A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy...

download A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in an SWOT analysis

of 25

Transcript of A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy...

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    1/25

    6

    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

    Uqsfqbk`e gflfkbgblq `u qmb psiebuu c {m`em gflfkbsu jisgrnfqb fla `gpnbgblq

    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

    2/25

    3

    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

    3/25

    5

    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

    4/25

    1

    ' 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

    5/25

    2

    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

    6/25

    :

    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.

    3?6?),

    F lb{ jrxx gfqmbgfq`efn gbqmia psbublqba `l qm`u pfpfbs mfu cbbl abzbnipba jis

    sbubfsem `l qmb Fsgba Jisebu ij Ubsc`f, Qmb abzbnipba gbqmia `u cfuba il

    bzfnrfq`il ij fnqbslfq`zbu c fppn`efq`il ij jrxx n`lkr`uq`e abues`pqisu, @q gfdbu qmb

    psiebarsb ij fnqbslfq`zbu sfld`lk grem bfu`bs `l u`qrfq`ilu {mbsb f ksbfq lrgcbs ij

    emfsfeqbs`uq`eu fla pfsfgbqbsu jis abe`u`il gfd`lk fsb psbublq, @j qmbsb fsb gisbnbzbnu ij es`qbs`il `gpisqfleb `l qmb psicnbg ij fnqbslfq`zb sfld`lk. qmb abues`cba

    psiebarsb `u eilareqba fq bfem icubszba nbzbn, Fq bfem nbzbn. qmb eibjj`e`blqu ij

    es`qbs`il' urc es`qbs`il `gpisqfleb mfz`lk fl `gpfeq il qmb eirsub ij sfld`lk `u

    abj`lba. {`qm qmb nbzbn ij sfld`lk cb`lk liq lbebuufs`n qmb ufgb jis fnn qmb es`qbs`f,

    Qmb j`lfn sfld`lk ij qmb fnqbslfq`zbu `u gfab fq sfld`lk xbsi nbzbn,

    Emfsfeqbs`uq`eu ij uigb grnq`pnb es`qbs`f gbqmiau mfu cbbl psbublqba `l qmb j`suq pfsq

    ij qmb pfpbs, @l qmb eilq`lrfq`il. f lb{ giabn jis qmb ubnbeq`il ij ipq`gfn zfs`flqu ijiskfl`ufq`il cfuba il jrxx nik`e mfu cbbl abzbnipba uqfsq`lk jsig qmb sbnbzflq

    qmbis fppsifem, Jrxx gfqmbgfq`efn giabn -JGG) `u fppn`ba `l qmb U[IQ flfnu`u

    -JG+[IQ giabn) qi ipq`g`xb qmb b}`uq`lk iskfl`ufq`ilfn uqsreqrsb ij qmb kizbsl`lk

    cia`bu ij qsflupisq urppisq, Qmb emi`eb ij iskfl`ufq`ilfn giabnu `u gfab ru`lk

    Jrxx grnq`'es`qbs`il fla uqflafsa qbeml`vrbu ij grnq`'es`qbs`il abe`u`il gfd`lk, Qmb

    fjisbgblq`ilba giabn `u umi{l `l qmb jinni{`lk ubeq`il ij qmb pfpbs,

    5, JG+[IQ GIABN

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    7/25

    ;

    @l qmb psiebuu ij abu`kl`lk qmb iskfl`ufq`ilfn uqsreqrsb. ebsqf`l abe`u`ilu mfzb qi cb

    gfab, Urchbeq`zb bzfnrfq`il ij ebsqf`l pfsfgbqbsu a`jjbs jsig ilb abe`u`il'gfdbs qi

    fliqmbs. `q `u {isqm pi`lq`lk irq, Vr`qb f eilzbl`blq fppsifem `l vrflq`j`lk qmbub

    pfsfgbqbsu `u jrxx ubq qmbis,

    5,6, Jrxx ubqu

    Jrxx ubqu qmbis abj`lbu jrxx ubq F fu f ubq ij isabsba pf`su -Xfabm. 60:2)8

    . . ? 6 .F F F } } } ] }

    {mbsb F } `u f gbgcbsum`p jrleq`il {m`em umi{u qi {mfq b}qblq } ] gbbqu qmb

    es`qbs`ilu jis gbgcbsum`p `l f ubq F, Jis qmb gbgcbsum`p jrleq`il ? 6F } .

    jis bzbs } F . `,b, 8 ?.6F ] ,

    Feeisa`lk qi qmb jrxx qmbis qmb emi`eb ij gbgcbsum`p jrleq`ilu `,b, qmb jisg ij qmb

    jrleq`il fla eilj`ableb `lqbszfnu {`aqm fsb rurfnn gfab cfuba il urchbeq`zb

    buq`gfqbu is b}pbs`bleb, Qmb giuq eiggiln ruba fsb qsfpbxi`afn fla qs`flkrnfs

    jrxx lrgcbsu, Qs`flkrnfs jrxx lrgcbsu {`qm gbgcbsum`p jrleq`ilu umi{l `l

    J`krsb 6 fsb ruba `l qm`u pfpbs,

    J`krsb 6, Qs`flkrnfs jrxx lrgcbs

    Qs`flkrnfs jrxx lrgcbsu fsb rurfnn k`zbl `l qmb jisg6 3 5

    - . . )F f f f . {mbsb3

    f `u

    qmb zfnrb {mbsb qmb gbgcbsum`p jrleq`il ij qmb jrxx lrgcbs `u 6,?. 6f `u qmb nbjq

    a`uqs`crq`il ij qmb eilj`ableb `lqbszfn fla5

    f qmb s kmq a`uqs`crq`il ij qmb eilj`ableb

    `lqbszfn ij qmb jrxx lrgcbs F ,

    Jrxx lrgcbs F gbgcbsum`p jrleq`il `u abj`lba fu8

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    8/25

    =

    6

    66 3

    3 6

    5

    3 5

    5 3

    5

    ?.

    .

    .

    ?.

    F

    } f} f

    f } ff f

    }f }

    f } ff f

    } f

    Jis abjrxx`j`efq`il fla gfpp`lk ij qmb jrxx lrgcbs6 3 5

    - . . )F f f f zfnrb `lqi f sbfn

    lrgcbsu. lrgbsiru gbqmiau fsb ruba. J`krsb 3,

    J`krsb 3, Abjrxx`j`efq`il

    Q{i gbqmiau mfzb cbbl ruba `l qm`u pfpbs8

    'Qmb eblqsb ij ksfz`q8

    6

    5 6 3 6 6F7 5abjrxxp f f f f f

    ' Qmb qiqfn `lqbksfn zfnrb8 65 3 6F7 6 3abjrxxp f f f

    -{`qm . ?.6

    cb`lk fl ipq`g`ug `lab})

    5,3, Cfu`e giabn

    @q `u emfsfeqbs`uq`e jis fnn grnq`'es`qbs`f psicnbgu qmfq qmbsb fsb grnq`pnb es`qbs`f `l

    abe`u`il'gfd`lk fla zfs`iru fnqbslfq`zbu qi ubnbeq qmb giuq fppsips`fqb feq`il,

    A`jjbsblq iskfl`ufq`ilu bzfnrfqb zfs`flq uinrq`ilu fla ipq`gfn zfs`flqu ru`lk qmb

    JGG giabn abues`cba `l qmb eilq`lrfq`il,

    U[IQ flfnu`u `u ruba jis fuubuu`lk {mfq qi bn`g`lfqb. pfsq`fnn dbbp is dbbp qi

    abj`lb abu`kl uqsfqbk`bu jis abu`kl`lk iskfl`ufq`ilfn uqsreqrsb, Ru`lk flfnu`u ij

    uqsblkqmu. {bfdlbuubu. ippisqrl`q`bu fla qmsbfqu jis qmb k`zbl iskfl`ufq`il.

    ipq`g`ufq`il giabn ij jrleq`il`lk `u psipiuba,

    Jrxx gfqmbgfq`efn giabn `lenrabu qmb jinni{`lk uqbpu8

    Uqbp 6, @ablq`j U[IQ urc'jfeqisu fla abqbsg`lfqb qmb fnqbslfq`zb uqsfqbk`bu

    feeisa`lk qi qmb U[IQ urc'jfeqisu, Abqbsg`lb qmb `gpisqfleb abksbbu ij qmb

    U[IQ jfeqisu,

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    9/25

    0

    @j qmb giabn ruba jis bzfnrfq`il ij fnqbslfq`zbu ij qmb fnsbfa psipiuba

    iskfl`ufq`ilfn uqsreqrsb fnqbslfq`zbu. qm`u uqbp `u ig`qqba, Qmb jinni{`lk uqbpu {`nn

    sbpsbublq f kblbsfn efub {mbsb D `u eilu`absba jsig qmb pi`lq ij a`jjbsblq ipq`gfn`q

    es`qbs`f `l qbsgu ij {m`em qmb cbuq fnqbslfq`zb jis f j`l`qb ubq ij fnqbslfq`zbu `u

    abqbsg`lba 6 3. . . . 3l F f f f l , Ipq`grg es`qbs`ilu fsb jisgfnn k`zbl fu

    6. . . .D d D . {mbsb D `u qmb izbsfnn lrgcbs ij qmb es`qbs`f eilu`absba,

    Grnq`pnb'fqqs`crqb psicnbg `l qmb abe`u`il'gfd`lk `u sbpsbublqba c qmb gfqs`} J

    a`gblu`il D F ,

    6

    66 66

    6

    6

    ,,,l g l

    l g l

    d dl g dld

    D Dl g DlD

    F F F

    j j j D

    J j j j D

    j j j D

    {mbsb 6. . 6.d` j ` F d D `u qmb n`lkr`uq`e is lrgbs`efn zfnrb ij qmb ipq`grg es`qbs`il

    d D jis fnqbslfq`zbu f f F , @j fq nbfuq ilb es`qbs`il `u abues`cba c n`lkr`uq e

    b}psbuu`il `l qmb abues`pq`il ij qmb ipq`grg es`qbs`il. uqbp 3 `u qfdbl,

    Uqbp 3, Abj`l`lk qmb ubq ij n`lkr`uq`e abues`pqisu, Es`qbs`il zfnrbu fsb abues`cba c f

    ubq ij n`lkr`uq`e abues`pqisu 6 3. . . . ?. .`U n n n ` M Q . {mbsb Q `u qmb izbsfnn

    lrgcbs ij n`lkr`uq`e abues`pqisu, N`lkr`uq`e zfs`fcnbu fsb sbpsbublqba c qs`flkrnfs

    jrxx lrgcbsu 6 3 5- . . )F f f f ,

    Uqbp 5, Lisgfn`ufq`il ij qmb ipq`g`ufq`il es`qbs`il, Jis qmb zfnrb 6. . 6.d` j ` F d D qi

    cb eigpfsfcnb. `q `u lbebuufs qi lisgfn`ub qmbg, @j qmb ipq`g`ufq`il es`qbs`f fsb

    k`zbl fu n`lkr`uq`e zfnrbu 6. . 6.d` j ` F d D . .d`

    d` d` jj j lisgfn`ufq`il `u

    pbsjisgba fu jinni{u8

    ' jis qmb cblbj`q es`qbs`il d d D lisgfn`ufq`il `u pbsjisgba fu jinni{u8

    gf}

    dd l

    d

    ``j

    j

    j -6)

    {mbsb gf}dj `u gf} zfnrb ij qmb jrxx lrgcbs - 6. . )d` j d D . jis

    ?d` d`j j ' jis qmb eiuq es`qbs`il d d D lisgfn`ufq`il `u pbsjisgba fu jinni{u8

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    10/25

    6?

    g`l

    gf}6 d` d

    `d ld

    j jj

    j

    -3)

    {mbsb g`ldj `u g`l`grg zfnrb ij qmb jrxx lrgcbs - 6. . )d` j d D . jis

    ?d`

    d`jj ,

    Qmb lisgfn`uba zfnrb ij qmb es`qbs`il - )d d D jis - )f f F fnqbslfq`zb `u abues`cba

    c jrxx lrgcbs8

    .`d

    `d `d jllj j -5)

    @j qmb ipq`gfn`q es`qbs`f fsb abues`cba `l lrgbs`efn zfnrbu 6. . 6.d` j ` F d D .

    lisgfn`ufq`il `u pbsjisgba fu jinni{u8

    66

    . 6d

    d`

    Dd`d` d`

    d

    Dj

    jj j

    -1)

    Uqbp 1, Bzfnrfq`il es`qbs`f, 6. . . .D d D `u f ubq ij ipq`gfn`q es`qbs`f. {mbsb D

    `u qmb izbsfnn lrgcbs ij qmb eilu`absba es`qbs`f, Bzbs es`qbs`il efl cb a`ufkksbkfqba

    `lqi urc'es`qbs`f, @jhd `u qmb izbsfnn lrgcbs ij urc'es`qbs`f `l h

    qm es`qbs`il qmb izbsfnn

    lrgcbs ij es`qbs`ilu efl cb k`zbl fu8

    6

    l

    h

    h

    D d

    -2)

    Bzbs es`qbs`il mfu qi cb a`z`aba `lqi urc'es`qbs`f, @l qmfq efubhd ij qmb es`qbs`il

    bvrfnu 6, Qm`u `u `gpisqflq jis rlabsuqfla`lk qmb fkksbkfq`il psiebuu ij hrakgblqu

    gfab fq q{i eiluberq`zb m`bsfsem`efn nbzbnu. {mbsb es`qbs`f fla urc'es`qbs`f fsb

    niefqba, Mbsb es`qbs`f fla urc'es`qbs`f fsb fkksbkfqba c um`jq`lk es`qbs`f fq qmb urc'

    es`qbs`f nbzbn, Fjqbs qmfq um`jq. qmb {minb es`qbs`f nbzbn aibu liq b}`uq flgisb,

    Sbnfq`zb `gpisqfleb ij qmb ipq`gfn`q es`qbs`il . 6. .dd d D [ d D `u a`jjbsblq,

    Qmb zfnrb sbpsbublq`lk qmb `gpisqfleb ij qmb ipq`gfn`q es`qbs`f `u abqbsg`lba c

    jisg`lk f gfqs`}D D

    d`h{[

    , Bnbgblqu ij qmb gfqs`} fsb n`lkr`uq`e abues`pqisu fla

    lrgbs`efn zfnrbu ruba qi abues`cb qmb `gpisqfleb ij qmb es`qbs`il d d D qi

    es`qbs`il d d D , Mfz`lk buqfcn`umba [ gfqs`}. lisgfn`ufq`il ij qmb {b`kmq

    eibjj`e`blqu `u pbsjisgba8

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    11/25

    66

    6

    6

    . 6. ?.6

    h

    h

    Dh d

    h

    d`h d d D

    h dh

    { { {{

    {

    -:)

    {mbsb h sbpsbublqu qmb psbjbsbleb ij abe`u`il gfdbs qi fqqs`crqb ` ,

    Qmb psiebuu ij abu`kl`lk qmb iskfl`ufq`ilfn uqsreqrsb `u giuq ijqbl `l qmb mflau ij

    gisb qmfl ilb b}pbsq `,b, abe`u`il'gfdbs, @l qm`u efub. ipq`gfn`q es`qbs`f bzfnrfq`il

    ij fnn qmb ksirp gbgcbsu umirna j`suq cb icqf`lba qi pfuu il qi qmb lbebuufs

    ulqmbu`u fla qmbl qi uqbp 2, @l iqmbs efubu. uqbp : `u qfdbl,

    Uqbp 2, Bzfnrfq`lk qmb es`qbs`f `l efub ij ksirp bzfnrfq`il, @l ksirp abe`u`il'gfd`lk.

    qmbsb `u ksirp ulqmbu`u {`qm eigpnbqb fla `leigpnbqb `ljisgfq`il,

    @l efub ij ksirp ulqmbu`u {`qm eigpnbqb `ljisgfq`il. psiz`aba qmfq fnn qmb gbgcbsu

    - 6.3.,,,. )b l ij qmb ksirp K fsb eilu`absba bvrfn `l qmb abe`u`il gfd`lk fla qmfq fnn

    qmb bzfnrfq`il ij qmb ipq`gfn`q es`qbs`il jis qmb k`zbl m`bsfsem mfzb cbbl

    pbsjisgba. qmbsb fsb q{i {fu jis ps`is`q`u`lk qmb fnqbslfq`zbu sbnfq`zb qi qmb kifn,

    Ilb `u qi fkksbkfqb fnn qmb icqf`lba ps`is`q es`qbs`il zbeqisu jis bzbs abe`u`il'

    gfdbs ru`lk qmb jinni{`lk bvrfq`il8

    6

    - )l

    K

    ` b `

    b

    { { b

    -;)

    {mbsb - )`{ b `u qmb {b`kmq zfnrb {m`em `u qmb l qm gbgcbs ij qmb ksirp K .

    - 6.3. ,,,. )b l jis qmb fnqbslfq`zb `F . b `u qmb {b`kmq zfnrb -u`kl`j`efleb) ij qmb l qm

    gbgcbs ij qmb ksirp. fla K`{ `u qmb rnq`gfqb ps`is`q ij qmb fnqbslfq`zb `F , @la`z`arfn

    {b`kmqu ij qmb b ksirp gbgcbsu mfzb j`suq cbbl faa`q`zbn lisgfn`uba, Qmb

    asf{cfed ij qmb psbublqba psiebarsb `u qmfq `q `u liq fppn`efcnb `l efub ij ksirp

    ulqmbu`u {`qm `leigpnbqb `ljisgfq`il. fu qmbsb fsb li eigpiu`qb zbeqisu jis ebsqf`l

    gbgcbsu ij qmb ksirp,Fliqmbs {f `u qi `ggba`fqbn fkksbkfqb fnn qmb `la`z`arfn psbjbsbleb fuubuugblqu

    il fnn m`bsfsem`efn nbzbnu,

    66 6 6

    66 6 66

    h

    h

    l l ll l ll

    h d

    ` h `h h `h h `h

    ` h h hh

    d

    dh

    `h D

    {{ f f{

    {f

    6

    6. ?.6d

    h

    D

    d{ {

    -=)

    {mbsb h sbpsbublqu qmb psbjbsbleb ij qmb abe`u`il'gfdbs qi fqqs`crqb ` ,

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    12/25

    63

    L efub ij ksirp ulqmbu`u {`qm `leigpnbqb `ljisgfq`il. g`esifkksbkfq`il ij qmb

    .` h piu`q`il fq qmb k`zbl gfqs`} `u ailb c kbigbqs`e gbfl ij qmb fuubuugblqu ij

    qmiub ksirp gbgcbsu {mi b}psbuuba psbjbsbleb `B eigpfsba qi qmb bnbgblq hB ,

    Qmb sbvr`sbgblq `l qm`u efub `u jis fq nbfuq ilb abe`u`il gfdbs qi abenfsb il qmb

    zfnrb ij`hf , Gia`j`lk qmb psbz`iru b}psbuu`il8

    66 66

    66 66 h

    h

    l GKGl l ll

    h dK

    ` h `h h `h h `hd`h

    `n N h hhh

    D K

    d

    {{ f n f f{

    {

    6

    6. ?.6d

    h

    D

    d{ {

    -0)

    {mbsbn

    `u f ubq ij ksirp gbgcbsu {mi mfzb bzfnrfqba qmb pf`s ij bnbgblqu .

    ` hB B

    .

    fla G `u qmb lrgcbs ij urem gbgcbsu,

    Uqbp :, Bzfnrfq`lk fnqbslfq`zbu, Mfz`lk abqbsg`lba qmb zfnrbu ij qmb {b`kmq

    eibjj`e`blqu jis fnn qmb fuubuuba es`qbs`ilu. f gfqs`}J [

    `heJ

    `u jisgba {mbsb qmb

    gfqs`} bnbgblqu `he fsb icqf`lba ru`lk qmb jinni{`lk b}psbuu`il8

    6

    `h`h dh

    d`

    d``

    j

    j

    e {

    -6?)

    {mbsb d`j

    `u qmb zfnrb ij qmb es`qbs`il jrleq`il jis qmb fnqbslfq`zb - 6. )` ` F fla

    es`qbs`il d d D

    . fla `hd{

    `u qmb zfnrb ij qmb {b`kmq eibjj`e`blq jis qmb es`qbs`il

    d d D,

    Faa`q`zb ulqmbu`u mfu cbbl fuurgba mbsb fla qmb j`lfn fnqbslfq`zb pbsjisgfleb

    {b`kmqu {`qm sbupbeq qi izbsfnn kifn fsb efnernfqba c qmb urggfq`il ij bnbgblqu `l

    qmb si{u ij qmb pbsjisgfleb gfqs`}J [

    `heJ

    fu8

    6

    D

    ` `h h

    h

    e e {

    -66)

    Zfnrb ij qmb es`qbs`il jrleq`ilu `Z jis bzbs fuubuuba fnqbslfq`zb `u icqf`lba jsig qmb

    J gfqs`} ru`lk qmb b}psbuu`il8

    6

    . - )h

    D

    ` hZ e d D

    -63)

    Qi j`lfnn sfld qmb fnqbslfq`zbu. qmb ps`is`q`ufq`il ij fkksbkfqba fuubuugblqu `u

    sbvr`sba, U`leb bfem`

    Z `u f qs`flkrnfs jrxx lrgcbs. `q `u lbebuufs qi fppn qmb

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    13/25

    65

    gbqmia ij sfld`lk qs`flkrnfs jrxx lrgcbsu, Qmbsb fsb ubzbsfn gbqmiau qmfq efl ai

    qm`u urem fu qmb eblqsb ij ksfz`q gbqmia. qmb aig`lfleb gbfursb gbqmia. qmb '

    erq {`qm `lqbszfn ulqmbu`u gbqmia fla qmb qiqfn `lqbksfn zfnrb gbqmia, Qmb nfuq ilb

    qiqfn `lqbksfn zfnrb gbqmia -N`ir fla [flk. 6003). `u eilu`absba qi cb f kiia

    emi`eb jis pbsjisg`lk qmb qfud bjj`e`blqn fla. qmbsbjisb. mfu cbbl psipiuba {`qm`l

    qm`u gbqmiainik, Jis qmb k`zbl qs`flkrnfs jrxx lrgcbs6 3 5

    - . . )F f f f qmb qiqfn

    `lqbksfn zfnrb `u abj`lba fu8

    65 3 6@ -F)7 6 3 . ?.6Q f f f -65)

    @l Bv, 65. sbpsbublqu fl ipq`g`ug `lab} {m`em b}psbuubu qmb abe`u`il gfdbsu

    fqq`qrab qi{fsau s`ud, F nfskbs zfnrb ij `la`efqbu f m`kmbs abksbb ij ipq`g`ug, @l

    psfeq`efn fppn`efq`ilu. zfnrbu ?. ?,2 fla 6 fsb ruba sbupbeq`zbn qi sbpsbublq qmb

    pbuu`g`uq`e. giabsfqb fla ipq`g`uq`e z`b{u ij qmb abe`u`il gfdbs,

    Jis k`zbl jrxx lrgcbsu F fla C `q `u uf`a qmfq `j @ -F)>@ -C)Q Q . qmbl F C 4 `j

    @ -F) @ -C)Q Q qmbl F C 4 fla `j @ -F) @ -C)Q Q

    . qmbl F C ,

    Qmb j`lfn sfld`lk ij fnqbslfq`zbu gbflu qi faipq ebsqf`l nbzbn ij ipq`g`ug ij qmb

    abe`u`il'gfdbs. qmbl qi fppn Bv, 65 il jrxx lrgcbsu Bv, 63. fla j`lfnn qi sfld

    fnqbslfq`zbu sbkfsa`lk icqf`lba zfnrbu jis @ - ). 6.,,,.Q `J ` L , Qmb cbuq fnqbslfq`zb jsig

    qmb ubq `u sbpsbublqba fu gf} . 6.,,.` `Z Z

    j j ` F ,

    Qmb psbublqba gbqmia u`kl`j`eflqn u`gpn`j`bu qmb psiebarsb ij sfld`lk qmb

    fnqbslfq`zbu `l u`qrfq`ilu {mbsb qmbsb fsb f lrgcbs ij emfsfeqbs`uq`eu fla pfsfgbqbsu

    ij abe`u`il gfd`lk, Il qmb cfu`u ij qmb psipiuba fnkis`qmg. f uuqbg jis abe`u`il

    urppisq `l qmb psiksfgg`lk nflkrfkb E {fu abzbnipba,

    1, ABU@KL@LK QMB GFLFKBGBLQ ISKFL@UFQ@ILFN UQSREQRSB IJ QMB

    QSFJJ@E UR__ISQ RU@LK JG+[IQ GIABN

    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

    14/25

    61

    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

    15/25

    62

    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

    16/25

    6:

    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

    17/25

    6;

    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

    18/25

    6=

    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

    19/25

    60

    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

    20/25

    3?

    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),

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    21/25

    36

    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;

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    22/25

    33

    {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

    23/25

    35

    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,

    :, FEDLI[NBAKBGBLQ

  • 8/3/2019 A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in

    24/25

    31

    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

    Q566?65,

    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

    25/25

    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,