( / / / / ) ( )..... TOPSIS... : Mult-attrbute Decso-makg to Rak Urba Water Supply Schemes Hojat Maabad Abbas Afshar 2 (Receved Mar. 6, 2007 Accepted Mar., 2008 ) Abstract The creasg tred (urba) water demad due to populato growth places a growg stress o avalable water resources ad calls for a effcet ad acceptable log-term maagemet of the resources. Hece, applcato of mult-attrbute decso-makg systems s essetal for evaluatg urba water supply schemes. A umber of mult-attrbute decso-makg methods have bee developed. Ths paper ams to survey the applcato of such systems to urba water supply problems ad the effects of each mult-attrbute decso-makg method selected o the fal rakg of alteratves. Three methods of Iduced Ordered Weghted Averagg (IOWA), Lear Assgmet (LA), ad TOPSIS have bee cosdered for a real urba water maagemet case study the cty of Zaheda Ira. The results revealed that the mult-attrbute decso-makg method selected had a cosderable effect o the fal rakg of a fte set of alteratves such that dfferet MADM techques yelded dfferet results for the same problem. It s, therefore, ecessary to select the. M.Sc., Hydraulc Structures, Dept. of Cvl Egeerg, Ira Uv. of Scece & Techology, hmaabad@ cvleg.ust.ac.r 2. Professor, Dept. of Cvl Egeerg, Ira Uv. of Scece ad Techology - hmaabad@ cvleg.ust.ac.r - - 34
method accordg to the specfc characterstcs of the problem at had, type of data avalable, ad the assessmets made. The ultmate alteratve must be, thus, selected oce evaluatos have bee made of the results obtaed from applyg dfferet decso-makg methods to the problem. Keywords: Mult Attrbute Decso Makg, Urba Water Supply, Iduced Ordered Weghted Averagg (IOWA), Lear Assgmet (LA), TOPSIS.. ELECTER.[-].[]. ELECTRE I-III TOPSIS PROMETHEE. TOPSIS. 5 Tecle 6 Netto 7 Aad Raj ad Kumar 8 Khereld ad Fahmy 9 Chuta ad Chau 0 Soghua Goal Programmg (GP) 2 Compromse Programmg (CP) 3 Multattrbute Utlty Theory 4 Aalytc Herarchy Process (AHP) 5 Lear Assgmet (LA) 6 Iduced Ordered Weghted Averagg (IOWA) -..[].. (MADM)...[] ( ). (MADM) ( : ( ( (....[] Mult Crtera Decso Makg (MDCM) 2 Mult Objectve Decso Makg (MODM) 3 Mult Attrbute Decso Makg (MADM) 4 Effcet Solutos 35
-- : - - - -..[].[]...[] (CP) (MADM). TOPSIS (IOWA).. - (MADM) - - : MADM -. -. MADM - - 36
- ( ) - ).(.[ ]....[]...[] -- /. --. MCDM. [ ] - --. F : I J I. I,J φ J I.......[]. MCDM MCDM.[] / - : : : - - "" "" : - (a,b) - :. - - -.[] --.[ ] -: 2 Wag ad Parka 3 Ordered Weghted Averagg (OWA) Herrera 37
A A a.. TOPSIS --. TOPSIS.[] A.. : :. :.w V = N D. W * () W. V (A ) : - :(A ) {(maxv j J),(mV j J ) =,2,...,m} = { V,V,..., V } = j j 2 a () {(mv j J),(maxV j J ) =,2,...,m} = { V,V,..., V } = j j 2 J = J = { j { j =,2,..., j BENEFIT =,2,..., j COST 0.5 2 d = (Vj Vj ) ; =,2,... j= 2 d = (Vj Vj ) ; =,2,... j= 2 Hwag ad Yoo 0.5 } } (). : () ().[] J OWA.[ ] OWA w [ ] =, w 0, = : F w (x) = = w. b, x I () b. X OWA. w :.. :[ ] w = Q( ) Q( ), =,..., (). Q. : 0 r-a Q( r) = b-a f : f : f : r < a b r a r > b ()» ( /) (/ /) «. (/ ) OWA.[] (IOWA) OWA : IOWA w {(u,a),(u 2,a 2 ),...,(u,a )} = j (u,a ) W = (w a (u,a ) u Flev w. b j j j= T, w 2,..., w ) w j b j () j =,w j [ 0,] u - 38
OWA /. TOPSIS. OWA.. OWA IOWA. IOWA.. OWA.[]. - /.. :.. :[] : - d d A : : cl d = d d () d = 0 A = A cl = : d = 0 A = A A. cl = 0 cl ( A ). cl :. --. :. :. Q G (w) : : Q G. q t = j= π tj. w j () t j. π tj = 0 π tj = - : h t : max : s.t : m = t= m = m t= h t h m h t t q t = = = 0.h t t =,..., m =,..., m () Lear Compesatory Process 39
[] - () () AHP ELECTRE MAUT TOPSIS OWA - -... :.[]. - :. -. () (VL,L,M,H,VH) () Provcal Water ad Sewage Compay () 2 Natoal Water ad Sewage Compay (). - ). ( -. -. -. ) - (.. -. - 40
( ).. MADM. - - - DM / / / / / / / / / / - / / / / / / / / / / / / / / / / / / DM 4
- / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / (IOWA) / / / / / / - / / / / DM (IOWA) TOPSIS --. -- Q G.... (CP).[] ( ). Excel r r j j = = j= a j a ( j ( a j a ) ). G, j=,.., G, j=,.., () j= j (). - IOWA --. IOWA IOWA... IOWA - 42
/ / / / / / / / / / / / TOPSIS - / / / / / / / / / / / / / / / / / / / / DM (CL ) - DM p= [] (CP) - p= DM.. IOWA...... IOWA. IOWA.. - TOPSIS IOWA. (CP). 43
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