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

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1 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, SA ISSN X/ vd My 2007; vd vd My h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER JULY

2 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

3 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

4 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

5 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 ( 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

6 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 m h-uh l d vg wdh f 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 FDM * 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

7 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 , 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 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 d h qu- mhd l wh 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

8 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% 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

9 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 UBC FDM C 2 Nhl UBC FDM (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

10 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, vl 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 EELE, R. d CHURCH, J. Mg Egg Hdbk, Jh Wly d S, INC vl 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 vl MORRISON, R.G.K. AQ hlhy f Gud Cl. MGll Uvy. Ml. Cd HARMAN, H.L. Iduy mg gg. Jh Wly d, I, Sd d 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 LABSCHER, D. Sl f M Udgud Mg Mhd. Dg d O f Cvg d Sublvl Sg M. 1981, Nw Yk, AIME, Ch NICHOLAS, D. d MARK, J. Fbly Sudy Sl f Mg Mhd Igg Rk Mh d M lg, 5h Rd Exv d ulg Cf S F. vl NICHOLAS, D.E. Sl du. Mg Egg Hdbk. Hm, H. SME. Nw Yk, MILLER, L., AKALNIS, R., d OULIN, R. UBC Mg Mhd Sl. Il ymum m lg d qum l. Sgh HARMAN, H.L. Iduy mg gg. Jh Wly d, I, Sd d YIMING, W., YING, F., d WEIXUAN, X. A Igd Mhdlgy f D Mkg f Mg Mhd Sl. Mufug hlgy d Mgm. Ch YIMING, W., YING, F., d WEIXUAN, X. Mull Objv gd mhdlgy f Glbl Omum D-Mkg Ml Exl. Cmu & Idul Egg, vl. 46, KESIMAL, A. d BASCEIN, A. Al f Fuzzy Mull Abu D Mkg Mg O. Ml Ru Egg. 2002, vl. 11, MIRANDA, C. d ALMEIDA. Mg Mhd Sl Bd Mul Mdl. Al f Cmu d h h ml duy. Ld 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 SHAHRIAR, K., SHARIAI, V., d SAMIMI NAMIN, F. Gmhl Ch Sudy f D Udgud Mg Mhd Sl. 11h ISRM Cf, 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, vl YAGER, R.R. A w mhdlgy f dl mul bjv d bjv bd Fuzzy, D S, 1978, vl BELLMAN, R.E. d ZADEH, L.A. D Mkg I Fuzzy Evm, Mgm S, vl. 17, SAAY,.L. D-mkg f Ld, RWS ubl, USA 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, SHYUR, H.J. C Evlu Ug Mdfd OSIS d AN. Ald mhm d mu, vl. 177, SHYUR, H.J. d SHIH, H.S. A hybd MCDM mdl f Sg vd l. Mhml d Cmu Mdlg, vl. 44, 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, SHIH, H.S., SHYUR, H.J., d LEE, E.S. A x f OSIS f Gu D Mkg. Mhml d Cmu Mdlg, vl. 45, ABO-SINNA, M.A. d AMER, A.H. Ex f f mul-bjv lgl l gmmg blm. Ald Mhm d Cmu, vl. 162, AGRAWAL, V.., KOHLI, V., d GUA, S. Cmu dd b l: h mull bu d mkg h. Il Jul f du Rh, vl. 29, 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, DENG, H., YEH, C.H., d WILLIS, R.J. I-my m ug mdfd wh bjv wgh. Cmu d O Rh, vl. 27, FENG, C.M. d WANG, R.. fm vlu f l ludg h d f fl. Jul f A Mgm, vl. 6, FENG, C.M. d WANG, R.. Cdg h fl h fm vlu f hghwy bu duy. Rvw, vl. 21, HWANG, C.L. d YOON, K. Mull bu d mkg: Mhd d l. Bl: Sg JEE, D.H. AND KANG, K.J. A mhd f ml ml l dd wh d mkg hy. Ml d Dg, vl. 21, 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, LAI, Y.J., LIU,.Y., d HWANG, C.L. F MODM. Eu Jul f Ol Rh, vl. 76, LIAO, H.C. Ug CR- mz guh mul- blm. h Il Jul f Advd Mufug hlgy, vl. 22, OLSON, D.L. Cm f wgh mdl. Mhml d Cmu Mdllg, vl. 40, ORICOVIC, S., d ZENG, G.H. Cmm lu by MCDM mhd: A mv ly f VIKOR. Eu Jul f Ol Rh, vl. 156, 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, ARKAN, C. AND WU, M.L. D-mkg d fm mum mdl wh l b l. Cmu d Idul Egg, vl. 36, 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, ZENG, G.H., LIN, C.W., d ORICOVIC, S. Mul- ly f lv-ful bu f ubl. Egy ly, vl. 33, 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, CHEN, C.. Ex f h f gu d-mkg ud fuzzy vm. Fuzzy S d Sym, , JULY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

11 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, Chu,. C. Fly l l ug fuzzy OSIS ud gu d. Il Jul f Uy, Fuzz d Kwldg-Bd Sym, Vl. 10, CHU,.C. Slg l l v fuzzy OSIS h. h Il Jul f Advd Mufug hlgy, 2002, vl. 20, CHU,.C. d LIN, Y.C. A fuzzy OSIS mhd f b l. h Il Jul f Advd Mufug hlgy, vl. 21, KAUFMANN, A. d GUA, M.M. Idu fuzzy hm: hy d l. Nw Yk: VNd-Rhld RIANAHYLLOU, E. d LIN, C.. Dvlm d vlu f fv fuzzy mulbu d-mkg mhd. Il Jul f Axm Rg, vl. 14, YING-MING WANG d AHA, M.S. Elhg. Fuzzy mhd bd lh lvl wh l bdg k m. Ex ym wh l, ZADEH, L.A. Fuzzy. Ifm l. vl. 8, MEAMARIANI, A. FDM fw (Fuzzy D Mkg). b Md Uvy. h, I 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), 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 z 2007 h lum mk w df by 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 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 mll u. Suh Af ul fll by 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 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 z 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 z 2007 fm dvm f 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 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