APPLYING LINGUISTIC PROMETHEE METHOD IN INVESTMENT PORTFOLIO DECISION-MAKING

Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No., pp. 39-48 (0 39 PPLYING LINGUISTI PROMETHEE METHOD IN INVESTMENT PORTFOLIO DEISION-MKING hen-tung hen *, We-Zhan Hung and Hu-Lng heng 3 Depamen of Infomaon Managemen Naonal Uned Unvey Maol(36003, Tawan Depamen of Inenaonal Bune Sude Naonal h Nan Unvey Nanou(5456, Tawan 3 ene of Geneal Educaon Hung-Kuang Unvey Tachung(4330, Tawan BSTRT The pape popoed a lnguc PROMETHEE appoach fo makng nvemen pofolo decon. F, we boh conde quanave and qualave nfomaon of each ock and ue -uple lnguc value fo expe o expe he opnon o oban qualave nfomaon wh epec o all evaluaon cea. Then, he anfomaon mehod of -uple lnguc vaable appled o aggegae he qualave nfomaon. Thu, a lnguc PROMETHEE mehod peened o deemne he nvemen pofolo e and make nvemen pofolo n accodance wh compeve elave poon ndex (RPI and nvemen hehold. Fnally, an example mplemened o demonae he paccably of he popoed mehod. Keywod: -uple Lnguc Vaable, PROMETHEE, Mul-cea Decon Makng, Invemen Pofolo Selecon *. INTRODUTION The pupoe of nvemen pofolo elecon how o allocae he capal o a lage numbe of ock n ode o bng a mo pofable eun fo nveo [8]. In 95, Makowz popoed he mean vaance mehod fo he nvemen pofolo decon poblem [9]. Thee ae a lo of leaue abou makng he nvemen pofolo decon ae developed. The capal ae pcng model (PM, Shape-Lnne model, Black model and wo-faco model ae deved fom he mean vaance mehod [6,5]. The capal ae pcng model (PM wa developed n 960. The concep of he PM ha he exceped eun ae of he capal wh k equal o he nee ae of he capal whou k and make k pemum [5]. The mehod and heoe of he fnancal decon makng can be found n [0,,3]. In 980, Saay popoed nalyc Heachy Poce (HP o deal wh he nvemen pofolo decon poblem by evaluang he pefomance of each company n dffeen level of * oepondng auho: cchen@nuu.edu.w cea [0]. Ednghe and Zhang [9] eleced he ecue by ung Daa Envelopmen naly (DE. Huang [8] defned a new defnon of k and ued genec algohm o cope wh nvemen pofolo decon poblem. Geneally, n he pofolo elecon poblem he decon make conde mulaneouly conflcng obecve uch a ae of eun, lqudy and k. Mul-obecve pogammng echnque uch a goal pogammng (GP and compome pogammng (P ae ued o chooe he pofolo [,,3]. ondeng he unceany of nvemen envonmen, Tyak and hlacoglu [5] anfeed expe lnguc value no angle fuzzy numbe and ued a new fuzzy ankng and weghng algohm o oban he nvemen ao of each ock. lhough much knd of mehod ae ued o deal wh nvemen pofolo poblem, a few of hem condeed ock value accodng o he company compeve ably whch can be meaued by eveal, omeme conflcng, cea. Bede, we mu conde ock value baed on quanave nfomaon (uch a EPS, cah enve ao ec and qualave nfomaon (uch a poduc

40 Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No. (0 and evce qualy, nnovaon ably ec. I mpoan o povde a flexble and funconal mehod o deal wh above ue. In fac, mulple cea decon makng (MDM mehod can be ued o deal wh he nvemen pofolo decon poblem. Mul-cea decon-makng (MDM he mo wdely ued decon mehodologe n he cence, bune, govenmen and engneeng wold [4]. MDM mehod can mpove he qualy of decon by makng he decon-makng poce moe explc, aonal and effcen [6]. MDM poblem can be concely expeed n max foma a [8]. n x x x n D x x xn ( m xm xm xmn W w w ( w n whee,,, m ae poble alenave among whch decon make have o chooe;,,, n ae evaluaon cea wh whch alenave pefomance ae meaued; x he ang of alenave wh epec o ceon and w he wegh of ceon. Howeve, we conde no only he pefomance of ock bu alo he developmen poenal of hem when we make nvemen pofolo whch he ock ae choen fom he ame nduy. The pefomance of ock can be colleced by quanave nfomaon and he developmen poenal mu be meaued by qualave nfomaon whch depend on expe knowledge and expeence o evaluae. PROMETHEE (Pefeence Rankng Oganzaon Mehod fo Enchmen Evaluaon a mul cea decon makng mehod developed by Ban [4]. I well adaped o poblem whee a fne numbe of alenave acon ae o be anked condeng eveal, omeme conflcng, cea []. Thee ae x bac ype of pefeence funcon n PROMETHEE mehod, o expe can eablh flexble andad accodng o he equemen of compeon condon n he ame nduy wh epec o each ceon by PROMETHEE mehod [5]. In geneal, boh quanave and qualave daa mu be condeed n he poce of nvemen pofolo decon. In h pape, we collec quanave nfomaon whoe daa ype ae cp value and ue -uple lnguc vaable o expe qualave nfomaon of each ock. The -uple lnguc epeenaon model baed on he concep of ymbolc anlaon [6,7]. I an effecve mehod o educe he make of nfomaon anlaon and avod nfomaon lo hough compung wh wod [4]. lnguc PROMETHEE mehod popoed o deal wh he nvemen pofolo poblem n h pape. Th pape oganzed a follow. In econ, we peen he conex of dffeen evaluaon nfomaon ncludng quanave and qualave nfomaon. In econ 3, we decbe he deal of he popoed mehod, and hen an example mplemened a he end of h pape o demonae he pocedue of he popoed mehod. Fnally, he concluon dcued.. EVLUTION INFORMTION In geneal, he evaluaon daa o nfomaon abou ock elecon n he nvemen pofolo decon can be dnguhed a wo ype [,,5].. Quanave nfomaon. Mo of he quanave nfomaon abou he pefomance of a company ae cp value (uch a eanng pe hae, ne pof magn, eun on ae, eun on equy, deb o equy ao, cuen ao, quck ao, nvenoy unove, and ae unove. The quanave nfomaon of a company can be epeened a he pefomance of he company n ho em peod.. Qualave nfomaon. Some cea abou he compeve ably of a company ae uually expeed by expe ubecve opnon accodng o he knowledge and expemen (uch a pepecve ably, nnovaon ably, nenaonal anpo bune ably, alened peon culvae ably, poduc and evce qualy, makeng ably, nfomaon cence and echnology ulzaon ably, enepe mage and eponbly. The qualave nfomaon of a company can ue be epeened a poenal ably and fuue pefomance of he company n long em peod. Qualave nfomaon can be expeed by -uple lnguc vaable n h pape. The membehp funcon of -uple lnguc vaable can be expeed a angle fuzzy numbe [7]. Thee ae hee ype of -uple lnguc vaable ae appled o expe he expe' opnon n h pape (hown a Table and Fgue o Fgue 3. Le S { 0,,,..., g} be a fne and oally odeed lnguc em e. -uple lnguc vaable can be expeed a,, whee he cenal value of -h lnguc em n S and a numecal value epeenng he dffeence beween calculaed lnguc em and he cloe ndex label n he nal lnguc em e. The ymbolc anlaon funcon peened o

. T. hen e al.: pplyng Lnguc Pomehee Mehod n Invemen Pofolo Decon-makng 4 anlae β no a -uple lnguc vaable [7]. Then, he ymbolc anlaon poce appled o anlae β (β [0, ] no a -uple lnguc vaable. The genealzed anlaon funcon can be epeened a [4]. :[0,] S [, (3 g g, (4 ( whee ound( g, [, g g and g Fgue : Membehp funcon of lnguc vaable a ype (= Fgue : Membehp funcon of lnguc vaable a ype (= Le x = {(,,, ( n, n } be a -uple lnguc vaable e and W = {(w, w,, (w n, wn } be he e of lnguc wegh of each lnguc vaable. The ahmec mean X compued a [3]. X n [3]. X w n (, m, m (6 The weghed lnguc aveage compued a n, * w, w n w, w w w, (7 In geneal, decon make would ue he dffeen -uple lnguc vaable baed on he knowledge o expeence o expe he opnon [5]. anfomaon funcon needed o anfe hee -uple lnguc vaable fom dffeen lnguc e o a andad lnguc e a unque doman. In he mehod of Heea and Manez [7], he doman of he lnguc vaable wll nceae a he numbe of lnguc vaable nceaed. To ovecome h dawback, a new anlaon funcon popoed o anfe a cp numbe o -uple lnguc vaable o a andad lnguc em a he unque doman [7]. Suppoe ha he neval [0, ] he unque doman. The lnguc vaable e wh dffeen emanc (o ype wll be defned by paonng he neval [0, ]. Tanfomng a cp numbe β (β [0, ] no -h lnguc em, of ype a (, (8 n whee ound( g, ( g g and he numbe of lnguc vaable of ype. Tanfomng -h lnguc em of ype no a cp numbe β (β [0, ] a Fgue 3: Membehp funcon of lnguc vaable a ype 3 (=3 evee funcon defned o eun an equvalen numecal value β fom -uple lnguc nfomaon,. ccodng o he ymbolc anlaon, an equvalen numecal value β obaned a follow [4]., g (5 n ( n ( n (, ( (9 g whee g and [,. g g Theefoe, he anfomaon fom -h lnguc em, of ype o k-h lnguc em k, k of ype + a neval [0, ] can be expeed a (, k n, ( k

4 Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No. (0 whee g and n ( [,. k g g 3. PROPOSED METHOD In fac, nvemen pofolo decon poblem may be decbed by mean of he followng e: ( e of expe called E E, E,, E K ; ( e of ock (alenave called,,, m ; ( e of cea,,, n wh whch ock pefomance ae meaued; (v e of pefomance ang of ock wh epec o cea called x,,,..., m,,...,n. If he pefomance of he -h ock wh epec o he -h ceon quanave nfomaon, can be expeed a cp value ( V. If he pefomance of he -h ock wh epec o he -h ceon qualave nfomaon, he pefomance of he -h ock wh epec o he -h ceon decded by he k-h expe can be epeened a a k k k -uple lnguc vaable F ( S,. Expe would ue he dffeen -uple lnguc vaable baed on he knowledge o expeence o expe he opnon. I needed o anfe hee -uple lnguc vaable fom dffeen lnguc e o a andad lnguc e a unque doman befoe aggegaed hee lnguc vaable of expe' opnon. If he expe' opnon have been anfomed o a andad lnguc e a unque doman, he aggegaed lnguc ang F of -h ock wh epec o he -h ceon can be calculaed a F K K k k ( ( S, ( S, (0 k Fo compang wo ock,, unde ceon, he dffeence can be calculaed a d V V n quanave nfomaon, o d F F n qualave nfomaon. Theefoe, a pefeence funcon P defned a: P, H ( d ( 0 P, whee H ( d pefeence funcon of d. The ymbol P, epeen he pefeence degee of ock ove wh epec o ceon. The H ( d a monooncally nceang funcon of he obeved devaon ( d beween F and F o beween V and V. Thee ae x ype of pefeence funcon n PROMETHEE mehod uch a uual ceon, qua ceon, ceon wh lnea pefeence, level ceon wh lnea pefeence, ceon wh lnea pefeence and ndffeence aea, and guaan ceon. In h pape, hee pefeence funcon ae ued and can be expeed a follow. Level ceon wh lnea pefeence fo qualave nfomaon can be expeed a H F, F,, q 0, q F F F F F F p p ( Level ceon wh lnea pefeence fo quanave nfomaon can be expeed a, V V p H V, V, q V V p (3 0, q V V eon wh lnea pefeence and ndffeence aea fo quanave nfomaon can be expeed a, p V V V q H V, V, q V V p (4 p q 0, V V q The aggegaed lnguc wegh ( w ~ ceon can be calculaed a of each w ~ K w w w w ( ( S k, k ( S, (5 K k The oveall pefeence ndex of ock ock can be epeened a n w w, S, * H d ove (6 d H he value of pefe funcon epec o ceon and d he pefomance ang of mnu epec o ceon. The leavng flow of can be calculaed a

. T. hen e al.: pplyng Lnguc Pomehee Mehod n Invemen Pofolo Decon-makng 43, b (7 b he meaue of he domnang degee of The eneng flow of of ove he ohe ock. can be calculaed a b, (8 b he meaue of he domnaed degee by he ohe ock. The ne flow of can be calculaed a (9 Defne he compeve elave poon ndex (RPI of ock a: RPI max mn mn (0 The ange of RPI beween 0 and. If he ock ha he bgge value of ne flow, hen RPI ; Ohewe, he ock ha he malle value of ne flow, hen RPI 0. The RPI of ock can be epeened a he compeve elave poon of ock, he hghe RPI mean ha ock ha moe ably o compee wh each ohe. Deemne he nvemen hehold value of RPI ( and ge he pofolo e. If RPI of alenave geae han he deemned hehold value, we conde alenave good enough o chooe n he nvemen pofolo e. Theefoe, he nvemen pofolo e can be deemned a RPI( ( Fnally, he nvemen ao of each ock accodng o he nvemen pofolo e can be calculaed a RPI P ( RPI 4. NUMERIL EXMPLE Suppoe ha a fund company dee o make nvemen pofolo n auomoble manufacue nduy. Thee expe wan o evaluae he ock and make nvemen pofolo decon fom fve ock accodng o x cea (hown a Table and Table 3. ccodng o he popoed mehod, he compuaonal pocedue of he poblem ae ummazed a follow. Sep. ollec quany nfomaon of each ock a Table 4. Fnancal epo daa come fom Tawan publc obevaon new aon dung 009, he econd eaon. Sep. Each expe elec he uable ype of lnguc vaable. Expe E choce ype, E choce ype, E3 choce ype 3 (efe o Table. nd hen, each expe ue he lnguc vaable o evaluae he wegh of each ceon a Table 5 and evaluae he pefomance ang of each ock wh epec o qualave cea a Table 6. Sep3. Tanfom dffeen ype of wegh lnguc vaable wh epec o each ceon no -uple lnguc vaable of ype and aggegae he lnguc wegh wh epec o each ceon a Table 7. Sep4. Tanfom ock qualave nfomaon no -uple lnguc vaable of ype and hen aggegae he lnguc ang of each ock wh epec o cea a Table 8. Sep5. Deemne he hehold value of each ceon a Table 9. Sep6. alculae he pefeence degee of all ock wh epec o each ceon accodng o pefeence funcon (hown n Table a Table 0,,,3,4 and 5. Sep7. alculae he oveall pefeence ndex of each ock wh epec o each ceon a Table 6. Sep8. alculae he leavng flow, he eneng flow, he ne flow, he compeve elave poon ndex of each ock a Table 7. Sep9. Expe deemne he nvemen hehold value of RPI ( =0.4, and hen we oban he nvemen pofolo e a {,, 4}. ccodng o he pofolo e, we oban he nvemen ao of hee ock ae = 0.30, =0.5, = 0.58 (hown a Table 7. 4 5. ONLUSION In h pape, we peen a lnguc PROMETHEE mehod o deemne he nvemen pofolo whch condeed boh quanave nfomaon n fnancal epo and qualave nfomaon of expe' opnon. Fnancal epo daa can eflec he pefomance of he ock n ho em peod. Expe opnon can eflec poenal ably and fuue pefomance of he ock n long em

44 Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No. (0 peod. ccodng o expe pecepon, hey can chooe he uable ype of pefeence funcon o expe he pefeence degee of one ock bee han anohe ock wh epec o each ceon. pplng he -uple lnguc vaable, expe can compae he value of each ock flexbly and compehenvely, and hen deemne a aonal nvemen pofolo. Lnguc PROMETHEE mehod no only can deal wh he nvemen pofolo decon poblem bu alo can ue n many knd of mul-cea decon-makng poblem uch a hd-pay logc upple elecon poblem, R&D poec elecon poblem, nfomaon yem elecon poblem. In he fuue, we wll degn a decon uppo yem o deal wh he nvemen pofolo elecon poblem baed on he popoed model n h pape. Th yem wll povde a flexble ool fo expe o collec, analyze and compue he fnancal daa. ddonally, wll help expe make he gh decon n eal fnancal envonmen. Table : Dffeen ype of lnguc vaable Lnguc vaable Type I: pefomance Type I: wegh Type II: pefomance Type II: wegh Type III: pefomance Type III: wegh 3 4 5 Exemely Poo 5 0, Poo 5, Fa 5, Good 5 3, Exemely Good 5 4 Exemely Low 5 0, Low 5, Fa 5, Hgh 5 3, Exemely Hgh 5 4 Exemely Poo 7 0, Poo 7, Medum Poo 7, Fa 7 3, Medum Good 7 4, Good 7 5, Exemely Good 7 6 Exemely Low 7 0, Low 7, Medum Low 7, Fa 7 3, Medum Hgh 7 4, Hgh 7 5, Exemely Hgh 7 6 Exemely Poo 9 0,Vey Poo 9, Poo 9, Medum Poo 9 3, Fa 9 4, Medum Good 9 5, Good 9 6, Vey Good 9 7, Exemely Good 9 8 Exemely Low 9 0,Vey Low 9, Low 9, Medum Low 9 3, Fa 9 4, Medum Hgh 9 5, Hgh 9 6, Vey Hgh 9 7, Exemely Hgh 9 8 Table : The company of ock ompany Name Yulon Moo o., Ld. hna Moo opoaon Sanyang Induy o., Ld. Hoa Moo o., Ld. Yulon Nan Moo o., Ld Table 3: The decpon of he cea Infomaon Pefeence Name ype funcon ceon wh lnea EPS Quany pefeence and ndffeence aea ah enve ao Quany 3 uen ao Quany Invenoy 4 unove ao Quany Poduc and 5 evce qualy Qualy Innovaon 6 ably Qualy ceon wh lnea pefeence and ndffeence aea level ceon wh lnea pefeence level ceon wh lnea pefeence level ceon wh lnea pefeence level ceon wh lnea pefeence Table 4: Quanave nfomaon EPS ah enve uen Invenoy ao (% ao (% unove ao.0 3.80 48.53 8.83.34 5.0 39.76 5.38 3. 6.44 8.85 4.35 4 6.3 5.77 35.88 39.77 4.90.33 6.59 333.44 5 Table 5: The wegh lnguc vaable ea Expe 3 4 5 6 E 5,0 5,0 5 3,0 5,0 5,0 5,0 E 7 4,0 7 6,0 7 4,0 7 3,0 7 6,0 7 3,0 E 3 5 9,0 9,0 9 4,0 9 3,0 9 3,0 9 4,0 eon Sock 5 6 Table 6: The lnguc ang Expe E E E 3 5 4,0 7 6,0 9 4,0 5 3,0 5 7,0 9,0 3 5 4,0 5 7,0 9 6,0 4 5,0 7 4,0 9 4,0 5 5,0 7 3,0 9,0 5 4,0 5 7,0 9 6,0 5 4,0 7 6,0 9 4,0 3 5 3,0 5 7,0 9 3,0 4 5,0 7 6,0 9,0 5 5 4,0 5 7,0 9 7,0

. T. hen e al.: pplyng Lnguc Pomehee Mehod n Invemen Pofolo Decon-makng 45 Table 7: Tanfe dffeen ype of wegh lnguc vaable no he lnguc vaable of ype Expe eon E E E 3 veage 7, 0.083 7 4,0 7 4, 0.04 7 3,0.4 7 3,0 7 6,0 7, 0.04 7 3,0.4 3 5 7, 0.083 7 4,0 7 3,0 7 4, 0.08 4 7, 0.083 7 3,0 7,0.04 7,0.04 5 7 3, 0.333 7 6,0 7,0.04 7 4, 0.04 6 7, 0.083 7 3,0 7 3,0 7 3, 0.083 Table 8: Tanfe dffeen ype of lnguc ang o he lnguc vaable of ype Expe eon Sock E E E 3 veage 7 6,0 7 6,0 7 3,0 5 7,0 Table : Pefeence degee beween alenave wh epec o ceon 3 3 4 5 0.000 0.000 0.000 0.000 0.000 0.500 0.000.000 0.000 0.500 3 0.000 0.000 0.000 0.000 0.000 4 0.500 0.000.000 0.000 0.500 5 0.000 0.000 0.000 0.000 0.000 Table 3: Pefeence degee beween alenave wh epec o ceon 4 3 4 5 0.000.000.000 0.000 0.000 0.000 0.000 0.500 0.000 0.000 3 0.000 0.000 0.000 0.000 0.000 4.000.000.000 0.000 0.000 5.000.000.000.000 0.000 5 6 5, 0.083 5,0, 0.04 3,0.069 3 6,0 5,0 5, 0.083 5,0.08 4, 0.083 4,0 3,0 3, 0.08 5, 0.083 3,0, 0.083,0 6,0 5,0 5, 0.083 5,0.08 6,0 6,0 3,0 5,0 3 5, 0.083 5,0,0.04 4, 0.04 4, 0.083 6,0, 0.083 3,0 5 6,0 5,0 5,0.04 5,0.069 Table 4: Pefeence degee beween alenave wh epec o ceon 5 3 4 5 0.000.000 0.000.000.000 0.000 0.000 0.000 0.500.000 3 0.000.000 0.000.000.000 4 0.000 0.000 0.000 0.000 0.500 5 0.000 0.000 0.000 0.000 0.000 Table 5: Pefeence degee beween alenave wh epec o ceon 6 hehol d Table 9: The hehold of each ceon ea 3 4 5 P= Q= P= Q= P=00 Q=50 P=3 Q= 6 P 6 P 6 Q Q Table 0: Pefeence degee beween alenave wh epec o ceon 3 4 5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3 0.000 0.000 0.000 0.000 0.000 4.000.000.000 0.000 0.330 5.000.000.000 0.000 0.000 Table : Pefeence degee beween alenave wh epec o ceon 3 4 5 0.000 0.000 0.000 0.000 0.470 0.0 0.000 0.000 0.000.000 3.000 0.40 0.000 0.000.000 4 0.970 0.000 0.000 0.000.000 5 0.000 0.000 0.000 0.000 0.000 3 4 5 0.000 0.000.000.000 0.000 0.000 0.000.000.000 0.000 3 0.000 0.000 0.000 0.500 0.000 4 0.000 0.000 0.000 0.000 0.000 5 0.000 0.000.000.000 0.000 Table 6: The oveall pefeence degee beween alenave wh epec o each ceon 3 4 5 0.000 0.3 0.54 0.335 0.83 0.4 0.000 0.400 0.34 0.478 3 0.74 0.74 0.000 0.68 0.375 4 0.557 0.86 0.49 0.000 0.43 5 0.86 0.86 0.40 0.54 0.000 Table 7: The leavng flow, eneng flow, ne flow of each ock a a a RPI( Invemen Rao.93.58 0.035 0.443 0.30.53.67 0.086 0.487 0.5 3.09.565-0.474 0.000 0.000 4.766.09 0.674.000 0.58 5.46.567-0.3 0.33 0.000

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48 Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No. (0 應用語意 PROMETHEE 方法於投資組合決策之研究陳振東 * 洪偉展 3 鄭慧翎國立聯合大學資訊管理學系苗栗市恭敬里聯大路號國立暨南國際大學國際企業研究所南投縣埔里鎮大學路號 3 弘光科技大學通識學院台中縣沙鹿鎮中棲路 34 號摘要本研究提出語意 PROMETHEE 方法應用於投資組合決策問題首先, 我們同時考慮影響投資股票的量化與質化因素其中, 有關各個質化因素, 本研究使用不同型態的二元語意值表達專家對於該項質化評估準則下的評價, 並應用二元語意轉換法以整合每位專家的語意評估值藉由 PROMETHEE 的計算過程, 本研究提出一個語意 PROMETHEE 決策分析法, 並透過相對應競爭對應位置指數及投資門檻, 以有效決定投資組合最後, 藉由範例說明此決策方法有效性關鍵詞 : 二元語意變數 PROMETHEE 多準則決策投資組合選擇 (* 聯絡人 :cchen@nuu.edu.w