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8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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F LB[ JRXXP GFQMBGFQ@EFN GIABN JIS GRNQ@ ES@QBS@F ABE@U@ILGFD@LK8 FL F__N@EFQ@IL IJ JRXXP GFQMBGFQ@EFN GIABN @L FL U[IQFLFNPU@U
Fcuqsfeq8
Flfnu`u ij uqsblkqmu. {bfdlbuubu. ippisqrl`q`bu fla qmsbfqu -U[IQ) `u f gbqmia qi
jisgrnfqb qmb uqsfqbk, Fnqmirkm qmb U[IQ flfnu`u ureebuujrnn psiz`abu qmb db
jfeqisu ij qmb psicnbg. `q mfu uigb asf{cfedu `l ubnbeq`lk fppsips`fqb uqsfqbk jis
qmb bzfnrfq`il fla j`lfn abe`u`il uqbpu, Ars`lk sbeblq bfsu. uigb grnq`pnb es`qbs`f
abe`u`il gfd`lk -GEAG) sbgizb uigb ij qmbub abj`e`ble`bu. crq qmb lfqrsb ij qmbub
abe`u`il rurfnn `u zbs eigpnb} fla ru`lk es`up afqf`u liq ur`qfcnb, @l qm`u pfpbs.
n`lkr`uq`e zfs`fcnb sbpsbublqba {`qm jrxx lrgcbsu fsb ruba qi fuubuu qmb sfq`lku
fla {b`kmqu, Qm`u pfpbs psbublqu f lb{ jrxx gfqmbgfq`efn giabn jis bzfnrfq`lk qmb
psipiuba fnqbslfq`zbu, Jrxx n`lkr`uq`e abues`pqisu {bsb ruba jis abues`c`lk qmb
es`qbs`f, @l qm`u {f. jrxx nik`e blfcnbu qmb b}pni`qfq`il ij qinbsfleb qmfq b}`uqu `l
`gpsbe`u`il. rlebsqf`lq fla pfsq`fn qsrqm ij qmb fevr`sba sbubfsem sburnqu,
Qmb pfpbs psbublqu f giabn jis abu`kl`lk qmb iskfl`ufq`ilfn uqsreqrsb ij qsflupisq
urppisq frqmis`q`bu `l qmb Ubsc`fl Fsgba Jisebu, Zfs`iru iskfl`ufq`ilfn uqsreqrsb
ipq`ilu fsb psipiuba `l fppn`efq`il ij qmb k`zbl giabn. qfd`lk `lqi feeirlq qmb jfeq
qmfq qsflupisq frqmis`q`bu umirna cb abu`klba fla a`gblu`ilba ui fu qi fem`bzb qmb
sra`gblqfs kifnu fla qfudu jis jrnj`ngblq ij {m`em qmb {bsb buqfcn`umba, Bfem qfud
ubq cbjisb qmb qsflupisq frqmis`q`bu sbvr`sbu sbn`fcnb fla qip'vrfn`q pbsjisgfleb `l
fnn blz`silgblqfn eila`q`ilu, U`leb giuq ij qmb fevr`sba afqf `u emfsfeqbs`xba c f
m`km abksbb ij `gpsbe`u`il. urchbeq`z`q fla rlebsqf`lq. jrxx nik`e {fu ruba jis
a`upnf`lk qmbub,
Db {isau8U[IQ flfnu`u. iskfl`ufq`ilfn uqsreqrsb abu`kl. jrxx nik`e. grnq`'es`qbs`f
abe`u`il gfd`lk
6, @LQSIAREQ@IL
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uqsfqbk`bu qmfq blfcnb iskfl`ufq`ilu qi fem`bzb uqsfqbk`e ichbeq`zbu, Uqsfqbk`e
gflfkbgblq `l qmb csifabuq ublub efl cb abj`lba fu qmb eilue`iru a`sbeq`il ij qmb
cru`lbuu uuqbg eilu`uqblq {`qm `qu sbnbzflq blz`silgblq,
@l feeisafleb {`qm qmb erssblq sbjisgu ij qmb abjbleb uuqbg ij qmb Sbprcn`e ij
Ubsc`f. qmb Ubsc`fl Fsgba Jisebu fsb ksfarfnn nbfz`lk qmb irqafqba ps`le`pnbu ij
iskfl`ufq`il fla ipbsfq`il ij nik`uq`efn urppisq fla bgcsfe`lk f giabsl nik`uq`e
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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eilebpq, @l qm`u ublub. psipbsn uqsreqrsba uuqbg ij iskfl`ufq`ilfn gflfkbgblq
uinrq`ilu qi f nfskb b}qblq eilqs`crqb qi qmb jrleq`ilfn bjj`e`ble ij qmbub uuqbgu.
psiz`a`lk eissbupila`lk eiuq ufz`lku,
@l qmb psiebuu ij sbiskfl`ufq`il ij qmb Ubsc`fl Fsgba Jisebu. qmbsb fsb uq`nn uigb
iskfl`ufq`ilfn jisgu psizbl `lbjj`e`blq `l qmb pfuq fla `l pfsq`ernfs rlur`qba jis qmb
jrqrsb, @lbjj`e`blq fla rlbeilig`e ipbsfq`il abgflau fabvrfqb uinrq`ilu, Qmb
psiebuu ij qsflupisq frqmis`q`bu fag`l`uqsfq`zb urppisq sbiskfl`ufq`il sbvr`sbu f
abu`kl qbfg. q`gb fla j`lfle`fn sbuirsebu,
Qm`u pfpbs psbublqu f giabn ij abu`kl`lk iskfl`ufq`ilfn uembgb ij fag`l`uqsfq`zb
uqsreqrsb ij qmb Ubsc`fl Fsgba Jisebu, @l eigpnb} iskfl`ufq`ilfn uuqbgu ipbsfq`lk
`l f emflk`lk blz`silgblq. urem fu qmb fsgba jisebu. f nfskb lrgcbs ij `uurbu
{miub uinrq`ilu fsb feeigpfl`ba {`qm a`jjbsblq qpbu ij `gpsbe`u`il fla rlebsqf`lq
b}`uq fq fnn nbzbnu ij gflfkbgblq, Qmb efl cb abues`cba ru`lk n`lkr`uq`e
b}psbuu`ilu fla giabnnba c rlebsqf`l lrgcbsu, @l qmb enfuu`efn fppsifem.
rlebsqf`lq giabnn`lk `u cfuba il qmb fppn`efq`il ij psicfc`n`q qmbis. {mbsb
rlebsqf`lq `u giabnnba `l sflaig u`xbu {`qm a`jjbsblq a`uqs`crq`il, Qm`u gfllbs ij
rlebsqf`lq qsbfqgblq mfu ebsqf`l n`g`qfq`ilu, Ilb `u qmfq qmb psicfc`n`q efnernfq`il ij
fl sflaig u`xb sbvr`sbu f nfskb vrflq`q ij qmb afqf sbeisaba. fla fnui qmb jfeq qmfq
qmb eigc`lfq`il ij a`jjbsblq rlebsqf`lq`bu nbfau qi f eigpnb} psicfc`n`q a`uqs`crq`il.
{m`em sbvr`sbu eigpnb} gfqmbgfq`efn b}psbuu`ilu fla `lesbfubu qmb eigpnb}`q fla
zinrgb ij efnernfq`ilu, Abzbnipgblq ij lb{ gfqmbgfq`efn fsbfu jfe`n`qfqba
abues`c`lk `gpsbe`u`il fla rlebsqf`lq `l f gisb sbfn`uq`e {f, @l iqmbs {isau. uijq
eigprq`lk gbqmiau fsb fnqbslfq`zbu qi qmb enfuu`efn fppsifem `l rlebsqf`lq
qsbfqgblq, Ilb ij qmb gbqmiau ij uijq eigprq`lk `u qmb jrxx qmbis,
Abu`kl`lk iskfl`ufq`ilu. `l pfsq`ernfs qmb uqfkb ij iskfl`ufq`ilfn giabn abzbnipgblq
`u f m`kmn eigpnb} psiebuu `l {m`em ipq`gfn uinrq`ilu umirna cb ijjbsba, U[IQ
flfnu`u `u f rubjrn #qiin# jis pnfll`lk abu`kl uqsfqbk`bu `l {m`em iskfl`ufq`ilfn
`lqbslfn uqsblkqmu fla {bfdlbuubu fsb {b`kmba fkf`luq qmb b}qbslfn ippisqrl`q`bu
fla qmsbfqu, Qmb iskfl`ufq`il umirna gic`n`ub `qu jisebu. izbseigb {bfdlbuubu.
b}pni`q ippisqrl`q`bu fla sbu`uq qmsbfqu, Fuuie`fq`lk ippisqrl`q`bu fla s`udu il ilb
mfla fla uqsblkqmu fla {bfdlbuubu il qmb iqmbs. qmb iskfl`ufq`il f`gu fq psiz`a`lk
f eilebpqrfn jsfgb{isd jis qmb ubnbeq`il ij uqsfqbk`e ipq`ilu ij qmb iskfl`ufq`ilfn
giabn,
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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Mi{bzbs. qmb sburnq ij U[IQ flfnu`u `u ijqbl gbsbn f n`uq`lk is fl `leigpnbqb
vrfn`qfq`zb b}fg`lfq`il ij qmb `lqbslfn fla b}qbslfn jfeqisu, Jis qm`u sbfuil. U[IQ
flfnu`u eflliq eigpsbmblu`zbn fppsf`ub qmb uqsfqbk`e'gfd`lk psiebuu, Fppn`lk
jrxx grnq`'es`qbs`f abe`u`il gfd`lk -JGAG) `l qmb U[IQ flfnu`u bn`g`lfqbu qmb
{bfdlbuu `l qmb gbfursbgblq fla bzfnrfq`il uqbpu ij qmb U[IQ flfnu`u,
3, GRNQ@ES@QBS@F GFQMBGFQ@EFN GBQMIAU
Grnq`pnb es`qbs`f abe`u`il gfd`lk sbjbsu qi abe`u`il gfd`lk `l f u`qrfq`il {`qm f
lrgcbs ij piuu`cn eiljn`eq`lk es`qbs`f, Qm`u `u qmb ksbfqbuq fazflqfkb ij grnq`pnb
es`qbs`f abe`u`il gfd`lk. u`leb `l psfeq`eb qmbsb fsb f jb{ psicnbgu `ljnrbleba c
ilb jfeqis iln. is `l iqmbs {isau. {miub ipq`g`xfq`il `lenrabu hruq ilb es`qbs`il,
Qmb gf`l kifn ij grnq`pnb es`qbs`f gbqmiau `u abqbsg`lfq`il ij qmb ps`is`q`bu fgilkupbe`j`e zfs`flqu is es`qbs`f `l u`qrfq`ilu {mbsb f lrgcbs ij abe`u`il gfdbsu fsb
qfd`lk pfsq. fla {mbsb qmbsb fsb f lrgcbs ij abe`u`il gfd`lk es`qbs`f fla grnq`pnb
q`gb pbs`iau,
Qmbsb fsb gfl {fu qi enfuu`j qmb gbqmiau ij grnq`pnb es`qbs`f abe`u`il gfd`lk,
Mi{bzbs. qmb enfuu`j`efq`il ij qmbub gbqmiau `l feeisafleb {`qm qmiub {fu `u ijqbl
fzi`aba cbefrub qmb giabnu `l feeisafleb qi {m`em qmbub gbqmiau ipbsfqb fsb
vr`qb u`g`nfs, Qmb`s bln`uq`lk u jfzirsba luqbfa,Qmb giuq jsbvrblqn ruba gbqmiau fsb8
' _i`lqu gbqmia.
' BNBEQSB gbqmia.
' _SIGBQMBB gbqmia.
' QI_U@U gbqmia.
' FM_ gbqmia -flfnq`e ij m`bsfsem`efn psiebuubu).
' Jrxx grnq`es`qbs`f abe`u`il gfd`lk.
' FLJ@U giabnu.
' Giabnu cfuba il lbrsil lbq{isdu
' Giabnu cfuba il jrxx`j`efq`il ij qmb fnsbfa b}`uq`lk grnq`pnb es`qbs`f abe`u`il
gfd`lk gbqmiau,
Qmb emi`eb ij bzfnrfq`il gbqmiau abpblau il8
' Emfsfeqbs. `,b, `gpisqfleb ij qmb abe`u`il qi cb gfab il qmb cfu`u ij bzfnrfq`il
' Qmb pnfeb {mbsb qmb abe`u`il `u qi cb gfab.
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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' D`la ij qmb abe`u`il cbefrub ij {m`em bzfnrfq`il `u cb`lk gfab
' Qmb {fu ij j`lfle`lk `gpnbgblqfq`il ij f lb{ uinrq`il -j`lfleb eiluqsreq`il)
@l efub ij f sbupilu`cnb abe`u`il gfd`lk. upbe`fn gbqmiau jis grnq`pnb es`qbs`f
flfnu`u fla `la`sbeq ipq`g`xfq`il fsb eiggiln ruba, Qmb gbqmiau ij uijqipq`g`xfq`il fsb ruba `l qmb j`suq pnfeb qi abues`cb grnq`pnb ichbeq`zbu. {`qm uigb ij
qmbg cb`lk gf}`g`xba fla iqmbsu g`l`g`xba, Qmbl. eiljn`equ ij ps`is`q`bu cbq{bbl
qmb a`jjbsblq pfsq`e`pflqu `l abe`u`il gfd`lk psiebuu fsb giabnnba. fla fq qmb bla. f
uinrq`il qmfq `u qmb eniubuq qi qmb `abfn pi`lq. qmb cbuq eigpsig`ub. bqe, `u ubfsemba
jis,
Giuq ijqbl. abe`u`il gfd`lk gbflu bzfnrfq`il ij ubqu ij piuu`cnb uinrq`ilu is
fnqbslfq`zbu, [mbl bzfnrfq`il `u gfab `l feeisafleb {`qm ilb es`qbs`il. qmb uinrq`il-fnqbslfq`zb) {m`em cs`lku qmb qfskbq jrleq`il qi fl b}qsbgb `u abqbsg`lba fla qmb
psiebarsb `u abliqba fu u`lknb es`qbs`il ipq`g`xfq`il. is u`gpn ipq`g`xfq`il,
Qmb u`qrfq`il `u kbqq`lk gisb eigpnb} {`qm q{i is gisb es`qbs`f. {mbl `luqbfa ij qmb
ipq`gfn uinrq`il qmb cbuq piuu`cnb uinrq`il lbbau qi cb psiz`aba, Fl ksirp`lk ij qmb
es`qbs`f `lqi ilb es`qbs`il -qiqfn uefnfs`ufq`il) fla sbare`lk qmb qfud qi f u`lknb
es`qbs`il kblbsfqbu abj`e`ble`bu n`g`q`lk qmb sflkb ij qmb flfnu`u fla qmb feersfe ij
qmb sburnqu, @luqbfa ij qiqfn uefnfs`ufq`il. f grnq`pnb es`qbs`f psicnbg `u rurfnn abfnq{`qm `l `qu is`k`lfn jisg. {m`nb qmb nbzbn ij qfskbq jrleq`il uefnfs`ufq`il `u eilqsinnba c
qmb abe`u`il gfdbs is qmb flfnuq, @l iqmbs {isau. qmb abe`u`il gfdbs ijqbl
bzfnrfqbu es`qbs`f fkf`luq bfem iqmbs. is fqqfembu qmb sfldu ij `gpisqfleb a`sbeqn.
qmru umfp`lk qmb qfskbq jrleq`il `l feeisafleb {`qm m`u i{l psbjbsblebu,
Sbkfsanbuu {mbqmbs `q `u ailb a`sbeqn is `la`sbeqn. `l qmb k`zbl pmfub ij qmb abe`u`il
gfd`lk psiebuu f gfqs`} ij fnqbslfq`zbu fla es`qbs`f `u esbfqba, Qm`u gfqs`} `u
flfnuba fla psiebuuba ui qmfq {b`km`lk ksfabu jis qmb fnqbslfq`zbu. cfuba il
{m`em qmb efl cb sfldba. gf cb buqfcn`umba,
Qmb {b`km`lk ksfabu fla sfldu gf cb ruba `la`z`arfnn is `lqbksfnn. abpbla`lk il
qmb d`la ij f psicnbg, @j iln qmb cbuq fnqbslfq`zb `u ubfsemba jis. iln sfld`lk {`nn
giuqn urjj`eb, [`qm sbupbeq qi fnniefq`il psicnbgu. ksfabu efl u`kl`j qmb
psipisq`ilu ij fnniefq`il sbuirsebu `l feeisafleb {`qm qmb sfldu ij qmb fnqbslfq`zbu,
Qmb qm`sa piuu`c`n`q `u qmfq `ablq`j`efq`il ij ubzbsfn cbuq fnqbslfq`zbu fla qmb abksbb
qi {m`em qmb pfsq`e`pfqb `l qmb qiqfn sbuirseb fnniefq`il fsb ubfsemba jis,
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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Grnq`pnb es`qbs`f fla m`bsfsem`efn uqsreqrsbu fsb pfsq ij f eigpnb} blz`silgblq jfe`lk
flfnuqu {mbl qmb abfn {`qm psicnbgu ij abe`u`il gfd`lk fla esbfq`il ij vrfn`q
gbqmiau jis qmb`s sbuinrq`il `l psfeq`eb, Qmb psbubleb ij a`jjbsblq es`qbs`f. uigb ij
{m`em mfzb qi cb gf}`g`uba fla uigb g`l`g`xba. gbflu qmfq abe`u`ilu fsb gfab `l
qmb eiljn`eq`lk eila`q`ilu fla qmfq `luqsrgblqu gisb jnb}`cnb qmfl f s`k`a
gfqmbgfq`efn qbeml`vrb sbnfqba qi kblr`lb ipq`g`xfq`il mfzb qi cb fppn`ba,
Upbe`fn flfnu`u fla uinrq`il qbeml`vrbu mfzb cbbl abzbnipba jis urem qfudu,
Fgilk qmb giuq `gpisqflq fsb _SIGBQMBB-Csflu bq fn. 60=:). BNBEQSB-Si.
60:=). FM_ -Uffq. 60=?). QI_U@U -M{flk fla Piil. 60=6) fla E_ -Xbnbl.
60=3), Qmbub qbeml`vrbu jfnn `lqi qmb efqbkis ij uijq ipq`g`xfq`il. u`leb qmb rub
mbrs`uq`e pfsfgbqbsu. a`uqfleb gbfursbgblqu. zfnrb uefnbu. bqe, `l faa`q`il qi
gfqmbgfq`efn uqsreqrsbu fla `luqsrgblqu, Drhfe` fla Cihiz` -3??5) psipiuba qmb
giabn jis ubnbeq`lk qmb iskfl`ufq`ilfn uqsreqrsb ru`lk qmb jrxx grnq`'es`qbs`f
flfnu`u, Qmb abzbnipba jrxx grnq`'es`qbs`f gbqmiainik qfdbu `lqi eilu`absfq`il
qmb rlebsqf`lq fla `gpsbe`u`il ij qmb `lprq afqf,
Bfem fcizb gblq`ilba gbqmia mfu ubzbsfn zbsu`ilu -jis b}fgpnb. _sigbqmbb6 fla
3), Qmb fnn mfzb fazflqfkbu fla a`ufazflqfkbu fla qmb`s fppn`efq`il `l a`jjbsblq
fsbfu `la`efqbu qmfq qmiub gbqmiau fsb kbqq`lk `lesbfu`lkn `la`upblu`cnb `l cfed`lk
sbupilu`cnb abe`u`il gfd`lk, Sbeblqn. uqflafsa fla jrxx zbsu`ilu ij gbqmiau fsb
ruba `l pfsfnnbn ui qmfq qmb eigpnb} ij mrgfl urchbeq`z`q. b}pbsq dli{nbakb fla
`len`lfq`il qi rub zbscfn `luqbfa ij lrgbs`efn ksfabu gf cb `lenraba -Qs`flqfpmnnir
fla N`l. 600:4 Cblabs fla U`giliz`e. 3???4 Ablk. 60004 Usbz`e bq fn. 3??34
_fgrfs. 3??0),
Qmb gbqmiau ruba jis giabnn`lk urchbeq`z`ug. fppsi}`gfqb sbfuil`lk fla b}pbsq
dli{nbakb ij abe`u`il gfdbsu. fu {bnn fu zfs`iru jisgu ij mbrs`uq`eu. fsb pfsq ij
sbnfq`zbn sbeblq abe`u`il gfd`lk en`gfqb `l qmb Fsgba Jisebu ij Ubsc`f, Qm`u en`gfqb
mfu csirkmq lb{ qbsg`linik fla `l f ebsqf`l {f f lb{ fppn`efq`il ij gfqmbgfq`eu
fla ipq`g`xfq`il qmbis `l qmb sbfn`uq`e eila`q`ilu ij pnfll`lk fla abe`u`il gfd`lk,
@l qmb Fsgba Jisebu ij Ubsc`f qiaf uqflafsa fla jrxx zbsu`ilu ij grnq`pnb es`qbs`f
gbqmiau fsb ruba `l pfsfnnbn. crq lb{ giabnu ij grnq`pnb es qbs`f abe`u`il gfd`lk
cfuba il jrxx nik`e giabnn`lk fla lbrsi'jrxx giabnn`lk fsb cb`lk abzbnipba
-_fgrfs fla Cifl`. 3?6?4 _fgrfs. 3??04 _fgrfs. 3?6?4 _fgrfs bq fn.
3?66), C giabnn`lk ij jrxx nik`e uuqbgu fla qsf`l`lk ij qmb lbrsi'jrxx giabn.
zbs pi{bsjrn qiinu jis abe`u`il gfd`lk. cfuba il b}pbs`blq`fn dli{nbakb ij qmb
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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ijj`ebsu ij qmb Fsgba Jisebu ij Ubsc`f. fsb esbfqba, Ijj`ebsu b}pbs`blq`fn dli{nbakb
`u qsflujisgba qi frqigfq`e gflfkbgblq -abe`u`il gfd`lk) uqsfqbk qmsirkm
giabnn`lk ij urem uuqbgu, Jrxx ubqu blfcnb vrflq`j`efq`il ij n`lkr`uq`e. `,b,
vrfn`qfq`zb fla `lfeersfqb `ljisgfq`il, Qmbsbjisb. jrxx sbfuil`lk `u `lesbfu`lkn
ruba `l qmb Fsgba Jisebu ij Ubsc`f fu f qbeml`vrb c {m`em mbrs`uq`e srnbu fsb
qsflunfqba `lqi frqigfq`e gflfkbgblq. `,b, abe`u`il gfd`lk. uqsfqbk,
Fppn`efq`il ij qmb jrxx qmbis fla jrxx ubqu `l grnq`'es`qbs`f abe`u`il gfd`lk mfu
eigb `lqi rub u`leb abe`u`il gfdbsu ijqbl feq `l qmb eila`q`ilu ij rlebsqf`lq is ui
efnnba pfsq`fn qsrqmu, Jrxx`j`efq`il ij uqflafsa grnq`pnb es`qbs`f gbqmiau {fu ailb `l
urem f {f qmfq qs`flkrnfs jrxx lrgcbsu {bsb ruba jis abqbsg`lfq`il ij jrxx
{b`km`lk zfnrbu jis es`qbs`f fla fnqbslfq`zbu. arb qi qmb`s u`gpn`e`q `l eigpfs`uil qi
qsfpbxi`a ilbu. {m`nb fnqikbqmbs. jrxx fs`qmgbq`e {fu. ij eirsub. ruba -_fgrfs.
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Abu`kl`lk f g`n`qfs gflfkbgblq uuqbg mfu f nfskb `ljnrbleb il qmb esbfq`il.
fafpqfq`il. b}`uqbleb fla vrfn`q ij qmb uuqbg ipbsfq`il, Li iskfl`ufq`ilfn uuqbg
{`qm`l qmb g`n`qfs efl ipbsfqb `labpblablqn ij `qu gflfkbgblq urcuuqbg
sbupilu`cnb jis `uur`lk eiggflau jis qmb abu`sba cbmfz`irs ij qmb uuqbg. {m`nb
qmb feqrfn cbmfz`irs efl abz`fqb jsig qmb abu`sba,
Qi gbbq qmb sbvr`sbgblqu ij f nfskb lrgcbs ij qsfjj`e fla qsflupisq ubsz`ebu rubsu
fla fq qmb ufgb q`gb bjj`e`blqn fla ps`gfs`n ubsz`e`lk qmb sbvr`sbgblqu ij qmb
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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g`n`qfs. fl iskfl`ufq`ilfn uqsreqrsb qmfq {`nn ureebuujrnn `gpnbgblq fnn qmbub gruq
b}`uq,
Fu pfsq ij qmb Kblbsfn Uqfjj fla qmb Nik`uq`eu abpfsqgblq. qsfjj`e gflfkbgblq `u qmb
m`kmbuq psijbuu`ilfn qsfjj`e frqmis`q ij qmb Ubsc`fl Fsgba Jisebu, Qsfjj`e
gflfkbgblq `u sbupilu`cnb fla feeirlqfcnb jis qmb eila`q`ilu. abzbnipgblq.
gflfkbgblq. iskfl`ufq`il. gil`qis`lk. qsf`l`lk. lisgfq`zb sbkrnfq`il fla qsfjj`e
eilqsin urppisq fla iqmbs qfudu {`qm`l `qu eigpbqbleb,
Bzblqu jsig qmb 0?+u. efnnba jis f sbz`b{ ij qmb iskfl`ufq`ilfn uqsreqrsb ij qmb
qsflupisq urppisq kizbsl`lk cia`bu, Qm`u u`qrfq`il m`kmn`kmqu qmb lbba jis jrsqmbs
uqra ij qmb iskfl`ufq`ilfn uqsreqrsb ij qsfjj`e gflfkbgblq,
1,6, Fl `nnruqsfq`zb fppn`efq`il ij U[IQ flfnu`uQm`u ubeq`il psbublqu fl `nnruqsfq`il ij qmb psipiuba fppsifem urggfs`xba `l qmb
psbz`iru ubeq`il,
@l isabs qi abj`lb qmb kizbsl`lk cia`bu jis qsfjj`e urppisq abu`kl uqsfqbk. f U[IQ
flfnu`u ij `ljnrbleb `,b, ippisqrl`q`bu fla qmsbfqu jsig qmb blz`silgblq il qmb
gflfkbgblq ij qmb qsfjj`e urppisq mfu cbbl ailb. J`krsb 5, U[IQ flfnu`u `u ruba
qi gflfkb qmb qiqfn iskfl`ufq`il. qmb izbsfnn pfqqbsl ij uqsreqrsfn eigpilblqu fla
fssflkbgblq,
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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J`krsb 5, JGG giabn jis U[IQ
Mfz`lk fppn`ba qmb U[IQ flfnu`u. jirs zfs`bq`bu ij qmb qsfjj`e urppisq kizbsl`lk
cia`bu iskfl`ufq`ilfn uqsreqrsb fsb abj`lba8
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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Fnqbslfq`zb 6 -6
F ), Qmb erssblq iskfl`ufq`il ij qmb kizbsl`lk cia`bu ij qmb qsfjj`e
urppisq. abj`lba il qmb cfu`u ij lisgfq`zb sbkrnfq`il jis abqbsg`l`lk qmb
iskfl`ufq`ilfn uinrq`ilu `l qmb g`n`qfs jisgfq`ilu fla b}pbs`bleb ij qmiub
pfsq`e`pfq`lk `l gfd`lk abe`u`ilu, Qmb erssblq iskfl`ufq`il eilu`uqu ij q{iiskfl`ufq`ilfn rl`qu8 Abpfsqgblq ij Qsfjj`e Ipbsfq`ilu fla Abpfsqgblq ij Qsflupisq,
Fnqbslfq`zb 3 -3
F ), Iskfl`ufq`ilfn uqsreqrsb ij qmb kizbsl`lk cia`bu ij qmb qsfjj`e
urppisq fjqbs qmb LFQI uqflafsa,
Fnqbslfq`zb 5 -5
F ), Iskfl`ufq`ilfn uqsreqrsb buqfcn`umba feeisa`lk qi qmb psiebuubu
{mbsb iskfl`ufq`ilfn rl`qu fsb abj`lba jis bfem ij qmiub psiebuubu, Upbe`fn`uqu
`la`upblufcnb jis `gpnbgblq`lk qmbub psiebuubu fsb psbublq `l bfem ksirp, @j qsfjj`e
gflfkbgblq `u z`b{ba fu qmb kizbsl`lk cia is gflfkbgblq ij qmb qsflupisq
urppisq. qmbl `q `u qmb minabs ij qmb `gpnbgblqfq`il ij ebsqf`l psiebuubu,
Fnqbslfq`zb 1 - 3F ),Qmb uqsreqrsb ij qmb qsfjj`e urppisq kizbsl`lk cia`bu ru`lk qmb
nik`uq`e fppsifem fla jrleq`ilfn ps`le`pnb ij iskfl`ufq`il ij qmb psbues`cba frqmis`q.
fu f upbe`j`e gfl`jbuqfq`il ij qmb `lqbslfn a`z`u`il ij nfcirs. a`jjbsblq`fq`il fla
upbe`fn`ufq`il. iskfl`ufq`ilfn rl`qu fla minabsu ij eiggfla fla eilqsin,
1,3, Fuubuugblq. Ulqmbu`u fla Sfld`lkJ`suq uqbpu `l qmb fppn`efq`il ij qmb jrxx gfqmbgfq`efn giabn {irna cb abj`l`lk qmb
ubq ij n`lkr`uq`e abues`pqisu, N`lkr`uq`e zfs`fcnbu fsb sbpsbublqba c f ubq ij n`lkr`uq`e
abues`pqisu 6 3t . .,,,. w. t?.6.,,,. w.`U n n n ` M Q {mbsb Q `u qmb izbsfnn lrgcbs ij
n`lkr`uq`e abues`pqisu, @l qm`u efub qmb lrgcbs ij n`lkr`uq`e abues`pqisu `u 0Q 8
Rlbuublq fn R. Zbs ni{ ZN. Jf`sn ni{ JN. Ni{ N. Gba`rg G. M`km M.
Gba`rg m`km GM. Zbs m`km ZM fla _bsjbeq _, N`lkr`uq`e abues`pqisu mfzb qmb
jinni{`lk zfnrbu. J`krsb 1,
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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J`krsb 1, N`lkr`uq`e abues`pqisu
?. ?
-?,632 ) ?,632 ? ?,632Rn
}
} }
-61)
?,632. ? ?,632
-?,32? ) ?,632. ?,632 ?,32ZNn
} }
} }
-62,)
- ?,632) ?,632. ?,632 ?,32?
-?,5;2 ) ?,632 ?,32? ?,5;2JNn
} }
} }
-6:)
- ?,32) ? ,632. ?,32 ?,5;2-?,2? ) ?,632 ?,5;2 ?,2?Nn} }
} }
-6;)
- ?,5;2) ?,632. ?,5;2 ?,2?
-?,:32 ) ?,632 ?,2? ?,:32Gn
} }
} }
-6=)
- ?,2?) ?,632. ?,2? ?,:32
-?,;2 ) ?,632 ?,:32 ?,;2Mn
} }
} }
-60)
- ?,:32) ?,632. ?,:32 ?,;2
-?,=;2 ) ?,632 ?,;2 ?,=;2
GMn
} }
} }
-3?)
- ?,;2) ?,632. ?,;2 ?,=;2
-6 ) ?,632 ?,=;2 6ZMn
} }
} }
-36)
- ?,=;2) ?,632. ?,=;2 6
6. 6_n
} }
}
-33)
Qi abqbsg`lb qmb sbnfq`zb `gpisqfleb ij qmb bzfnrfq`il es`qbs`f U[IQ. qmb {bsb
pf`s'{`ub eigpfsba {`qm sbupbeq qi qmb kifn c ru`lk qmb jrxxj`ba, @l Qfcnb 6 qmb
bzfnrfq`il ij n`lkr`uq`e es`qbs`ilu jis bfem ij qmb psbublqba fnqbslfq`zbu feeisa`lk qi
icubszba ipq`gfn`q es`qbs`ilu fsb k`zbl,
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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Qfcnb 6, Ipq`gfn`q es`qbs`il nbzbn ij `ljnrbleb il qmb icubszba fnqbslfq`zbu,
Es`qbs`f fla urc'es`qbs`fN`lkr`uq`e es`qbs`f Cblbj`q'eiuq es`qbs`f
F6 F3 F5 F1 G`l Gf}
Uqsblkqmu6, Efpfcnb fla eigpbqblq
pbsuillbnG GM M M
3, Qfeq`efn'ipbsfq`ilfn rl`qu u{`jqa`uniefq`il efpfc`n`q
G ZM M GM
5, Uqsilk gflfkbgblq qbfg G ZM M GM
[bfdlbuubu
6, Lrgcbs ij m`bsfsem`efn nbzbnu M G G G
3, _bsuillbn giq`zfq`ilpiuu`c`n`q`bu
N ZM M M
5, Iskfl`ufq`ilfn uqsreqrsbbjj`e`ble
N ZM G GM
1, Eiisa`lfq`il ZN ZM G ZM
2, Umfs`lk b}pbs`bleb {`qmjisb`kl fsgba jisebu
ZN ZM G _
:, _fsq`fn ipq`g`ufq`il ZM ZN N JN
;, Sbuirsebu b}pni`qfq`il G ZM M ZM
Ippisqrl`q`bu
6, Eiipbsfq`il {`qm jisb`kl
fsgba jisebu N ZM GM ZM
3, N`cbsfn`ufq`il ij pbsuillbnbarefq`il fcsifa
G ZM GM ZM
5, Giabsl `ljisgfq`ilfnqbemlinik`bu `lqsiareq`il `l qmbfsbf ij cru`lbuu iskfl`ufq`il
N ZM G ZM
1, Buqfcn`um`lk ij nik`uq`e urppisqiskfl`ufq`il efpfcnb ijufq`uj`lk eiggfla abgflau
ZN ZM G M
2, Ksirp`lk ij iskfl`ufq`ilfnrl`qu feeisa`lk qi LFQI
uqflafsauN M G ZM
:, _fsq`e`pfq`il `l nik`uq`e urppisqij qmb LFQI jisebu
ZN GM G ZM
Qmsbfqu
6, _in`q`efn fla beilig`e`luqfc`n`q `l Ubsc`f
ZM G ZM M
3, Vrfn`j`ba pbsuillbn irqjni{ ZM GM ZM GM
5, Emflkbu `l nik`uq`e urppisqaieqs`lb
ZM G M M
1, Emflkbu `l qmb eirlqsu
abjbleb aieqs`lb ZM G M M
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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N`lkr`uq`efnn b}psbuuba psbjbsblebu fgilk es`qbs`f mfzb cbbl ruba qi esbfqb f
hrakgblq gfqs`} [ fu k`zbl `l uqbp 1,
Jinni{`lk qmb abe`u`il'gfdbsu es`qbs`il fuubuugblq. lisgfn`ufq`il ij ipq`gfn`q
es`qbs`f ru`lk Bvu, 6 fla 3 `u pbsjisgba, Qmb {b`kmq`lk zbeqis d`h{ ij es`qbs`f gfqs`}
[ {fu abqbsg`lba c fppn`lk Bv, :,
Bfem blqs ij qm`u zbeqis `u qmb urg ij bnbgblqu `l qmb sbnfqba si{ ij gfqs`} [ .
a`z`aba c qmb urg ij fnn `qu bnbgblqu,
-?,53.?,5?.?,3;) ?,55
-?,1?.?,5:.?,53) ?,30
-?,6:.?,6=.?,36) ?,3?
-?,63.?,62.?,3?) ?,6;
u
{
U[IQ
i
q
{
{[
{
{
@l qmb lb}q uqbp qmb hrakgblq gfqs`ebu jis urc'es`qbs`f sbnfqba qi sbupbeq`zb es`qbs`f
{bsb icqf`lba, Sbnfqba urc'es`qbs`f {b`kmq`lk zbeqisu {bsb efnernfqba fu abj`lba c
Bvu, : -Qfcnb 3),
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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Qfcnb 3, Qmb ps`is`q`bu ij qmb U[IQ jfeqisu fla ksirpu
U[IQNiefnps`is`q
U[IQ jfeqisuKnicfnps`is`q`bu
Uqsblkqmu ?,55Efpfcnb fla eigpbqblq pbsuillbn ?,50Qfeq`efn'ipbsfq`ilfn rl`qu u{`jq a`uniefq`ilefpfc`n`q
?,3:
Uqsilk gflfkbgblq qbfg ?,52
[bfdlbuubu ?,30
Lrgcbs ij m`bsfsem`efn nbzbnu ?,63_bsuillbn giq`zfq`il piuu`c`n`q`bu ?,65Iskfl`ufq`ilfn uqsreqrsb bjj`e`ble ?,61Eiisa`lfq`il ?,6;Umfs`lk b}pbs`bleb { qm jisb`kl fsgba jisebu ?,6?_fsq`fn ipq`g`ufq`il ?,6:
Sbuirsebu b}pni`qfq`il ?,6=
Ippisqrl`q`bu ?,3?
Eiipbsfq`il {`qm jisb`kl fsgba jisebu ?,62N`cbsfn ufq il ij pbsuillbn barefq il fcsifa ?,6=Giabsl `ljisgfq`ilfn qbemlinik`bu`lqsiareq`il `l qmb fsbf ij cru`lbuuiskfl`ufq`il
?,?0
Buqfcn`um`lk ij nik`uq`e urppisq iskfl`ufq`ilefpfcnb ij ufq`uj`lk eiggfla abgflau
?,3?
Ksirp`lk ij iskfl`ufq`ilfn rl`qu feeisa`lk qiLFQI uqflafsau
?,63
_fsq`e`pfq`il `l nik`uq`e urppisq ij qmb LFQIjisebu
?,63
Qmsbfqu ?,6;
_in`q`efn fla beilig`e luqfc`n`q l Ubsc`f ?,52Vrfn`j`ba pbsuillbn irqjni{ ?,?;Emflkbu l nik`uq`e urppisq aieqs`lb ?,5?Emflkbu l qmb eirlqsu abjbleb aieqs`lb ?,3;
Mfz`lk abqbsg`lba qmb zfnrb ij qmb {b`km`lk eibjj`e`blqu jis bfem ij qmb icubszba
es`qbs`ilu. gfqs`}J [
`heJ
`u jisgba -Qfcnb 5),
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fcnb 5, Faa`q`zb ulqmbu`u
U[IQ jfeqisu Fnqbslfq`zb 6 Fnqbslfq`zb 3 Fnqbslfq`zb 5 Fnqbslfq`zb 1 [3 [6
Uqsblkqmu U6 -?,660.?,665.?,6?0) -?,660.?,665.?,6?0) -?,?;=.?,?=1.?,?==) -?,?;=.?,?=1.?,?==) ?,50
?.55U3 -?,630.?,6?5.?,?03) -?,630.?,6?5.?,?03) -?,???.?,?3:.?,?5;) -?,???.?,?3:.?,?5;) ?,3:
U5 -?,66:.?,6?=.?,6?3) -?,66:.?,6?=.?,6?3) -?,?;;.?,?=?.?,?=5) -?,?1?.?,?25.?,?:3) ?,52
[bfdlbuub
u[6 -?,?3;.?,?3=.?,?5?) -?,?3;.?,?3=.?,?5?) -?,?6=.?,?36.?,?31) -?,?1:.?,?13.?,?5:) ?.63
?.30
[3 -?,?5?.?,?56.?,?53) -?,?12.?,?13.?,?50) -?,?5?.?,?56.?,?53) -?,?5?.?,?56.?,?53) ?.65
[5 -?,?31.?,?3;.?,?5?) -?,?5:.?,?5:.?,?5;) -?,?31.?,?3;.?,?5?) -?,?:?.?,?25.?,?12) ?.61
[1 -?,?6:.?,?33.?,?3=) -?,?1:.?,?12.?,?1:) -?,?5?.?,?55.?,?5;) -?,?;:.?,?:;.?,?2:) ?.6;
[2 -?,?3=.?,?3;.?,?3;) -?,?3=.?,?3;.?,?3;) -?,?6=.?,?3?.?,?33) -?,?3=.?,?3;.?,?3;) ?.6?
[: -?,?1?.?,?1?.?,?1?) -?,?1?.?,?1?.?,?1?) -?,?1?.?,?1?.?,?1?) -?,?1?.?,?1?.?,?1?) ?.6:
[; -?,?32.?,?30.?,?52) -?,?:5.?,?2=.?,?23) -?,?32.?,?30.?,?52) -?,?:5.?,?2=.?,?23) ?.6=
Ippisqrl`q`bu I6 -?,?6;.?,?36.?,?3;) -?,?15.?,?13.?,?1?) -?,?15.?,?13.?,?1?) -?,?15.?,?13.?,?1?) ?.62
?.3?
I3 -?,?35.?,?3=.?,?51) -?,?2=.?,?22.?,?2?) -?,?2=.?,?22.?,?2?) -?,?52.?,?5;.?,?13) ?.6=
I5 -?,?63.?,?61.?,?6;) -?,?56.?,?30.?,?3:) -?,?56.?,?30.?,?3:) -?,?63.?,?61.?,?6;) ?.?0
I1 -?,?35.?,?3=.?,?5:) -?,?2=.?,?2:.?,?21) -?,?2=.?,?2:.?,?21) -?,?2=.?,?2:.?,?21) ?.3?
I2 -?,?6=.?,?36.?,?32) -?,?1:.?,?13.?,?5;) -?,??0.?,?61.?,?60) -?,?1:.?,?13.?,?5;) ?.63
I: -?,?61.?,?6;.?,?33) -?,?52.?,?51.?,?53) -?,?52.?,?51.?,?53) -?,?52.?,?51.?,?53) ?.63
Qmsbfqu
Q6 -?,?2?.?,?20.?,?;6) -?,63;.?,66=.?,6?:) -?,?2?.?,?20.?,?;6) -?,63;.?,66=.?,6?:) ?.52
?.6;Q3 -?,??0.?,?66.?,?65) -?,?33.?,?36.?,?60) -?,?65.?,?61.?,?6:) -?,?33.?,?36.?,?60) ?.?;
Q5 -?,?;:.?,?;:.?,?;:) -?,?;:.?,?;:.?,?;:) -?,?;:.?,?;:.?,?;:) -?,?;:.?,?;:.?,?;:) ?.5?
Q1 -?,?:0.?,?:0.?,?:0) -?,?:0.?,?:0.?,?:0) -?,?:0.?,?:0.?,?:0) -?,?:0.?,?:0.?,?:0) ?.3;
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{mbsb qmb gfqs`} bnbgblqu `he fsb efnernfqba ru`lk Bv, 6?,
6 3 5 1
-?,5?.?,53.?,5:) -?,5:.?,53.?,5?) -?,6:.?,60.?,36) -?,63.?,6:.?,60)
-?,3?.?,36.?,35) -?,31.?,3:.?,35) -?,60.?,36.?,35) -?,5?.?,55.?,52)
-?,?;.?,?=.?,66) -?,30.?,56.?,53) -?,3:.?,3;.?,30) -?,3:.?,3;.?,3
F F F F
J
?,55
?,30
0) ?,3?
-?,61.?,61.?,6;) -?,5?.?,56.?,53) -?,36.?,35.?,32) -?,30.?,56.?,51) ?,6;
Qfcnb 1, J`lfn sfld`lk ij fnqbslfq`zbu
Abe`u`ilfnqbslfq`zb
@lab} ij ipq`g`ug
J`lfn sfld7?,?-pbuu`g`uq`e)
7?,2
-giabsfqb)
76,?
-ipq`g`uq`e)
Fnqbslfq`zb 6 ?,3?2 ?,363 ?,33? 1Fnqbslfq`zb 3 ?,3=2 ?,302 ?,5?2 6
Fnqbslfq`zb 5 ?,36? ?,33? ?,35? 5
Fnqbslfq`zb 1 ?,312 ?,322 ?,3:2 3
Qmb fuubuugblq ij fnqbslfq zbu mfu cbbl pbsjisgba ru`lk sbnfq`ilu 6? fla 63, Qmb
j`lfn fnqbslfq`zb pbsjisgfleb {b`kmqu. {`qm sbupbeq qi qmb izbsfnn kifn. mfzb cbbl
efnernfqba c Bv, 53 fu8
6
3
5
1
-?,3?.?,36.?,35)
-?,3=.?,30.?,53)
-?,3?.?,33.?,31)
-?,33.?,3:.?,3;)
Z
ZZ
Z
Z
Jis qmb qp`efn zfnrbu ij qmfq b}psbuu qmb abe`u`il'gfdbsu fqq`qrab qi{fsa s`ud. qmb
j`lfn sfld`lk ij fnqbslfq`zbu `u icqf`lba c fppn`lk Bv, 65, Qmb lisgfn`uba zfnrbu
psbublqba `l Qfcnb 1 umi{ qmfq Fnqbslfq`zb 3 `u qmb cbuq, @q `u jinni{ba c Fnqbslfq`zb
1. Fnqbslfq`zb 5 fla Fnqbslfq`zb 6 sbupbeq`zbn. sbkfsanbuu ij qmb abe`u`il'gfdbsunbzbn ij ipq`g`ug,
C ru`lk qmb eblqsb ij ksfz`q gbqmia qi abjrxx`j qmb Z zfnrbu k`zbl fcizb. qmb
j`lfn {b`kmqu ij fnqbslfq`zbu icqf`lba fjqbs lisgfn`xfq`il {bsb8 ?,365 -Fnqbslfq`zb 6).
?,30; -Fnqbslfq`zb 3). ?,33? -Fnqbslfq`zb 5) fla ?,325 -Fnqbslfq`zb 1), Icz`irun. qmb
j`lfn sfld`lk `u bvrfn qi qmb psbz`iru ilb,
2, A@UERUU@IL FLA EILENRU@IL
Iskfl`ufq`il `u liq f urg ij gbemfl`efn pfsqu. sfqmbs fl #iskfl`e {minb# {`qm fprspiub fla g`uu`il, @l qmb psiebuu ij abu`kl`lk qmb iskfl`ufq`ilfn uqsreqrsb `q `u
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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lbebuufs. mfz`lk abj`l`lk qmb ichbeq`zbu fla abu`kl es`qbs`f. qi flfnub qmb uqfqb ij
qmb iskfl`ufq`il,
@l faa`q`il qi iskfl`ufq`ilu ipbsfq`lk `l fl rlebsqf`l blz`silgblq. qmbsb `u f abksbb
ij rlebsqf`lq fla `gpsbe`u`il ij es`qbs`f ruba `l qmb psiebuu ij iskfl`ufq`ilfn
abu`kl, Jrxx grnq`'es`qbs`f fppsifem abzbnipba `l qm`u pfpbs fnni{u qmb
vrflq`j`efq`il ij qmbub es`qbs`f fla ubnbeq`il ij qmb cbuq fnqbslfq`zb irq ij psipiuba
iskfl`ufq`ilfn giabnu, Qmb psbublqba giabn blfcnbu qmb bzfnrfq`il ij qmb psipiuba
ipq`ilu ij iskfl`ufq`ilfn uqsreqrsb. sbkfsanbuu ij qmb lrgcbs ij ipq`gfn`q es`qbs`f fla
urc'es`qbs`f, Qmb giabn fnni{u jis qmb emi`eb ij cbuq fnqbslfq`zb jsig f ubq abues`cba
ru`lk D ipq`gfn`q es`qbs`f fla urc'es`qbs`f, Qmb es`qbs`f abues`cba efl cb ij cblbj`q
is eiuq qpb, Qmb es`qbs`f sbnbzflq qi qmb abu`kl ij iskfl`ufq`ilu fu {bnn fu qmb`s
`ljnrbleb il qmb emi`eb ij fnqbslfq`zbu mfzb qmb`s zfnrbu a`upnfba fu lrgbs`efn
zfnrbu is jrxx n`lkr`uq`e abues`pqisu, U`leb qmb psiebuu ij iskfl`ufq`ilfn abu`kl
ijqbl `lzinzba f lrgcbs ij b}pbsqu. qmb giabn fnni{u jis f piuu`c`n`q ij ipq`gfn`q
es`qbs`f zfnrbu ulqmbu`u `l efub ij ksirp abe`u`il'gfd`lk, Abe`u`il'gfd`lk `l f
ksirp a`jjbsu jsig `la`z`arfn abe`u`il'gfd`lk il gbqmiainik`efn fla gfqmbgfq`efn
nbzbnu, Ksirp ulqmbubu {`qm eigpnbqb fla `leigpnbqb `ljisgfq`il fsb a`ueruuba `l
qmb giabn, @l faa`q`il. qmb giabn blfcnbu eigpfs`uil ij qmb es`qbs`il jrleq`ilu
irqprq zfnrbu ru`lk q{i gbqmiau abpmfu`j`efq`il ij qmb eblqsb ij ksfz`q fla qmb qiqfn
`lqbksfn zfnrb gbqmia,
Fppn`efq`il ij qmb k`zbl giabn `u umi{l il qmb b}fgpnb ij abu`kl`lk qmb
iskfl`ufq`ilfn uqsreqrsb ij qmb kizbsl`lk cia`bu ij qsflupisq urppisq, Qmb eigpnb}
blz`silgblq. `l {m`em qmbub kizbsl`lk cia`bu feq. aibu liq qinbsfqb iskfl`ufq`ilfn
`gpsiz`ufq`il. sfqmbs sbvr`sbu f pnfllba fla gbqmiainik`efn iskfl`ufq`ilfn psihbeq
fla `qu eiluqflq gia`j`efq`il fla fafpqfq`il, Ubnbeq`il ij qmb fppsips`fqb
iskfl`ufq`ilfn uqsreqrsb `u ilb ij qmb giuq u`kl`j`eflq abe`u`ilu. fu qmb efpfc`n`q`bu ij
qmb kizbsl`lk uuqbg {`nn cb u`kl`j`eflqn uni{ba ai{l `j fl iskfl`ufq`ilfn uqsreqrsb
`u `lfabvrfqb jis qmb e`serguqflebu `l {m`em qmb iskfl`ufq`il `u,
Fnqmirkm qmb giabn fppn`efq`il {fu umi{l il qmb b}fgpnb ij abu`kl`lk kizbsl`lk
cia`bu {`qm`l qmb fsgba jisebu. `q piuubuubu ksbfq jnb}`c`n`q fla efl cb fafpqba qi
fl pfsq`ernfs psicnbg, Zbs bfu`n. {`qm g`lis gia`j`efq`ilu. `q efl cb fppn`ba jis qmb
ubnbeq`il ij iskfl`ufq`ilfn uqsreqrsb ij fl cru`lbuu uuqbg,
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Qm`u pfpbs `u f pfsq ij qmb psihbeq jrlaba c qmb G`l`uqs ij abjbleb ij qmb Sbprcn`e
ij Ubsc`f fla Rl`zbsu`q ij abjbleb ij qmb Sbprcn`e ij Ubsc`f. _sihbeq lrgcbs8
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SBJBSBLEBUCblabs GH. U`giliz`e U_ -3???), F jrxx eigpsig`ub fppsifem qi {fqbs sbuirsebu
uuqbgu pnfll`lk rlabs rlebsqf`lq, Jrxx Ubq, Uuq,.6628 52'11,
Cixfl`e A. _fgrefs A -3?6?), Bzfnrfq`lk niefq`ilu jis s`zbs esiuu`lk ru`lk jrxx
nik`e, G`n`q, Qbeml, Eirs,. 68 630'612,
Csflu H_. Z`ledb _. Gfsbuemfn C -60=:), Mi{ qi ubnbeq fla mi{ qi sfld psihbequ c
qmb _sigbqmbb gbqmia, Brs, H, Ipbs, Sbu,. 318 33='35=,
Ablk M -6000), Grnq`es`qbs`f flfnu`u {`qm jrxx pf`s{`ubeigpfs`uil, @lq, H, Fppsi},Sbfuil,. 368 362'356,
M{flk EN. Piil DU -60=6), Grnq`pnb fqqs`crqb abe`u`il gfd`lk8 gbqmiau fla
fppn`efq`ilu, Ups`lkbs. Cbsn`l,
Drhfe`e G. Cihiz`e L -3??5), Iskfl`xfq`ilfn abu`kl ij piuq eispisfq`il uqsreqrsb
ru`lk jrxx grnq`es`qbs`f abe`u`il gfd`lk, Eigprq, Gfqmbgfq`efn Iskfl, Qmbis. 08
2'6=,
N`ir QU. [flk GHH -6003), Sfld`lk jrxx lrgcbsu {`qm `lqbksfn zfnrb, Jrxx Ubq,
Uuq,. 2?8 31;'32:,
_fgrefs A -3??0), Abu`kl ij qmb iskfl`ufq`ilfn uqsreqrsb ru`lk jrxx nik`e
fppsifem, Gfuqbs pfpbs, Ubsc`f8 Jfernq ij Qsflupisq fla Qsfjj`e Blk`lbbs`lk.
Cbnksfab,
_fgrefs A -3?6?), Ru`lk jrxx nik`e fla lbrsfn lbq{isdu ars`lk abe`u`il gfd`lk
psiebu `l qsflupisq, G`n`q, Qbeml, Eirs,. 58 632'615,
_fgrefs A. Cixfl`e A. Aisiz`e C. G`n`e F -3?66f), Giabnn`lk ij qmb jrxx nik`efn
uuqbg jis ijjbs`lk urppisq `l gfd`lk abe`u`ilu {`qm`l qmb blk`lbbs`lk rl`qu ij qmb
Ubsc`fl fsg, @lq, H, _mu, Ue`. 58 203':?0,
Si C -60:=), Sfld`lk fla ubnbeq`il `l qmb psbubleb ij grnq`pnb z`b{pi`lqu, Eigprq,
Ipbs, Sbu,. =8 2;';2,
Uffq QN -60=?), Qmb flfnq`e m`bsfsem psiebuu, GeKsf{'M`nn. Lb{ Pisd,
Usabz`e C. Gbab`siu P. Usabz`e X. Uemfbs G -3??3), Bzfnrfq`lk gflfkbgblq
uqsfqbk`bu `l _fsfkrfer s`zbs cfu`l c flfnq`e m`bsfsem psiebuu, J`suq C`bll`fn
8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in
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Gbbq`lk ij qmb @lqbslfq`ilfn Blz`silgblqfn Giabn`lk fla Uijq{fsb Uie`bq. 68 13'
1;,
Qs`flqfpmnnir B. N`l EQ -600:), Abzbnipgblq fla bzfnrfq`il ij j`zb grnq`fqqs`crqb
abe`u`il gfd`lk gbqmiau, @lq, H, Fppsi}, Sbfuil,. 618 3=6'56?,
Xfabm NF -60:2), Jrxx ubqu, @lj, Eilqsin, =8 55='525,
Xbnbl G -60=3), Grnq`pnb e`qbs`f abe`u`il gfd`lk, GeKsf{'M`nn Ciid Eigpfl. Lb{
Pisd,
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