht biu tp lut di dng ngn ng t nhin Nu th. iu

ny lm cho phng logic m tr nn mm do v linh hot hn cc phng php ton v thng k truyn thng. Tp lut trong h logic m c th do chuyn gia cung cp hoc c rt ra t tp d liu qu kh nh vo cc phng php khai ph d liu (data mining).

Hin nay c rt nhiu cng c mnh h tr vic ng dng logic m gii quyt cc bi ton trong lnh vc kinh t v k thut nh: SPSS Clementine, MATLAB,

Vi nhng bng chng thc nghim, chng ti nhn thy rng logic m c xem nh l mt phng php tip cn mi gii quyt cc bi ton trong lnh vc ti chnh.

Ti liu tham kho

[1] Duan, J. C., & Shrestha, K. (2011), Statistical Credit Rating Methods, Global Credit Review, 1, 43-64.

[2] Duc, V. H., & Thien, N. D. (2013), A new approach to determining credit rating & Its applications to Vietnams listed firms.

[3] Jang, J. S. R., & Sun, C. T. (1996), Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence , Prentice-Hall, Inc..

[4] Korol, T. and Korodian, A. (2011), Evaluation of effectiveness of fuzzy logic model in predicting the business bankruptcy, Romanian Journal of Economic Forecasting, pp 92 107.

[5] Korol, T. (2012), Fuzzy logic in financial management, Fuzzy logic-emerging technologies and applications.

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Thng tin tc gi

Phan Hin, Khoa H Thng Thng Tin Kinh Doanh H Kinh T HCM, Email: [email protected]

Thi Kim Phng, Khoa H Thng Thng Tin Kinh Doanh H Kinh T HCM, Email: [email protected]

logic mo va cac ung dung trong linh vuc tai chinh

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