A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units

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1 Jo o Ozo I Egg A w D Ro Fzz DEA Mo o P Po o Do Mg U A gho * Mgho A Azoh S Sgh A Poo D o I Egg F o Egg P--oo U Th I Poo D o I Mg Ah T U Th I A Poo D o I Egg F o Egg P--oo U Th I R Oo 4; R 3 J 5; A 6 J 5 A D o DEA hooog o g h o o g DMU whh o h o og h o o. Ag h g g h o o DMU h w o zz DEA o DRF-DEA wh oo wgh g o DEA oh o h o DMU h o o h o o. I h oo DRF-DEA o h o o hz o g zz wh o o whh hgg q. U h o h oo o o. So w h o h oo DRF-DEA o o q -o oh ogg whh h o o h o o o h o o h o o o o o. I o o o oo w h o h q -o oh o o o o oh o wh g zz o ogg oh. To o w g w h goh gg Mo Co MC o G Agoh GA. S o h h o w. Th oo how h o h goh oo h h GA goh whh w oo Q o oo q. wo: Soh D o ; D ogg; o zz ; Mo Co o; G goh.. Ioo D o o g oo o g og h o o o g. D o DEA whh w oo Ch Coo Rho 978 h w o h o o DMU o. S h DEA o CCR h h q o o. Th g o h hq h o o q h o o o o w h o o h o wgh. How wh w h o DMU h o DEA o o o h o o DMU o o o ow h oh o h h o o. Wh og oh o o DMU whh o oh DMU o o. Coo Hg 996 h o who o oh DEA o wh h o ogg g ho o ho o hoog. U w o zz o DMU o h o o h g. Sg 99 h o who o zz oh o o z h zz DEA o. E M T hg zz o o g α- gg wo DEA o. S wo o o o h o wh o zz o o h h o h o zz o hz h h. R h o zz w 978 o ho.q... ho Coog ho E-: 75

2 A gho./ A w D Ro Fzz... h ho 4 h oo o zz ho g - o. 5 w o o zz o RFMRP h h h RFMRP o h oo-oo o wh o zz. B. 5. Wg W 9 h o o h o o o o o zz o o ho. Rz Aooz 3 o w zz o oh o ogg. Th o h oo ho o o h og DEA o o q ogg o g h oo o α-. Az J Fzoo 4 oo w zz DEA o o o h o h g o. Th o g DEA h R ERM o zz o o h. B. 5 oo Fzz ho- DEA o o o oo og w h o. Th o o h " " h. I h h o o g o DMU wh g DEA o zz o oh o who og h o g o o g o DMU. So h o h w zz oh DEA o o h o DMU. Th o h ogz oow. So w h o o DEA o wh oo wgh o. So 3 w o o o zz ho h oh h o zz o whh h o. I o o o DMU o 4 w o zz DEA o wh oo wgh o DRF-DEA whh h o o hz o g zz wh o o hgg q. U h o So 5 w h o h h o o o o o DRF-DEA o o h q o wh g h h o o3 h w o h q o oh ogg o o o oh o wh g zz o ogg oh o o oo. I o 6 w g MC o GA o g w h goh MC-GA o og h oo q o o oh ogg. So 7 o o h og h o o oo ho. W o o h o o g goh MC-GA wh h h GA goh whh w oo Q h o. F So 8 w o oo.. Rw ow oo wgh oh DEA o -o ogg oh o o q q o o h o w DEA o h o-o o g o wh DEA o o o o h o o h o o. Go 988 h o who g -o ogg MOP o o h o g g h o DEA wh oo wgh o o o h g ow o h DEA o. DEA o whh oo h o o o o h oog o g h h Tho Do 99. M h oh o DEA o wh oo wgh o. Sg 995 h o who oh o -o DEA o wo o q- oo o wo o DEA oo Goo 3. Th o h h. Th h h h h o o how o o RTS h wo o h -o DEA. Soh S 5 w o -o DEA wh wo o DEA. Th h DEA o oo Goo 3 h h o o o RTS oo o h DEA. Ch 5 o - o DEA o whh oo o h o h g. Th o hg DEA o g h h o q o o. H how h Go MOP DEA g g o og oh o o o - o h DEA o. A w DEA o wh oo wgh whh o ggg o h o g hozo h o Too 6. ozo V 7 wo oo wgh DEA oh o g g. O o h o h ow o og o o h o h o. Th oh ogh oh h o q o o whh o o wgh o. g Wog Sw 76

3 Jo o Ozo I Egg q o w MOP DEA o how DEA o o who o g og o MOP oo. F wo DEA o wh oo wgh o o hg o 69 J Sh g o 9. O 3 o o ozo oh o oo wgh DEA wh. Rz hohh 3 oo o o g DMU wh g oo wgh DEA o. Th o h o how h Wog. Wg 4 oo w o wo g zz DEA o o o g h o o US hog o. Th o o o oo wgh o og o h g ow. wgh To T 4 h o J ho g wo DEA o wh oo wgh. To T 4 oo w oh DEA wh wo oo wgh. I o o o o wo. T. 5 oo o wgh CSW o o g h DMU wh h oh h o o. Th oo ho z h w h DMU h DMU. H-M. 5 oo DEA o o o o o o o. Th oo o wgh ho o oog h wgh g h oo o. Th o o DEA o o o zz zz oh o og wh h g h g o h o h o o. I w h h o zz oh o whh w wh h zz o wh o o o g o. I zz oh ogg h h h o zz o o o oh o. B. 5. So o o o g o zz oh o h o DMU w o h o o o h h o o wh g o o oo w o zz DEA o wh oo wgh o. I g h h o h o o o o w o h h o o h q oh o og o h o o h h o o 3. To o h o o h o h h o o g zz o w h q oh o o h o o. A oq h oo o o o q oh ogg o. S h o o h h o o o o h o o w o o h oo ozo goh. To oo h w o MC o hq g goh o o. 3. P 3.. C oh ξ zz wh o o o μ. Th o zz {ξ } o R Q : C Ao C h h oowg o: C {ξ }+C{ξ<}= A h o o zz ξ : E C C ξ -o o zz o B Bo o R. Th h o o zz {ξ B} : Ch C P A h o o zz ξ Q : E Ch Ch 3.. M h o o o g zz Th o h o o o h h o o o g zz whh w h o. Tho 3.. oo o g zz whh o g o. I ~ h w h:

4 Ch wh h o o o o o o Q. Tho 3.. g zz =. I ~ wh h w h: Ch 7 wh =... og o o h ozo Q. Tho wo o g zz. I ~ ~ g o h w h Q : Ch wh og o o h ozo. Tho So wo g zz whh R g o h w h Q : E 9 4. D o zz DEA o DRF-DEA oo Th o DEA o CCR whh w oo Ch Coo Rho 978 : 6 8 A gho./ A w D Ro Fzz... 78

5 M : : wh h h h o o DMU. h wgh o h h o h. Fg o =.. =.. h oo o h o h CCR o o h h o o o z o DMU. G CCR h o whh o o g o o. B o h h "" DMU h T o = T whh hgg q. I h h o h DMU =.. wo go o : o o o q- o o o o o wo go o o: o o o o o o o q o oo Goo 3. A how Fg. h hozo o h o o o h h o o DMU. I h g h q- o o h h o h q- o o h + o. A o o o h CCR o oowg: : : o M T Wh h wgh o h q o q o =..T. Th CCR o o h o DMU wh o. How wo o h o o g og o h o o zz o h. I w o o h o o o h o. Th h w h h o o g zz wh o o oowg : Fg.. Eo o h DEA o wo Jo o Ozo I Egg

6 A gho./ A w D Ro Fzz... wh h o o o o zz o o DMU =.. o. h q o zz o o o o DMU o h q o zz o o o DMU o +. h q o zz o o o DMU o h q o zz o o o o DMU o -. Ao o ~ ~ ~ ~ wh g o o h =.. =.. =.. whh o o h o o h o h DMU. I h h o o o o o o zz h g o h o o. I w o h o o DMU w h h h o ogg whh oo wgh o ozo V 7. I h w w h -o o g MODM ho o w -o DEA o wh oo wgh o whh hgg q. To g o w z h o o o zz h o o h h h o o o h oo DRF-DEA o wh oo wgh: M: M: : Ch E E T... 3 wh o o o g o h h o o. Th o o "" o o o o o oo wgh wh h o h o o o =..T wh h zz wh o o =... I o CCR o h o o o w o h o DMU. DMU o h o q o. I oo DRF-DEA o 3 w h o α- o h o DMU. Th o o oo wgh o h α-. Th o o oo DRF-DEA o 3 o h h o o zz whh o o o w o o h g h oo o. I h oowg w h q oh o og o h o o h h h Tho So h q o zz o o o o DMU o whh w o h h o o oo DRF- DEA o o o h oowg q oh o: 5. Eq Soh Pogg o DRF-DEA Mo 5.. Eq oh o o h h o 8

7 * * * Ch g * Jo o Ozo I Egg

8 * * Eq oh o o h o o o Tho 5... g zz wh R ; h -wh gh-wh o ; h -wh gh-wh o ; h -wh gh-wh o h -wh gh-wh o. Th og o Tho 3..4 w h: ]* ]* E Poo. h α- o. Th o h w h: B h o o h o o o h h w h: A gho./ A w D Ro Fzz... 8

9 Wh h α- o h zz o. So w h: E ] ]* ]* Th oo o h ho o. So o g zz o o DMU o h w h: B B Tho 5.. h h o o o DRF-DEA o 3 h h oowg q oh o: E 4 }* ]* ]* { wh: }* ]* * ] { 8 9 Jo o Ozo I Egg

10 A gho./ A w D Ro Fzz... A h wh h o o g zz w h o h oo DRF-DEA o 3 o q -o oh ogg o og o h o h o 5 oow: M : M : g : ; T wh g Roo o h oo q o oh ogg o Th oo q -o oh o h "" o o h o h zg h o h DMU whh o h oo. I o o q o o oh o g zz o ogg oh whh w oo 99. Th oh z h h o o o h q o ogg o o o o. I W h o oo o R R W W. wh W whh o h o h o R o o h h h g o h o. So R M W. W. ho h o o o oowg o: R M : W. W. : ;... R W. W. ;... W g T R S o o o o o w oowg: M : W g : ;... W ;... W T Mo h q o o oh o o h q o o oo DRF-DEA o whh h o o DMU wh o o h o h o ho h oo. S h q oh o 9 h o o o h g w o o h oo ozo goh. I o o oo h h o w g w h goh o o oo DRF-DEA o oog MC o GA whh MC o w o o o h g o h o GA w o h o o o. 6. Soo Mhooog I h o o g g goh GA h h h h o o o w oo Ho h o Gog 989 oh. A GA o o wo oo: oo o. Coo h wg w wo g o g wo og g wh Mo o o hg h o g. Th h o h GA h o h oo. Th o o o h goh o og h oo DRF-DEA o z oow. 6.. Soo o So h o-z hooo h oo g h oo o h oo DRF-DEA o whh h o o h =.. =.. =.. R ] hz hooo o how o o o =..T. 6.. Izo o G o o h. Co g o 4 o 9 o =.. o wh h g 84

11 Jo o Ozo I Egg o MC o whh w o 6.5. I R h o o o h hooo. R h o o-z hooo R R... R o. oz Roo o F oo oo w h hooo... o z. Fo oo oo R h oowg o o h o hoooo o = o o-z: g o o h ]. I h hooo R w P hoooo wh h P h o o oo. Th go h hoooo R R R... o h R R R R 3 R Th oo o o h R how oow. G o λ o h h h oo oo o R R w g wo og R R oowg: R R R R R R 3 I oh og h o o o h w h wh h. Ohw w h o h oo o oh o wo og o. F w g oz hooo g h w g hooo. So h hooo R o oo. R h oowg o = o o-z: o o o h ] P h hooo R w hoooo wh h P h o o o. Fo h R h o oo h oowg: R R M. 4 wh M o g o. I R h w M o w M. W M = h o o o oo o o. Aw w h R wh og R. F w g o-z hooo g h w g hooo Eoo o W o h o h hoooo h o o 9. Th hooo R R... R o h g o oz goo o og o h. S h hooo o w oo whh h hooo wh hgh w h g h o o. A h o o-z w o o-z o hooo o o R Mo Co MC o MC o ho o wh h oh ho o Ch W. I o o o h oo DRF-DEA o o g oo w o h. S h o o 9 g whh o o h oo ozo goh o w ho o h. MC o ho hg h o o o o oowg: h h h h h 5 Ao h o o MC o o o g 5 oow: Po: MC o o og 5 g -o o = o o h G o o o h ]=-] D h g o h o: ^ h h * h h Co h oo o h g: ^ B gg GA MC o w g w h goh MC-GA o og h q o o oh o whh z oow: Iz o_z hooo who h o o o MC o. 85

12 A gho./ A w D Ro Fzz... U h hooo oo o oo whh h o og h o o o MC o. E h o h hooo 9 MC o. S h hooo -ooo o. R h o o oh o g o go. S h hooo h o oo. 7. P E I h o o h h o. A g g o h I o w o o h g oo o h oo o g o DMU o o o h o h wo o. H DMU og wh h wo o h o whh T. Th h : o : o R oh oo o : o R oh o : o R oh. Th wo o : h o o o go : oh o. o q- o o o o o h o o DMU h o. S h o o g zz h o o how o o h. I J 3 h ' g h -wh gh-wh o h o o h A o W o 3 o o. Th o o DMU h o o oow h o o whh T. To o h og h o h oo hoog h oo DRF-DEA o h oo MC- GA goh o h o g o. T o h o. 5 o h wo o. Th o o o o g h Moo Wow 7 og h goh w C++ ogg gg wh h oowg h GA: h oo z 3 h o o oo.3 h o o o. go 9. Fo h oo o h o w h oo o h DMU. Fo h o DMU h h gg α-.98 oow DMU4 DMU DMU3 DMU5 whh h DMU h o DMU. Ao wh h oo h goh h o o o DMU o h wo o o T 3. T Th o g zz o o G o DMU o h wo o o = = DMU Eo.6.6 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I Oo o.3.3 ~.... ~ ~ ~ ~ ~.3... ~ ~ ~ ~ o.. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~.. 5 Go.3.3 ~ 4. O.. ~ ~ ~ ~ ~ ~ ~ ~ ~ o.. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

13 Jo o Ozo I Egg T Th o o DMU o oh o wh. 5 o DMU O oo α- = = T 3 Th o o DMU o o h wo o o DMU = = T 4 o h o o o o o h A W o 3. Th h J 4 o o whh h o o o. So h o o wh g oo DEA CCR o whh how T 4 o DMU. G h h o o:. 5 o g DEA. I hogh h h oo o DEA og o h - oo Goo 3. Th g o og h wh h. 5. Th wo DEA oh h o o. Fo o o o 4 h DMU h h h 5h g o o o h h wh h h o h o h. T 4 h h hgh Po oo h o o oh o w o wh. 5. I o o h h o o h o w o o g h o h h GA goh whh w oo Q. Th oo o h o o DMU o T 5 whh CPU h oo o h wo h goh o g o o *. I o T 5 h h oo h GA goh o o g o h 6 o CPU q o oh o. A w o h o h GA goh oo h Q h GA goh o. I o h o o o h goh o o h o oo o h Q h goh. 87

14 A gho./ A w D Ro Fzz... T 4 A o o DMU wh h o o oh o Po DMU Eo I Oo o o Go O o A P wh. 5 R P = = Po oo o w o o DMU = :.73 Po oo o w o o DMU = :.957 T 5 Coo w h o o MC-GA goh Q h GA goh oo goh Q h GA goh Po = * CPU * CPU Ag = Ag E DMU DMU DMU3 DMU4 DMU5 Th Th h oo DRF-DEA o o h goh Th h oo DRF-DEA o Q h GA goh Fg.. Coo w wh o Fg. how h oo w o. 5. So h oo h GA goh oo h Q h GA goh o oo q. Aog o whh w oo Q o h h o h oo h GA goh o o h o o o P h o o oo P GA w o h o C o h oo q o DMU wh. 5 h o =. Th oo o T 6. To o h w g h o oow: 88

15 Jo o Ozo I Egg o % o - T 6 Coo oo o DMU GA o. 5 P C P G α- R o % wh h o α- h o o h α- T 6. G g o h o z oow: Fg : T 3 h h o h DMU g o o g h o. Fg : T 4 h hgh oo h o o oh o w o; h o h oo DRF-DEA o. Fg 3: Th oo w o T 4 g o g ow. Fg 4: T 5 h o h goh oo h Q h GA goh o oo q. Fg 5: I o T 6 h h o o o.67% whh h h o MC-GA goh o o o o og h oo DRF-DEA o. 8. Coo Th o w o zz DEA o wh oo wgh h o h o o o o; whh w hgg q. Th oo DRF-DEA o oo oo o o o wo o o o DMU o h o. Th o o h h oowg : A w -o DEA o w o whh h o hz o g zz wh o o. U h o h oo DRF-DEA o o o q o oh o; whh o o o h o o o oh h h o o o o h o o. I o o o oo g h oo o h q o oh o o o o o oh o o o DRF-DEA o zz o ogg oh. To o h DRF-DEA o h g w h GA goh oog MC o GA whh h MC o w o o o h g whh o o o h o wh GA w o h o oo o o. To o h DRF-DEA o w o o g o I o o o h wo o. Th oo how h o h goh oo h h goh whh w oo Q o oo q. Aowg Th ho wh o h h Eo h. Th wo o h Th P--oo U I Az U h o Qz I. R Az M. J M. Fzoo R. 4. "A w zz DEA o o o o o h g o ". Co & Oo Rh. B S. Cgg. Oo M. 5. "Mg To S E U U Fzz S Tho B D Eo A: Tho P Coo wh To DEA Mo" Too Rh Po Ch A. Coo W. Rho E "Mg h o o g ". Eo Jo o Oo Rh Ch. 5. "O o ". Io Jo o Ioo Thoog Do Mg

16 A gho./ A w D Ro Fzz... Ch T.. W P.. "Mo Co D Eo A wh G Agoh o owg Mg o ". E S wh Ao Coo W. Hg.M. S "Sg DEA o h o". A o oo h E T. M. T H.. "D o o DEA o o ". Eo Jo o Oo Rh F H. W. 3. "A D wo DEA Mo wh Ao o J Coo Sh B". Foo Po E Po Gowh: Mog h F S I W: oo Ch 9. Go B "A MOP o o h o o DEA o ". Jo o h Oo Rh So Gog D.E "G Agoh Sh Ozo Mh g" Ao W Boo. H-M A. T M. Ag P; Hozh o F. Gh Bg. 5. "A oo-wgh DEA o o z o o g g" Co & I Egg Ho J. 975 "Ao A S". U o Mhg P A Ao 3. wgh H. To. T M. 4. "Eo o h o J ho g wo o o". Hh C g 7 -. w H "Fzz o I: o ho". Ioo S 5 9. B. 4. " U Tho: A Ioo o Ao Foo S". Sg S & B M 54.. B. 5. "O - o zz o o ". Co & Oo Rh Q.... "T- Fzz V h Ah". So Cog ozo S. V G. 7. "M o g g o g AHP". Jo o Co Oo Rh oo J. Goo M. 3. "M o E Poo: A Ao o D Eo A o J E U". Jo o Po A O H. 3. "Coo wgh D Eo A wh : A o ozo oh". Co & I Egg Q R... "A w o o wh zz o o" Jo o A Mh Cog Rz R. hohh M. 3. "Rg o-g g oo wgh DEA". A Mh Mog Rz S.H. Aooz H. E.. 3. "A Fzz D Eo A Aoh o P Pogg". Io Jo o Co Coo Sg J. 99. "A zz oh o ". Co Mh wh Ao Sg J "D o D Eo A: Tho o S E". Sg S & B M h. Soh T. S. 5. "R o S D DEA". Eo Jo o Oo Rh T M. z S. -M R. 5. "A oh o o g oo o wgh h o o" Io Jo o A Mg S 7. Too A. 6. "D Eo A D Fwo". A Mh Coo 8-8. Tho E. Do R.G. 99. "Eg P g -o g o ". Eo Jo o Oo Rh To. T M. 4. "D DEA wh wo : A - oh ". Og Wg S. W J. 9. "Sg o o o zz o o o o". Io o o o og oo oo Wg W. W. P. 4. "A zz -o wo-g DEA o o g h o o US hog o ". E S wh Ao g J.B. Wog B..H. D.. Sw T.J. 8. "Ig DEA-O Po g g g MOP ho". Eo Jo o Oo Rh H. 99. "Fzz ho o" Sg Boo. 9

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