A new model for mining method selection of mineral deposit based on fuzzy decision making

July_23-34:ml Jul 7/15/08 12:46 M g 385 Sy A w mdl f mg mhd l f ml d bd fuzzy d mkg by F. Smm Nm*, K. Shh*, M. A-u*, d H. Dhgh* O f h m k xl f m l mhd ubl f h d, f fu ludg gm, gmhl d glgl fu. h u f lg mg mhd h g h m mhd() hvg h m d wh h d d d xl f, ludg h lld budg d ll hlgy f dld fbly ud. Svl mhd hv b dvld h vlu ubl mg mhd f d, bd hyl h. h h b lfd h gu: (1) fl d hkl mhd, (2) uml kg (g) mhd, d (3) d-mkg mdl. M f h mhd hv hmg. Cdg h f h m f h f f ml d, uh d d dh, lgu vbl, blu f h xlg m by vu mhd b md h m m ddvg f h mhd. h du h Fuzzy hqu f d fm by mly dl lu (Fuzzy OSIS) dm h mg mhd. h fuzzy d mkg (FDM) fw l mlyd dvl Fuzzy OSIS bd mdl. Al f h mdl wh vu vlu (, lgu d fuzzy) f h d lmd h xg ddvg f h mhd. w ml llu dm h ffv d fbly f h vlu du. h hw h h d mdl fm b h lv. Kywd: mg mhd l, fuzzy OSIS, d mkg, mg gg, lgu vbl. Idu Mg mhd l l d g u h mg gg. Sl f mhd uubl f d h my mk xl f h bdy ublm d mm uml. S, vlbl d huld b vlud fully mum m. I h, h l f h m mg mhd f g m fm h ml, hl d fy f vw. I h mhd l, my llbl d ullbl m huld b k u. hf, h m mu b bd wh f d hl ud f h d1. I h, l f x mhd w bd mly g x ml y f m d mhd ldy u h d f h d. h h f dg h m mg mhd h f ghbug lwy. Hwv, h d m h l fm mg mg l f xg h d, f ml d2. h gl mg mhd f d. Uully w m fbl mhd bl. Eh mhd l m h blm. Cquly, h ml mhd h h ff h mmum umb f blm. h ky u f mg mhd l mxmz h f by lg h mhd wh h hgh vy f h ml u d h lw mg h fbl lv. h h h l f h mg mhd b lfd h g: fl d hkl mhd, uml kg (g) mhd, d d mkg mdl. I h, h blm wh h mhd dud d h ul f lyg fuzzy d mkg fw l h f lg h x mhd f vl ffd. h m u f h fuzzy mul- d mkg mdl f h mg mhd l. I d du h uggd fuzzy d mkg mdl, fly, h xg mg mhd l mdl d h ddvg d. h, h * Dm f Mg, Mllugl d lum Egg, Amkb Uvy f hlgy, h, I. h Suh Af Iu f Mg d Mllugy, 2008. SA ISSN 0038 223X/3.00 + 0.00. vd My 2007; vd vd My 2008. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY 2008 385

July_23-34:ml Jul 7/15/08 12:46 M g 386 A w mdl f mg mhd l f ml d b f h hqu f d f by mly dl lu (OSIS) d h Fuzzy OSIS dud. Mv, h fuzzy d mkg (FDM) fw l dud bd h Fuzzy OSIS. A l f h FDM fw l d u hugh vl ud. Exg mg mhd l mdl d h lm Svl mhd hv b dvld h vlu ubl mg mhd f d bd hyl h uh h, gd d gmhl f h lg k d d lf. h h h lu f mg mhd l blm b lfd h gu: (1) fl d hkl mhd, (2) uml kg (g) mhd d (3) d mkg mdl. A gu f mg l uh l3, Bhkv d Wgh4, M5, Hm6 d Aghkv7 uggd f h f lg ubl mg mhd. h gu f ud w h ugh ml, bl dg mhdlgy h wll umlly h mg mhd f h bdy udd.2 Vu h hv b ffd by h uh Lbh8, Nhl9,10, kl l.11 l h mg mhd. h m ld h dvlm f uml h l h mhd f xg ml d. Numl kg (g) mhd ly kg f umb f gm, gmhl d glg m v g vlu f dff lv. I h mhd, dd h lm f umb d lv, mbguy d mulu flu f hv b gld h d mkg. h gu f mhd, uh Uvy f Bh Clumb (UBC) mhd11 h mhd ffd by Nhl10, bd kg m, whh xl h ml d u. Ddvg f h h lud lm h umb f d h l f lv. I h mhd ffd by Nhl, gm m uh gl h, hk, d d gd dbu m dd. Alhugh h mhd, h d dh dd ffv m lg h mhd f d x, dd f flu. Fuhm, ly h gmh f j fquy, k quly dg (RQD), k ub gh () d h h gh f f j h d d uudg k dd. I h UBC mhd, lhugh h dh d h k m g (RMR) ddd, h lm ll bdg. C uh d dm, hk hg ufmy, vlbly f x l x, vy y mg mhd, ubd ff g lk ff, udgud w u d, gld bh mhd. h lm l x h h d lv f l. I h g h, mg mhd dd f l. h mhd h d f g g : mg, blk vg, ublvl g, ublvl vg, lgwll, m d ll, hkg, u d fll, lg d qu-. Alhugh h dl mg mhd dvdd gh x mhd, h f whh my lud vl dff lv.12 Amg h mhd ludd h bv l h d ll mg, vl mg (VCR), mg d vl x mhd uh hydul mg d bhl mg. Mv, udgud mhd uh lgwll my b fmd h dv md d h gud l my b fmd by vg fllg. hf h h mg mhd l muh m umu h h dd mhd. Cdg h f h m ffg l f h m x mhd dvdd h l f (dm), lgu d fuzzy m, h dm xl uml kg mhd b md h m m ddvg, bu h mhd ffd by Nhl d h UBC mhd, m xld by vlu. Bu m f h m dug h ml d lgu m. F xml, f h d f bdy, uully lw d (fl), md d (md) hgh d () m ud d f h vbly f h d hgg wll, h m, md vbly ud. Al dug ml d dvdd l, whh hv x df budy u d hv m mbgu. I uml kg mhd, h flu f h m vfd ly d h muul ff f m gd. F xml, d, hk d dh m mululy ffv dm f h mhd. I uml kg mhd, h bdy d, h bbly f hg h mhd d. Wh h hk d, h dg f h d huld m h h. F ld d hk d, h mhd myb fd. Al h mhd, ll h umd hv qul wgh d mkg, bu dg h u f h d mk uh um ul. Cdg h lm d ddvg, ff hv ly b md d dvl d mkg mdl f lg h mg mhd. Amg h ff ud f h uh W-Xu d Ymg13,14, Kml d B15 Md l..16, Smm d Shh17,18, Bf d A2, B l.19, Kdg l.1. R mhd f d mkg hv bld d-mk dd m qukly, ly d vly1. Alhugh h ddvg f uml kg mhd hv b mvd ly h d mkg mdl ffd, h mhd hv h w ddvg. I d mkg mdl, whh bd mul d mkg (MCDM) hqu, h lm h umb f d lv, bu h mdl f h blm f m-umg lul. M f h mhd bd h Yg mdl. h Yg mdl20 fllw h mx-m mhd f Bllm d Zdh21, wh h mvm f h lyl hhy (AH) mhd, whh d h u f l mx x h -w m 386 JULY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

July_23-34:ml Jul 7/15/08 12:46 M g 387 A w mdl f mg mhd l f ml d d h ulg gv ubjv wgh.2 h ddvg f h AH hqu h fu mly h d mk wh h mk my -w m h d, whl bly ug ubjv f. Fuhm, m ddvg f h AH mhd h fl lm f h u f h - l. F, f Alv A fv m m m h Alv B, whh u fv m m m h Alv C, u vlu blm. h Sy mhd22 wh h f h Alv A wy fv m m m h Alv C.23 h mhdlgy uful ly wh h d mkg fmwk h udl hhl lh mg d lvl. Mv, AH lly ubl f h umb f lv d lg h v m my u fgu h d mk.24,25 h xg d mkg mdl f mg mhd l uful bu hv d l. h mhd dl wh d mk mbgu, u d vgu, whh b hdld by vlu. Hvg u vlu f h m blm h. I h l, h f h h ud f lvg h mg mhd l blm bd h fuzzy hqu f d f by mly dl lu (Fuzzy OSIS). h bu fu dvg ddd: (1) ud lg h h l f hum h, (2) l vlu h u f bh h b d w lv mululy, (3) ml mu h b ly gmmd, d (4) h fm mu f ll lv bu b vulzd lyhd, l f y w dm. h dvg mk OSIS mj d mkg hqu md wh h ld hqu uh AH.26,27 Ch46 xdd h mhd fuzzy gu d mkg u by dfg Euld d bw y w fuzzy umb. hyllu d L52 dvld fuzzy v f h mhd bd fuzzy hm, whh ld fuzzy lv l f h lv d by Wg d Elhg53. h OSIS mhd hqu f d f by mly dl lu d d by Hwg d Y34. h dl lu (l lld h v dl lu) lu h mxmz h bf /bu d mmz h /bu, wh h gv dl lu (l lld h -dl lu) mxmz h /bu d mmz h bf /bu. h -lld bf /bu h f mxmz, whl h /bu h f mmz. h b lv h h l h dl lu d fh fm h gv dl lu. Su MCDM blm wh m lv, A 1,...,A m, d d /bu, C 1,...,C. Eh lv vlud wh m /bu. All h vlu/g gd h lv wh h fm d mx dd by X = (x j ) xm. L W = (w 1,...,w ) b h lv wgh v f h, fyg w = 1, h h mhd b =1 ummzd fllw:24 ) Clul h d mx (D) : b) Clul h mlzd d mx R mx. h mlzd vlu j luld : [1] Mhdlgy d h d mdl OSIS d fuzzy OSIS OSIS ul h h MCDM mhd d h b wdly ud h lu (Ab-S d Am28; Agwl l.29; Chg l.30; Dg l.31; Fg d Wg32,33; Hwg d Y34; J d Kg35; Km l.36; L l.37; L38; Ol39; Ov d zg40; k d Wu,41,42; g d Su43; zg l.44; Zk l.45). h mhd h l b xdd dl wh Fuzzy MCDM blm. F xml, Ch46 f vd fuzzy MCDM blm v d dfuzzf d h lvd h fuzzy MCDM blm ug h mhd. Ch d zg47 fmd fuzzy MCDM blm fuzzy MCDM ug fuzzy gl. Id f ug d, hy mlyd h gy l gd df h lv l f h lv. Chu48,49 d Chu d L50 l hgd fuzzy MCDM blm d lvd h MCDM blm ug h mhd. Dffg fm h h, hy f dvd h mmbh fu f ll h wghd kg wghd mlz d mx ug vl hm f fuzzy umb d h dfuzzfd hm vlu ug h kg mhd f m f mvl (Kufm d Gu51). ) Clul h wghd mx : [2] [3] [4] d) Clul h wghd mlzd d mx. h wghd mlzd vlu ν j luld : wh w j h wgh f h jh d w = 1. =1 ) Dm h v dl d gv dl lu, A + d A vly. [5] [6] h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY 2008 387

July_23-34:ml Jul 7/15/08 12:46 M g 388 A w mdl f mg mhd l f ml d wh I d wh bf, d J d wh. f) Clul h mu, ug h - dml Euld d. h d f h lv fm h dl lu gv : Smlly, h d fm h gv dl lu gv : [7] [8] [9] g) Clul h lv l h dl lu. h lv l f h lv A j wh A + dfd : [10] S d J 0 d d + J 0, h lly RC j [0,1]. h) Rk h lv dg h lv l h dl lu: h hgh RC j, h b lv A j.53 h fuzzy hy md hy, whh w d by Zdh54. I l lg, v hv w vlu: b b, x x, blk wh, d z. Bu fuzzy lg, d w v, um dd bw x d x d wld hm gy h blk wh. h u f fuzzy hy llw u uqufbl fm, ml fm, -bbl fm, d l f h d mdl. h fuzzy d mx (D ~ ) d wghd (W ~ ) b ly xd mx fm : [11] [12] wh x ~ j, = (1,2,...,m), j = (1,2,...,)d w ~ j, j = (1,2,...,) fuzzy umb, x ~ j = ( j, b j, j ) d w ~ j = (w j1, w j2, w j3 ). h x ~ j h fm g f h h lv, A, wh h jh, C j d w ~ j h wgh f h jh bu, C j. h mlzd fuzzy d mx dd by R ~ hw : [13] If x ~ j = ( j, b j, j ), = (1,2,...,m) d j = (1,2,...,) gul fuzzy umb, h h mlz b dud by:53 wh Ω b d Ω h f bf d, vly d + j = mx j, j Ω b d j = m j, j Ω. [14] [15] h wghd fuzzy mlzd d mx hw : [16] h fuzzy v-dl (A + ) d h fuzzy gvdl (A ) lu hw : h d f h lv fm A + d b uly luld ug Equ [19] d [20]. If ~ = ( 1, 2, 3 ) d b ~ = (b 1, b 2, b 3 ) w gul fuzzy umb, h h vx mhd ud lul h d bw hm d luld : A h d, h lv l f h lv h dl lu luld blw: RC h ud k h lv. h hgh h RC, h m ubl h mg mhd. h hgh vlu f RC d h lv l h v dl lu d fh fm h gv dl lu mululy. A vlu f 1 ( 100 ) f lv d h h lv qul h v dl lu d vlu f 0 ( 0 ) qul h gv dl lu. h b lv h wh h g lv l h v dl lu. h fuzzy d mkg (FDM) fw l [17] [18] [19] [20] [21] [22] h fuzzy d mkg (FDM) fw l55 h b d mk d dg f d h ff f qulv m d h u wh h d mk d hv 388 JULY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

July_23-34:ml Jul 7/15/08 12:46 M g 389 A w mdl f mg mhd l f ml d fm, by Mm h gg fuly f b-md Uvy I. h FDM fw l h b dgd bd h Fuzzy OSIS hqu, d h vu. I h, md mv h df xg mg mhd l mdl by ug h fw l d lyg ymlly. h m m dvg f lyg h fw l bly wh dvy f d x. h l v h y f fm, ludg dm, lgu, d fuzzy fm. h h y f d dd m ffg h d mkg f lg h mg mhd. Bu vu mhd ly h (dy) vlu u h d mkg u. F xml, bl I, h vy f h d h b xld h x mhd l h b ffd. Rgdg fuzzy umb ld h m md h l l f bl I, huld b ddd h h ld h blk vg mhd, d m h h m blk vg mhd bu $12.5 d d b vlu lf d gh lm, vly.6 Mv, h lm h umb f lv d. h vlu du b ld h mg mhd l, hw Fgu 1. h d mdl f vl. h f dfy h h dd h mg mhd l d mg mhd lv. h h wgh f h dmd d d mx d. I d fm h fuzzy d mkg, h f h d ll f h wgh vd fuzzy umb (fuzzf). I h, vlu d lgu vbl vd fuzzy umb. h lld fuzzf bu fuzzy ud v lgu vbl fuzzy vbl. h d mk u h lgu vbl vlu h lv m wgh f d h g f lv f vu bu. F h, h lgu vbl fmd fuzzy gul mmbh fu. h h f f h Fuzzy OSIS ly. I h FDM fw l, h lgu vbl dvdd v-lvl, fuzzy lgu vlu vy lw, lw, m l (ML) lw, mdum, m l (ML) hgh, hgh d vy hgh. Bd h um, fm bl b d hw bl II. F xml, h fuzzy vbl lw h d gul fuzzy umb wh h mmum vlu f 0.00, h md vlu f 0.10, d h mxmum vlu f 0.3. h m df h ld h h fuzzy vbl vy lw, ML lw, mdum, ML hgh, hgh d vy hgh. h x fuzzy ddu. I h, h ul dmd by h Fuzzy OSIS hqu. h d mkg fuzzy vm h m h d mkg h hum b, bu vydy lf, l ly muh u fuzzy fm d h mk d. Bf y lul, lgu d vlu vd fuzzy umb wh fm f fuzzy mmbh fu (by ug bl II). fm f h d mx fuzzy umb d u by h fw l f u v d h u h y l h. h d u f ll u ludg, wgh d h d mx fm. h, d mv dm, h d mx mlzd d luld ug wghd mlzd g umlly. h x fd h gv wll h v dl lu. Af fdg h dl d gv lu, h d f h lv bd - dml ( h umb f ffg d mkg). bl I Vu d u FDM fw D y D Vlu C vlu Aum du 300 000 ( y) Lgu D hk Imd Fuzzy vlu M (m=12.5,=5,b=20) bl II fm f fuzzy mmbh fu Rk Df f C Fgu 1 Sl fmwk f mg mhd Mmbh fu Vy lw (0.0, 0.0, 0.1) Lw (0.0, 0.1, 0.3) ML lw (0.1, 0.3, 0.5) Mdum (0.3, 0.5, 0.7) ML hgh (0.5, 0.7, 1.0) Hgh (0.7, 0.9, 1.0) Vy hgh (0.9, 1.0, 1.0) Df f Alv C D Mx & Wgh f C (Lgu, C d Fuzzy vlu) Fuzzf f D Mx Al f Fuzzy OSIS Rkg f Mg Mhd h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY 2008 389

July_23-34:ml Jul 7/15/08 12:46 M g 390 A w mdl f mg mhd l f ml d h fl f h m lv l h v dl lu. h fmd by h fw l lf d h u ly h u fm uh l, h ffv wgh d l lv. Eml llu I h, h ml xml xmd ug h d mdl. h f xml k fm Nhl10. Oh ud l l f h d mdl mg mhd l. Exml 1: h xml d h vgd by Nhl10. Ud d gv bl III. L u u h g ( vlu d h lv m wgh) f um kg mhd dg bl IV. Af vlu h fu lv dmd, dg h d mdl wll h ul f Nhl mhd. h ul ummzd bl V. h Nhl d d mdl ld h h f h f y. C udy 1:56,57 I d vg h m f h d mdl, h Gl--Gh (GEG) d, uh f I, w h h f. h d ld 55 km uh-w f Sj (Fgu 2). h bv md d lud x ml. Amly N. 1 h b xd f my y wh mg. Rly, xl f mly N. 3 h b dd. D N. 3 h lgh f 2 200 m h-uh l d vg wdh f 1 800 m h w f mly N. 1, whh ld ud lvly fl fld. h gm d m gmh f f mly N.3 d bl VI bd h l dld xl ul. I d l h m ubl x mhd f h d, 11 mhd dd f m d m. Exmd x mhd lud: mg, blk vg, ublvl g, ublvl vg, lgwll, m d ll, hkg, u d fll, lg, qu- d d ll mhd. h mhd d h FDM mdl lv. C vlvd h l lud h ubly f d h, gd dbu, d d, d hk, d dh, hggwll k m g (RMR), d RMR, hggwll k ub gh () ( = vbud u/ uxl mv gh UCS), d, fwll, mg mhd vy, x wk f, du y, hggwll k quly dg (RQD), h gh f d j, hggwll j h d m. bl III Nhl xml u m 10 C D O z D h bul ly O hk 90 m (hk) O d 15 dg(fl) Gd dbu ufm Dh 130 m RQD 40 % Sg J d Cl wh ugh uf Hggwll RQD 65% Sg J d Cl wh ugh uf F wll RQD 40% md J d Cd wh h ly bl V Summy f vlu f xml 1 Mhd O S BC SQ SC SH Nhl 33.8 28.3 27.3 26.6 26.3 25.8 FDM 70.74 58.13 57.26 56.49 55.91 56.34 * Wh O:, S: lg, BC: blk vg, SQ: qu, SC: ublvl vg d SH: hkg mg mhd bl IV Lgu vlu f Nhl d wgh D Lgu k C vlu -49 Vy lw 0 Lw 1 ML lw 2 Mdum 3 ML hgh 4 Hgh Wghg f 0.5 Mdum 0.8 Hgh 1 Vy hgh Fgu 2 L f GEG d Chh Gbd m 390 JULY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

July_23-34:ml Jul 7/15/08 12:46 M g 391 A w mdl f mg mhd l f ml d h m d bu. h f gh u fm f h mdl. h d mx f GEG mly N. 3 w d h FDM mdl dg Fgu 3. I h, mg d (gv ff d mkg) d h h m d f. h d mkg mx d ld wgh f hw Fgu 3. h mly f hgg h wgh d udyg dff d mkg u dvg f h mdl. bl VI Sf f GEG I O mly N. 3 C D O z Gl h bul O hk 15 130, Avg 40 m O d 20 dg Gd dbu Gdl Dh 95 ~ 600 m RQD 75% 8.9 RMR Gd (60-80) O v 643 mll J d Flld (lw gh ) Hgg wll RQD 38% 6 RMR Gd (60 80) J d Cl wh mh uf Fwll RQD 15% 6.5 RMR Gd (60 80) J d Cl wh ugh uf Fgu 4 hw h bd by h mg mhd fuzzy d mkg, f h d h b d by h FDM mdl. h mg mhd d f wh f 75.71d h qu- mhd l wh f 30.86. C udy 2: 56,57 h Chh Gbd d ld 50 km h f Sj, uh f I (Fgu 2). bl VII hw h hyl d mhl h f h d. I d l mg mhd f h d, 11 mhd d f m uh h GEG mg mhd l. h h ff h l, dd h udy, d Fgu 5. h fl bd by h mg mhd h fuzzy d mkg mhd hw Fgu 6. h mg mhd f wh 78.90 d h qu- mhd l wh 28.03. Rul d du I xml 1, h ly dff bw h ul f h Nhl d d mdl h kg f h ublvl vg d hkg (bl V). h Fuzzy OSIS f h my d mkg mhd. A md bf, h mhd dg h f m md by g h f h m() d v v. I f h hkg l h h ublvl vg h dl lu l f h hkg mhd ublvl vg. h ulg lv f GEG mly N. 3 vy mg h dff mhd m x. h gh lv, dg h uml kg mhd Fgu 3 Gml d gmhl u d f GEG d N. 3 h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY 2008 391

July_23-34:ml Jul 7/15/08 12:46 M g 392 A w mdl f mg mhd l f ml d bl VII Sf f Chh Gbd C O z Hggwll Fwll Fgu 4 h bd by h mg mhd f GEG d N. 3 D Gl h ly O hk Avg 8.5 m O d 70 dg Gd dbu Igul Dh Lw dh (<100 m) RQD 75% 8.7 RMR Gd (60 80) O v 700 mll J d Flld (lw gh ) RQD 38% 15.63 RMR Gd (60 80) J d Cl wh mh uf RQD 15% 9.1 RMR Avg (40 60) J d Cl wh ugh uf Fgu 5 Gml d gmhl u d f Chh Gbd d 392 JULY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

July_23-34:ml Jul 7/15/08 12:46 M g 393 A w mdl f mg mhd l f ml d Fgu 6 h bd by h mg mhd f h Chh Gbd d bl VIII S f dff xl mhd dg h mhd vl GEG d N. 3 Mhd O Cu d fll Shkg Sublvl g lg Squ- Blk vg Sublvl vg C 1 Nhl 32.9 30 29.1 28.8 28.8 28 26.1 20.7 UBC 33 33 22 34 16 10 24 28 FDM 75.71 55.43 46.85 60.88 45.40 30.86 58.36 56.02 C 2 Nhl 32 30 25 21-25 - - UBC 33 34 34 32 13 15 - - FDM 78.9 60.46 53.91 66.88 37.91 28.03 53.61 51.73 (Nhl d UBC), wll h ul by FDM, d bl VIII. Cdg bl VIII: h mg h Nhl mhd h bd h b. h ul ug dg h f h h UBC mhd, g h b d wh f Cd mg d gv y g mhd uh ublvl g. Bu h UBC mg mhd l mdf f h Nhl h, whh l m mh g mhd (ublvl g, m d ll d u d fll), hu b g yl Cd mg dg.11 Cdg h ul f h mg mhd l f Chh Gbd ( 2), mg h Nhl mhd h bd h b. By lyg h FDM mdl, bd Fuzzy OSIS, gy w ffd x ml d. h gy h dvg m wh vu uml kg (g) mhd uh Nhl d UBC. h dvg g hl b fuzzy lg, h hgh d hvg h ul, h bly f vy ly, h d ug f lgu vbl h mg mhd l, ulmd lv d, d, m m f ll, h bly f dg h muul ff f dff m h l. I f, OSIS f h my mulbu d mkg mdl. Mv, h mdl d h uy d wh h u m (lgu vbl) ud h l. h mdl h l bm ubl l mg mhd l. Clu h mg mhd l f xld bdy l d g u h mg gg. h d vlv my m h ld h hg m m ff h h. h h dud mg mhd l fuzzy vm d u lgu vlu f vbl. Fuzzy OSIS vbl mhd f h d blm d ubl f h u f lgu vbl. Wh h d mkg d vgu d u, h h mhd h fd hqu. h udy xld h u f Fuzzy OSIS mg mhd l. h d mdl b ubl l l h mg mhd. h mg mhd l f GEG mly N.3 d Chh Gbd w xmd by h mdl. A h d f h xm, mg w gd h b x mhd f h d d. h ym vlu by Fuzzy OSIS f mg mhd l blm du h k f h. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY 2008 393

July_23-34:ml Jul 7/15/08 12:46 M g 394 A w mdl f mg mhd l f ml d Rf 1. KARADOGAN, A., KAHRIMAN, A., d OZER, U. Al f fuzzy hy h l f udgud mg mhd. h Jul f h Suh Af Iu f Mg d Mllugy, 2008. vl. 108.. 73 79. 2. BIARAFAN, M.R. d AAEI, M. Mg mhd l by mull d mkg l. h Jul f h Suh Af Iu f Mg d Mllugy, Ob 2004.. 493 498. 3. EELE, R. d CHURCH, J. Mg Egg Hdbk, Jh Wly d S, INC. 1941. vl. 1. 4. BOSHKOV, S., d WRIGH, F. B d m C h Sl, Dg d Dvlm f Udgud Mg Sym. SME Mg Egg Hdbk. Cumm d Gv. SME. Nw Yk. 1973. vl. 1.. 12.2 12.13 5. MORRISON, R.G.K. AQ hlhy f Gud Cl. MGll Uvy. Ml. Cd. 1976.. 125 159. 6. HARMAN, H.L. Iduy mg gg. Jh Wly d, I, Sd d. 2002. 7. AGOSHKOV, M., BORISOV, S., d BOYARSKY, V. Clf f O D Mg Sym. Mg f O d N-Ml Ml. U f Sv Sl Rubl. 1988.. 59 62. 8. LABSCHER, D. Sl f M Udgud Mg Mhd. Dg d O f Cvg d Sublvl Sg M. 1981, Nw Yk, AIME, Ch 3. 9. NICHOLAS, D. d MARK, J. Fbly Sudy Sl f Mg Mhd Igg Rk Mh d M lg, 5h Rd Exv d ulg Cf. 1981. S F. vl. 2.. 1018 1031. 10. NICHOLAS, D.E. Sl du. Mg Egg Hdbk. Hm, H. SME. Nw Yk, 1993.. 2090 2105. 11. MILLER, L., AKALNIS, R., d OULIN, R. UBC Mg Mhd Sl. Il ymum m lg d qum l. Sgh. 1995. 12. HARMAN, H.L. Iduy mg gg. Jh Wly d, I, Sd d. 2002. 13. YIMING, W., YING, F., d WEIXUAN, X. A Igd Mhdlgy f D Mkg f Mg Mhd Sl. Mufug hlgy d Mgm. Ch. 2003 14. YIMING, W., YING, F., d WEIXUAN, X. Mull Objv gd mhdlgy f Glbl Omum D-Mkg Ml Exl. Cmu & Idul Egg, vl. 46, 2004.. 363 372. 15. KESIMAL, A. d BASCEIN, A. Al f Fuzzy Mull Abu D Mkg Mg O. Ml Ru Egg. 2002, vl. 11,. 59 72. 16. MIRANDA, C. d ALMEIDA. Mg Mhd Sl Bd Mul Mdl. Al f Cmu d h h ml duy. Ld. 2005. 17. SAMIMI NAMIN, F., SHAHRIAR, K., d KARIMI NASAB, S. Fuzzy D Mkg f Mg Mhd Sl hd Amly Gl-E-Gh D. 18h Il mg g d xhb f uky, I MCE. 2003. 18. SHAHRIAR, K., SHARIAI, V., d SAMIMI NAMIN, F. Gmhl Ch Sudy f D Udgud Mg Mhd Sl. 11h ISRM Cf, 2007. ugl. 19. BASCEIN, A., OZAS, O., d KANLI, A.I. Mg mhd l by mull d mkg l. h Jul f h Suh Af Iu f Mg d Mllugy, 2006. vl. 106.. 63 69. 20. YAGER, R.R. A w mhdlgy f dl mul bjv d bjv bd Fuzzy, D S, 1978, vl. 12.. 589 600. 21. BELLMAN, R.E. d ZADEH, L.A. D Mkg I Fuzzy Evm, Mgm S, vl. 17, 1970.. 141 164. 22. SAAY,.L. D-mkg f Ld, RWS ubl, USA. 1990. 23. MACHARIS, C., SRINGAEL, J., DE BRUCKER, K., d VERBEKE, A. ROMEHEE d AH: h dg f l yg mul- ly, Sghg ROMEHEE wh d f AH. Eu Jul f l Rh, vl. 153, 2004.. 307 317. 24. SHYUR, H.J. C Evlu Ug Mdfd OSIS d AN. Ald mhm d mu, vl. 177, 2006.. 251 259. 25. SHYUR, H.J. d SHIH, H.S. A hybd MCDM mdl f Sg vd l. Mhml d Cmu Mdlg, vl. 44, 2006.. 749 761. 26. KIM, G., ARK, C.S., d YOON, K.. Idfyg Ivm Ou f Advd Mufug Sym wh Cmv-Igd fm Mum, Il Jul f du Em, vl. 50, 1997.. 23 33. 27. SHIH, H.S., SHYUR, H.J., d LEE, E.S. A x f OSIS f Gu D Mkg. Mhml d Cmu Mdlg, vl. 45, 2007.. 801 813. 28. ABO-SINNA, M.A. d AMER, A.H. Ex f f mul-bjv lgl l gmmg blm. Ald Mhm d Cmu, vl. 162, 2005.. 243 256. 29. AGRAWAL, V.., KOHLI, V., d GUA, S. Cmu dd b l: h mull bu d mkg h. Il Jul f du Rh, vl. 29, 1991.. 1629 1644. 30. CHENG, S., CHAN, C.W., d HUANG, G.H. A gd mul- d ly d x mxd g l gmmg h f ld w mgm. Egg Al f Afl Illg, vl. 16, 2003.. 543 554. 31. DENG, H., YEH, C.H., d WILLIS, R.J. I-my m ug mdfd wh bjv wgh. Cmu d O Rh, vl. 27, 2000.. 963 973. 32. FENG, C.M. d WANG, R.. fm vlu f l ludg h d f fl. Jul f A Mgm, vl. 6, 2000.. 133 142. 33. FENG, C.M. d WANG, R.. Cdg h fl h fm vlu f hghwy bu duy. Rvw, vl. 21, 2001.. 449 467. 34. HWANG, C.L. d YOON, K. Mull bu d mkg: Mhd d l. Bl: Sg. 1981 35. JEE, D.H. AND KANG, K.J. A mhd f ml ml l dd wh d mkg hy. Ml d Dg, vl. 21, 2000.. 199 206. 36. KIM, G., ARK, C.S., d YOON, K.. Idfyg vm u f dvd mufug ym wh mv-gd fm mum. Il Jul f du Em, vl. 50, 1997.. 23 33. 37. LAI, Y.J., LIU,.Y., d HWANG, C.L. F MODM. Eu Jul f Ol Rh, vl. 76, 1994.. 486 500. 38. LIAO, H.C. Ug CR- mz guh mul- blm. h Il Jul f Advd Mufug hlgy, vl. 22, 2003.. 649 655. 39. OLSON, D.L. Cm f wgh mdl. Mhml d Cmu Mdllg, vl. 40, 2004.. 721 727. 40. ORICOVIC, S., d ZENG, G.H. Cmm lu by MCDM mhd: A mv ly f VIKOR. Eu Jul f Ol Rh, vl. 156, 2004.. 445 455. 41. ARKAN, C. d WU, M.L. O h quvl f l fm mum d mull bu d mkg. Il Jul f du Rh, vl. 35, 1997.. 2963 2988. 42. ARKAN, C. AND WU, M.L. D-mkg d fm mum mdl wh l b l. Cmu d Idul Egg, vl. 36, 1999.. 503 523. 43. ONG, L.I. d SU, C.. Omzg mul- blm h guh mhd by fuzzy mull bu d mkg. Quly d Rlbly Egg Il, vl. 13, 1997.. 25 34. 44. ZENG, G.H., LIN, C.W., d ORICOVIC, S. Mul- ly f lv-ful bu f ubl. Egy ly, vl. 33, 2005.. 1373 1383. 45. ZANAKIS, S.H., SOLOMON, A., WISHAR, N., d DUBLISH, S. Mul-bu d mkg: A mul m f l mhd. Eu Jul f Ol Rh, vl. 107, 1998.. 507 529. 46. CHEN, C.. Ex f h f gu d-mkg ud fuzzy vm. Fuzzy S d Sym, 2000.. 114, 1 9. 394 JULY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

July_23-34:ml Jul 7/18/08 10:56 AM g 395 A w mdl f mg mhd l f ml d 47. CHEN, M.F. d ZENG, G.H. Cmbg gy l d f lg x h uy. Mhml d Cmu Mdllg, vl. 40, 2004.. 1473 1490. 48. Chu,. C. Fly l l ug fuzzy OSIS ud gu d. Il Jul f Uy, Fuzz d Kwldg-Bd Sym, 2002. Vl. 10,. 687 701. 49. CHU,.C. Slg l l v fuzzy OSIS h. h Il Jul f Advd Mufug hlgy, 2002, vl. 20,. 859 864. 50. CHU,.C. d LIN, Y.C. A fuzzy OSIS mhd f b l. h Il Jul f Advd Mufug hlgy, vl. 21, 2003.. 284 290. 51. KAUFMANN, A. d GUA, M.M. Idu fuzzy hm: hy d l. Nw Yk: VNd-Rhld. 1991 52. RIANAHYLLOU, E. d LIN, C.. Dvlm d vlu f fv fuzzy mulbu d-mkg mhd. Il Jul f Axm Rg, vl. 14, 1996.. 281 310. 53. YING-MING WANG d AHA, M.S. Elhg. Fuzzy mhd bd lh lvl wh l bdg k m. Ex ym wh l, 2005.. 1 11. 54. ZADEH, L.A. Fuzzy. Ifm l. vl. 8, 1965.. 338 353. 55. MEAMARIANI, A. FDM fw (Fuzzy D Mkg). b Md Uvy. h, I. 2003. 56. SHAHRIAR, K., SAMIMI, F., d DEHGHAN, H. Mg Mhd Sl f Chh Gbd D Bd Fuzzy D Mkg (FDM), 2007, 20h Il Mg Cg f uky (IMCE),. 143 150. 57. SAMIMI NAMIN, F. Udgud mg mhd l bd d hy. h.d. h. Fuly f Mg d Mllugl Egg. Amkb Uvy f hlgy. h. I. LAINUM 2008 Jh Mhy l lum 2008 duy vw* lum mk df by 480-000 z 2007 h lum mk w df by 480-000 z 2007 dg lum 2008, ld dy by Jh Mhy. Du du Suh Af dv glbl lum ul dw 6.55 mll u. Dmd f lum by 8.6 7.03 mll u wh d uh f ml f uly d f dul u. h lum by 35, hg f d hgh. Jwlly dmd fll mglly ud u fm h hgh. Suh Af uly fll lum ul 2007 fll by 4.1 6.55 mll u. Suh Af ul fll by 4.9 5.04 mll u; uhduld ml lu, fy blm d dfful dul l lm hd gv m. Sul f lum fm Ru d lwh fll lghly. Auly uh f lum w d Glbl lum uh by h uly by 8.2 2007 4.23 mll u. h umb f dl vhl dud Eu, J d Nh Am fd wh lum-bd xhu fm m m ul ud, uwghg h ff f ubu f lum by lldum m gl d dl ly. Hgh hv ll m jwlly dmd D g, uh f lum by h jwlly duy, xludg, fll ly mglly 1.59 mll u. Rl l d mufug vlum w l m gghl mk. Ch dmd f mufug lum jwlly mdly fm 760-000 z 780-000 z. h quy f d-hd jwlly d uld l k ud f ylg bh Ch d J d du h hgh ml. Exhg dd fud b vm dmd lum vm dmd lmbd hly 170-000 z 2007 fm dvm f 40-000 z h vu y. h luh f w w lum-bd xhg dd fud Eu h f hlf f 2007 d gf w vm dmd. lum dul dmd 1.94 mll u, x u fm h 2006 l. h w dd by bmg l l f l gd, whh d lum qum f hd dk d f h mufu f fl l dly gl. lum m vll h uywd w uly Suh Af d h my lu f h Amdlbul m du fldg ly 2008 wll ff du f lum h y. Wh dul d umv dmd xd m g d ul udfm, h lum mk lkly b ubl df 2008. h glbl m lwdw d y ghg h US dll uld u h lum f bu hgh vlly xd u dug h x x mh. Jh Mhy f h lum wll d wh wd g f $1-775 $2-500 v h d. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY 2008 395