ATTITUDE INDEX GROUP DECISION-MAKING METHOD OF PERFORMANCE EVALUATION FOR COAL ENTERPRISES ENERGY CONSERVATION AND REDUCTION OF POLLUTANT EMISSIONS

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1 ATTITUDE INDEX GROUP DECISION-MAKING METHOD OF PERFORMANCE EVALUATION FOR COAL ENTERPRISES ENERGY CONSERVATION AND REDUCTION OF POLLUTANT EMISSIONS GAO YAN LIU CHENCHEN Bussess admstrato ost dotor researh stato Shadog Uversty Ja 006 Shadog Cha Iformato ad Egeer College Jg Medal Uversty Jg 7000 Shadog Cha ABSTRACT For the erformae evaluato of oal eterrses eergy oservato ad reduto of ollutat emsso a ew atttude dex grou deso-mag method s roosed based o traezodal fuzzy umbers. Uder the odto whh the formato of attrbutes weghts ad deso maer weghts s etrely the atttude dex s trodued frstly. By solvg the fuzzy obet rogrammg for the etrely formato the weghts of the atttude ad deso mag matrx are determed. Seodly the value of grou rs atttude s got by tegratg the atttude dex of the deso maers ad the grou omrehesve attrbute values of eah alteratve ad the rortes are aheved. At last the ratal examle of erformae evaluato for oal eterrses eergy oservato ad reduto of ollutat emsso shows the feasblty ad effetveess of the roosed method. Keywords: Atttude Idex; Traezodal Fuzzy Number; Eergy Coservato ad Reduto of Pollutat Emsso. INTRODUCTION Our eoomy has radly develoed se the mlemet of the reform ad oeg u oly 978. As the thrd largest eoomy our GDP reahed 30 trllo RMB 008 wth a average aual growth rate of 9.88%. Meawhle ths ahevemet has also gve rse to serous evrometal ad eologal roblems. To rotet evromet ad realze sustaable develomet Chese govermet has ut forward the strateg obetve to buld a resoure-savg ad evromet-fredly soety. Therefore eergy oservato ad reduto of ollutat emsso beomes a mortat ob amog govermet deartmets. Before the 00 Coehage oferee Chese govermet has also aoued ts target of redug CO emssos er ut GDP by 0 5% tll 00 wth that 005 as the base. Uder ths odto the oly exeutor etrereeur eseally oal eterrses reeve more oers gradually for ther erformae evaluato of eergy oservato ad reduto of ollutat emsso. So oal eterrses are assve dealg wth eergy oservato ad reduto of ollutat emsso whh s adverse to the maagemet of eergy oservato. At the data weghtg ad aggregato stage mult-attrbute grou deso mag (MAGDM) has reetly gaed muh oularty erformae evaluato. MAGDM s a wellestablshed tehque that ould hel deso maers to evaluate exstg or otetal alteratves wth multle oflt rtera. I the ast deades MAGDM has bee otuously studed ad suessfully aled may alato domas. But all these researhes have ot osdered the deso maers atttude dex the grou. The results of the grou deso mag are dfferet beause the dfferet atttude of deso maers. I ths aer a ew atttude dex grou deso mag s roosed based o traezodal fuzzy umbers. By ths ew method ths aer evaluates the erformae of oal eterrses eergy oservato ad reduto of ollutat emsso.. TRAPEZOIDAL FUZZY NUMBER Defto Geeralzed traezodal fuzzy 76

2 umbers a be defed a vetor A % = ( a b d) < a b d < ad the membersh futo µ : R [0] s defed a follows: A ( x a) ( b a) a x b b x µ A = () ( x d) ( d) x d 0 Defto Let A % = ( a b d) be a traezodal fuzzy umber the the left exeted value ad the rght exeted value of the traezodal fuzzy s defed by L I ( A% R ) = ( a + b) I ( A% ) = ( + d) ad the exeted value of the traezodal fuzzy umber s defed by L R I( A% ) = ( I ( A% ) + I ( A% )). Let X = [ x ] m be the traezodal fuzzy umber deso matrx: x x L x m x x xm X L =. M M O M x x L xm For elmatg the dfferee of the roerty dmeso ad sale we must ormalze the roerty of the dators. Now gve the stadardzed formula. The reveue tye stadardzed formula: m m a m m b x = [ d m m m m d ] b a The ost tye stadardzed formula: a b x = [ max max d max max max max b d ] max max a 3. ATTITUDE INDEX GROUP DECISION MAKING BASED ON TRAPEZOIDAL FUZZY NUMBER DECISION MATRIX I a grou deso mag there are deso maers ad the weghts of them are λ = { λ L λ }. Let X = { x x L x m } be a set of alteratves ad let C = { L } be a set of rtera. The weghts of rtera are W = ( ω L ω ) satsfyg ω = ad ω 0 = L. The = evaluato value of deso maer e about rtera o a alteratve x s rereseted by the followg matrx X where the elemet of the matrx s traezodal fuzzy umber x = [ a b d ]. I order to faltate we let the stadardzed matrx stll be X. Let Θ be a set of mathematal exresso whh the formato about weghts of the rtera s omleted uow. The set s dvded to sx tyes: ω ω ;ω ω α ;3ω β ω ; γ ω γ + ε ;5 θω ( θ + ε ) ω or θ ω ω ( θ + ε ) ω 0 ;6ω ω ω ωl l where α β ε θ γ s o-egatve. 3. Atttude Idex Of Traezodal Fuzzy Number Defto 3 Let A % = ( a b d) be a traezodal fuzzy umber we deote L I ( A% R ) = ( a + b) I ( A% ) = ( + d) L R I( A% ) = ( I ( A% ) + I ( A% )) R L D( A% ) = ( I ( A% ) I ( A% )). Defte the futo o [0] as the followg: F ( α ) :[0] ( a b d ) A % F ( α) = I( A% ) + (α ) D( A% ). A % So all α as the traezodal fuzzy umber atttude dex of the deso maer. Obvously F ( α ) A % s a reasg futo o [0] ad () If α = 0 the Fα ( α ) = I( A% ) D( A% ) L R R L = ( I ( A % ) + I ( A % )) ( I ( A % ) I ( A % L )) = I ( A %). It dates the deso maers have essmst atttude; () If α = the Fα ( α ) = I( A% ) + D( A% ) L R R L = ( I ( A % ) + I ( A % )) + ( I ( A % ) I ( A % R )) = I ( A %). It dates the deso maers have otmst atttude; (3)If α = 0.5 the Fα ( α ) = I( A% ). It dates the deso maers have moderate atttude. 77

3 Suose α α [0] s the atttude dex of the deso maer e the traezodal fuzzy umber matrx X s trasformed to the deso mag matrx wth atttude dex F ( α ) = ( f ( α )) where m f ( α ) = I( x ) + (α ) D( x ) ( ) ( ) ( ) a + b + + d = [ ] + (α ) ( ) ( ) ( ) ( ) + d a b [ ]. ( f ) ( α ) s osdered as value of the obetve referees. The value v = [ w x y z ] of the subetve referees also s trasformed to the value wth atttude dex ( w ) + x + y + z v ( α ) = [ ] y + z w x + (α )[ ]. 3. Itegrato Of Idvdual Alteratve Ad Soluto Of Crtera Weghts Due to the restrto of varous odtos there are some devatos betwee the obetve ad subetve referees. The absolute devato betwee the obetve ad subetve referees s ( ) ( ) ( ) exressed asσ ( α ) = f ( α ) v ( α ). So for the deso maer e the devato betwee the alteratve x ad subetve referee s exressed as m = = σ ( α ) ω. Establsh otmza -to model of the mmum devato betwee the obetve ad subetve referees by whh the weghts of the rtera are solved: m m σ ( α ) ω = = W Θ s. t. ω = () = ω Itegrato Of Grou Alteratve Ad Soluto Of Deso Maers Weghts m ( ) ( ) = = = Defte Z( x ) λ f ( α ) ω = so we ow Z( x ) s a traezodal fuzzy umber. The soluto of deso maers weghts by the followg model: m = λ f α ω = = = max Z( x ) ( ) λ Θ s. t. λ = (3) = λ 0 3. Itegrato Of Grou Rs Atttude Ad Order Method Eah deso maer has a atttude dex ad a orresodg weght so the rs atttude value of the grou s η = λ α.beause the formato = of the deso maer weght s uerta so the rs atttude value of the grou may ot be oly oe. But we a get a otmal value λ of the deso maer weght by the model (3). Ad the we a solve the rs atttude value of the grou η by η = λ α. Itegrate Z( x ) ad the rs atttude = value of the grou usg the followg method: F ( Z( x )) = I ( Z( x )) + (η ) D( Z( x )) η Aordg the order from small to large we get the whole order of the alteratve.. NUMBERICAL EXAMPLES FOR EVALUATION OF COAL ENTERPRISE ENERGY CONSERVATION AND REDUC-TION OF POLLUTANT EMISSION Selet 3 oal eterrses of Yazhou Cty Shadog Prove as evaluato obets ad use samle survey aroah to evaluate the erformae of eergy oservato ad reduto of ollutat emsso. We vte two exerts to evaluate them from three rtera: resoure outut resoure osumto olluto emsso 3. The stadard evaluato s see table ad table. The formato about the weght s the followg: H = { } 3 H = { }. The weghts of the deso maers are { λ λ 0.3 λ 0.58}. The atttude dexes of the two exerts are α = 0. α = 0.7 ad the subetve referee 78

4 value are ( ) ( ) ( ). ()Itegrato of dvdual alteratve ad soluto of rtera weghts Usg the model () we solve the rtera s weghts: ω = { } ω = { }. For the exert e alteratve s the tegrato of the Table : THE EVALUATION OF E A ( ) B ( ) C ( ) A ( ( ) ( ) (0.8 ) Table : THE EVALUATION OF E ( ) ( ) ( ) ) B ( ) C ( ) ( ) ( ) (0.8 ) A : ( ) B : ( ) C : ( ). ( ) ( ) ( ) For the exert e the tegrato of the alteratve s A : ( ) B : ( ) C : ( ). ()Itegrato of grou alteratve ad soluto of deso maers weght. Usg the model (3) we solve the exerts weghts: λ = ( ). The the grou tegrato s A : ( ) B : ( ) C : ( ). (3)Itegrato of grou rs atttude ad order method. The rs atttude s η = λα + λα = = By the formula we a get the order of the 3 oal eterrses grou: A :.06 B :.37 C :. amely C f Bf A. 5. CONCLUSION Ths aer roosed a ew atttude dex grou deso-mag method based o traezodal fuzzy umbers. Uder the odto whh the formato of attrbutes weghts ad deso maer weghts s etrely the atttude dex s trodued. By solvg the fuzzy obet rogrammg for the etrely formato the weghts of the rtera ad deso maer are determed. Ad the grou omrehesve attrbute values of eah alteratve ad the rortes are aheved. At last usg the method we evaluated the erformae for oal eterrses eergy oservato ad reduto of ollutat emsso. ACKNOWLEDGEMENTS The atoal atural see foudato fuded roet (70070); Shadog Uversty selfreovato foudato fuded roet (0GN0); Cha Postdotoral surfae Proet (0M503) REFERENCES: [] Ataassov K Itutost fuzzy sets Fuzzy Sets ad Systems Vol. No [] Shu M H Cheg C H Chag J R Usg tutoost fuzzy sets for fault tree aalyss o rted rut board assembly Mroeletros Relablty Vol. No [3] Xu Z S Yager R R Some geometr aggregato oeratos based o tutost fuzzy sets It J of Geeral Systems Vol. No

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