A Fuzzy GM(1,1) Model Based Possibility Check for Predicting CO2 Emissions

Transcription

1 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 A Fuzzy GM(,) Model Bsed Possibility Check for Predicting CO Emissions Zhiyi Meng intensity in this region hs incresed quickly from 0.5 in 005 yer to 0.7 in 008 yer, which reflects the environment protection of the world nturl nd culturl heritge fcing gret chllenge. Previously, vrious studies predicted CO in mny wys. King [4] predicted regionl CO exchnge between the tmosphere nd the terrestril biosphere by using ecosystem models. Bcstow nd Keeling [5] discuss the models to predict future tmospheric CO concentrtions. Rich [6] studies globl ptterns of crbon dioxide emissions from soils. Kim [7] focus on solubility mesurement nd prediction of crbon dioxide in ionic liquids. Prk [8] reserched correltion nd prediction of the solubility of crbon dioxide in queous lknolmine nd mixed lknolmine solutions. However, there re few studies predicted CO emissions use GM(,) model under fuzzy environment. Grey theory, developed originlly by Deng [9], is truly multidisciplinry nd generic theory tht dels with systems tht re chrcterized by poor informtion or for which informtion is insufficient. The fields covered by grey theory include systems nlysis, dt processing, modeling, prediction, decision mking nd controlling. The grey theory minly works on systems nlysis with poor, incomplete or uncertin messges. Grey forecsting models hve been extensively used in mny pplictions. Furthermore, there re mny uncertinties when setting the objectives. Using one kind of vrible to describe those uncertinties is very importnt. Thus, fuzzy vrible is considered. Since Zimmermnn [0] first introduced conventionl liner progrmming nd multi-objective liner progrmming into fuzzy set theory, there is now n overwhelming mount of reserch on using fuzzy method to solve uncertinty problem. However, combing GM(,) with fuzzy method to provide support for decision mkers is bsent from current reserch. In ddition, the dt of CO emissions is locked nd inccurcy, policy mkers' high demnd for relible model results hs not yet been fulfilled. In this pper, fuzzy grey method will be employed to mke prediction on emissions in the world nture nd culture heritge res. The rest of the pper is orgnized s follows. Section II presents the generl fuzzy gry prediction model nd discusses th CO e model checking method. Section III discusses the use of fuzzy gry prediction method nd its ppliction on CO emissions in Leshn city, besides nlysis nd corresponding countermesures nd mesures lso presents in Section IV. Finlly, conclusions re presented in Section IV. Abstrct Incresing emissions of CO nd other greenhouse gses s result of humn ctivities hve bring bout globl wrming, which is one of the mjor threts now confronting the environment. CO hve impct on the environment is the gretest s it ccounts for the lrgest shre of totl GHG. The greenhouse effect will further destroy the environment for humns nd ll other living beings, thretening the existence of humnkind if nthropogenic CO emissions re llowed to increse without limits. The reduction of CO emissions hs become key issue tht must be ddressed for the protection of the environment. This pper ims to develop fuzzy gry prediction model on CO emissions, nd the world nturl nd culturl heritge re will be tken s n exmple. The fuzzy possibility is used to check the error of the proposed model, nd the test results show tht the ccurcy of the model is quite high, providing scientific bsis for policy mkers. Index Terms CO emission, fuzzy gry prediction, world nturl nd culturl heritge re, fuzzy possibility. I. INTRODUCTION Incresing emissions of CO nd other greenhouse gses s result of humn ctivities hve brought bout globl wrming, which is one of the mjor threts now confronting the environment []. CO hve impct on the environment is the gretest s it ccounts for the lrgest shre of totl GHG []. The greenhouse effect will further destroy the environment for humns nd ll other living beings [], thretening the existence of humnkind if nthropogenic CO emissions re llowed to increse without limits. To chieve CO emissions reduction, the first thing to do is to cquire ccurcy quntity nd trend of CO emissions in globl nd regionl scope. In other words, we should mke prediction on the CO emissions in the next few yers to gurntee the decision mkers to tke scientific nd effective mesures. The city chosen in this pper is the world nturl nd culturl heritge re, Leshn, in Western Chin, which is n ncient city with three thousnd yers of history. The Leshn Gint Buddh is the lrgest seted stone Buddh in the world nd Mount Emei is mountin scenic re tht contins both Buddhist culture nd nturl beuty. In 996, the Leshn Gint Buddh-Mount Emei region ws recognized s world nturl nd culturl heritge re. However, the crbon Mnuscript received September 0, 04; revised November, 04. This reserch ws supported by the Key Progrm of NSFC (Grnt No ), nd the Key Project of Chin Petroleum nd Chemicl Corportion (Grnt No. GJ ). Zhiyi Meng is with the Uncertinty Decision-Mking Lbortory, Sichun University, Chengdu 60064, Chin (e-mil: zhiyimengscu@sin.com). DOI: 0.776/IJMLC.05.V5.477 II. METHODOLOGY This prt minly includes the following points. Firstly, of 4

2 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 with continuum of membership grdes. A membership function, which ssigns to ech object grde of membership, is ssocited with ech fuzzy set. Usully, the membership grdes re in the intervl [0, ]. When the grde of membership for n object in set is one, this object is bsolutely in tht set; when the grde of membership is zero, the object is bsolutely not in tht set. Borderline cses re ssigned numbers between zero nd one. Precise membership grdes do not convey ny bsolute significnce s they re context-dependent nd cn be subjectively ssessed. the CO emissions in Leshn city is bsiclly introduced. Secondly, fuzzifiction method is described. In ddition, the Grey prediction method is shown here s well s the fuzzy possibility check method. A. Bsic Introduction Fig. shows the CO emissions in Leshn city. From 000 to 0, the emissions in Leshn city hs incresed to T from 5574 T, the chnge is overwhelming, which multiplies pressure for environmentl protection in world nturl nd culturl heritge res. In order to mke scientific decisions, policymkers need to hve specific understnding of emissions in Leshn city. So, predict the emissions ccurtely re of gret importnce for environmentl protection in the world nturl nd culturl heritge res. Fig.. The CO emissions of Leshn city in As the level of detection technology nd mens of CO is limited, in the process of detecting CO, some fctors cnnot be ccurtely mesured, so the results re often displyed in n estimte. If we directly mke predictions bsed on this set of dt then the dt obtined is obviously inccurte. So, before we predict, we should del with the originl dt. In this pper, the bsic theory of fuzzy will be used to mke fuzzifiction on originl dt, then we will mke predictions bsed on the fuzzy dt. This model is trgeted t trends of the emissions. It dels with issues of combining globl nd locl constrints vrious ctors re t stke. The min vribles nd the influentil fctors of the model re identified on the bse which refers to the relevnt informtion worldwide, s well s the nlysis of the other relted fctors. This model consists of two prts: ) Fuzzifiction ) Grey prediction. Here, we first introduce the bsic theory of Fuzzifiction. The whole process of the modeling is shown in Fig.. Fig.. Modeling process of Fuzzy Grey (,). Sometimes, we might only need object of fuzzy set insted of its chrcteristic function, tht is, to trnsfer fuzzy set into crisp set. In order to do so, we need one concept, αcut. It is often necessry to consider those elements in fuzzy set which hve nonzero membership grdes. These elements re the support of tht fuzzy set. Zdeh regrds tht the αcut for fuzzy set, A should be defined s A x A ( x) 0?nd?x U B. Fuzzifiction It is difficult to detect the CO for its own chrcteristics. As mentioned, before detection techniques nd tools for CO emissions levels is limited, which led to some errors in the dt collected. So, if we ignore these errors, nd nlyze these dt nd mke predictions bsed on them, then the ccurcy nd science of the results obtined will be reduced. In this pper, we first mke fuzzifiction bsed on the originl dt. Fuzzy set theory hs been developed to solve problems the descriptions of ctivities nd observtions re imprecise, vgue, or uncertin. The term "fuzz" refers to sitution in which there re no well defined boundries of the set. To cope with this difficulty, Zdeh [] proposed the fuzzy set theory. A fuzzy set is regrded s clss of objects () The term fuzzy number is used to hndle imprecise numericl quntities. A generl definition of fuzzy number is given tht ny fuzzy subset H ( x, ( x)), x tke number on the rel line R nd H ( x) [0,]. Here, we use the bsic theory of tringulr fuzzy numbers proposed by Vn [0]. He climed tht tringulr fuzzy number H cn be defined by triplet (Q, Q, Q ) (The chrcter Q stnds for CO in the following text). Its membership function is shown in Fig.. The whole process of fuzzifiction cn be summrized s follows. Step : Clculted the left vrition α nd the right vrition β ccording to the empiricl dt. 5

3 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 Step : Determine the fuzzy intervl [Q, Q ] ccording to the left nd right vritions, Q Q nd ( Q Q., Step : Construct the membership function tht dq () ) Z u, dt ( x) Z ( k ) Q()( k ) ( )Q()( k ), k,, such (Q) ccording to experts' suggestion., n. α denotes horizontl djustment coeffcient, nd 0 < α <. The selecting criterion of α vlue is to yield the smllest forecsting error rte. Step 4: Form Step, we hve u u Q() (k ) (Q(0) () )e k z () z () T T ˆ ( B B) B Y, B u z ( n) Fig.. The membership function of tringulr fuzzy number. Step 4: Define the fuzzy time series. It cn be expressed s follows. ([Q, ( x)]$,$[q, ( x)],,[qm, m ( x)]), Qi is the empiricl vlue of CO emissions ccording to the survey nd i ( x) Y ((Q(0) (), Q(0) (), Q(0) (4)), is the membership,(q(0) (n))t. function experts suggested on the i th yer. Step 5: Inverse ccumulted genertion opertion (IAGO). Becuse the grey forecsting model is formulted using the dt of AGO rther thn originl dt, IAGO cn be used to reverse the forecsting vlue. Nmely C. Grey Prediction The GM(,) forecsting model dopts the essentil prt of grey system theory nd it hs been successfully used in finnce, integrted circuit industry nd the mrket for ir trvel. The dvntges of the grey model re: () it cn use only few dt to estimte n unknown system, nd () it cn use first order differentil eqution to chrcterize the unknown system behvior []. In contrst to sttisticl methods, the potency of the originl series in the time series grey model, clled GM(,), hs been proved to be more thn four. In ddition, ssumptions regrding the sttisticl distribution of dt re not necessry when pplying grey theory. The ccumulted genertion opertion (AGO) is one of the most importnt chrcteristics of grey theory, nd its min purpose is to reduce the rndomness of dt. In fct, functions derived from AGO formultions of the originl series re lwys well fitted to exponentil functions. Set the originl vlue of CO emissions s group of originl sequence Q(0) (k ) (Q() (k ) Q() (k )), k,, D. Fuzzy Possibility Check Input the CO emissions dt of the pst yers in Leshn city into the fuzzy grey prediction model, we get group of forecst dt nd prediction curve. In order to view the fitting degree between the forecst dt nd historicl dt, we hve to test the fuzzy grey forecsting model. Here, fuzzy possibility is used to check the ccurcy of the model, nd some relted theories will be introduced s follows. Definition. Assume M, N s two fuzzy numbers,to ny binry opertions, membership function of fuzzy number is defined s: M ( ) N ( z ) sup min{ M ( x), N ( y)} Q (0), hving observing the dtum. M, N still the tringulr fuzzy number, tht mens M (ml, m, mr ), N (nl, n, nr ), then the sum, If Q (0), Q(0) (Q(0) (), Q(0) (), Q(0) ()), Step : A new sequence Q () difference of them lso is tringulr fuzzy number, exist:,(q(0) (n)). () M () N (ml nl, m n, mr nr ) is generted by the M ( ) N (ml nr, m n, mr nl ). ccumulted generting opertion (AGO), Q() (Q() (), Q() (), Q() ()),,(Q() (n)). u E. Since the clss of closed r r intervls {[ ] { : [u], r [0,]}} determines Definition. Let () k (5) x, y:z x y Step : Set the originl vlue of CO emissions s group of originl sequence, n. (4) Q () (k ) Q () (i ) unique fuzzy number, we denote this fuzzy number s u, nd cll it to be the bsolute vlue of i r u, [ u ] Step : Estblishing first-order differentil eqution. 6 [ u r, u r ],,

4 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 u r mx{ (ur u r ), ( u r ur )}, u r mx{ uk, ur } Error checking process: Let Qi (i, bi, ci )(i number Cse C: If (6) (Qi Qi ) (Qi Qi ) we get the following formuls Qi Qi 0 9) be tringulr fuzzy such Qi Qi (Qi Qi ) tht 0 i bi ci, Qi (i, bi, ci )(0 i bi ci ) s well s be POS ( Qi Qi fi ) i the predicted vlue which is lso tringulr fuzzy number. If the by the formul POS ( Qi Qi fi ) i Cse (7) D: It is shown s Qi Qi 0 Qi Qi is lso fuzzy number Qi Qi (Qi Qi ) stisfying tht nd the followed formul is vilble Qi Qi (i ci, bi bi, ci i ), POS ( Qi Qi fi ) i ccording to the definition of αcut set, we hve (Qi Qi ) ( i )(ci ˆi ) i (bi bi ) From Definition, we know tht () 0 fi (bi bi ) i ( i )(ci i ) (Qi Qi ) i (bi bi ) ( i )(i ci ) E. Defuzzifiction An importnt concept regrding the ppliction of fuzzy numbers is defuzzifiction, which trnsform fuzzy number into crisp vlue. Mny different methods for this trnsformtion cn be utilized. The most commonly used defuzzifiction method is the centroid defuzzifiction method, which is lso known s the center of grvity (COG) or center of re defuzzifiction. The defuzzifiction method cn be presented s follow: Qi Qi is lso fuzzy number. There re four different cses which cuse ll kinds of results s follows. Cse A: If (Qi Qi ) 0 (Qi Qi ), nd If (Qi Qi ) (Qi Qi ) then we obtin the formuls. Qi nd Qi re both tringulr fuzzy numbers, it follows Definition tht (0) 0 fi ( i )(ci i ) i (bi bi ) f is the error the decision mker permits. Then we cn check Since (Qi Qi ) 0 (Qi Qi ), nd (Qi Qi ) 0, the following formuls re vilble Qi Qi (Qi Qi ) d Q A(Q)dQ Q( A) A(Q)dQ Qi Qi (Qi Qi ), which result in POS ( Qi Qˆ i fi ) i i (bi bi ) ( i )(i ci ) Q( A) is the defuzzified vlue. For trpezoidl fuzzy number (,,, 4 ), the centroid-bsed defuzzified (8) vlue turns out to be: fi ( i )(ci i ) i (bi bi ) Cse B: If () d 4 ] () Q( A) [ 4 (4 ) ( ) (Qi Qi ) 0, then we hve Qi Qi (Qi Qi ) Especilly, when follows. Qi Qi (Qi Qi ) Q( A) [ 4 ] menwhile, the followed formul obtined It is the defuzzifiction formul of tringulr fuzzy number POS ( Qi Qi fi ) i (bi bi ) i ( i )(i ci ), the bove formul becomes s (,, ), which is utilized in this pper. (9) Step fi (bi bi ) i ( i )(ci i ) : Compute A (,, ). 7 the member function A of

5 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 Step : Compute Step : Output Q( A) ccording to Step. Q( A), end. III. RESULT AND DISCUSSION As mintined bove, the fuzzy GM(,) predicting model is employed for CO emissions prediction in Leshn city. A. Computing nd Result Stge. In order to get the tringulr fuzzy number of CO emissions, we first mke fuzzifiction on it for the pst yers. We ssume tht Q0 (k ) (Qk, Qk, Qk ), Qk Qk, emissions from 0 to 00. Fig. 5. CO Qk Qk, the number is gotten by experts of sttistics deprtment bsed on their experience nd the current sitution of locl economic development. According to the bove methods, we mke fuzzifiction on the originl rel dt, nd get the tringulr fuzzy number of CO emissions in Leshn city. Stge. The prediction model is employed to clculte the dt bove nd obtin the predicted vlue of CO emissions in Leshn city. Stge. Defuzzifiction on the predicted vlue use the centroid defuzzifiction method: Q ( A% ) = [Qˆ + Qˆ + Qˆ + ] CO emissions from 00 to 0. Fig. 6. CO Then, input the tringulr fuzzy number of the predicted vlue Q into formul, get the defuzzificted vlue. B. Reson nd Trend Anlysis In this section, we predict the CO emissions in Leshn city region by using the fuzzy gry prediction model, nd get series of dt in Fig. 4-Fig. 9. Now, we nlyze these dt, menwhile, try to seek resons, nd find trend bsed the resons. In ddition, the lw bout the chnge of CO emissions will be sought out nd mke pproprite policies nd mesures vilble. emissions from 0 to 00. Fig. 7. CO Fig. 4. CO emissions from 00 to 0. Fig. 8. CO emissions from 00 to 0. 8

6 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 Fig. 9. CO emissions from 0 to 00. Firstly, it cn be seen from the figure tht the CO emissions re incresing. In the pst yer, due to dvnces in science, technology nd the grdul improvement of ntionl economic policy, nd tourism ws no longer the only developed industry in Leshn city. A number of industril enterprises hve been introduced, which led to the increse of GHG emissions, especilly the shrp growth in CO emissions. Secondly, s it is shown in the figure, the loction of historicl dt points nd forecsted dt points on the curve is consistent, which shows tht the ctul dt nd forecsted dt is in high degree of dt fit. Menwhile, it illustrtes the high ccurcy of the model, s well s of the forecst dt. Thirdly, we cn see from the figure in the next few yers, the increse rte of CO emissions in Leshn city is still high. This mens tht the environment pollution of the world double inheritnce res will be further deepened. Due to the world double inheritnce regions' uniqueness nd irreplcebility, environmentl protection efforts in these regions is prticulrly impertive. C. Contrst Anlysis Just s introduced bove, we use the fuzzy possibility method nd the dt get form the fuzzy GM(,) check the model. According to the experts' dvice, we suppose [ f Q Q Q ] nd 0.9, then put the dt into formul, 04 ( )808 f ( )9 04 s [ f Q Q Q ] nd 0.9, this formul is vilble. Similrly, we put ll the dt into this formul, nd results re ll right which shown fuzzy GM(,) model meet test. Furthermore, the men bsolute error method (MAE) is employed to mke contrst nlysis on the result obtined from GM(,) model, fuzzy GM(,) model s well s Moving verge method, nd the result shown in Tble II. Tble II nd Fig. 0 shows tht the MAE of Moving verge method is lrger thn the other two methods, nd the MAE of fuzzy GM(,) model is the lest. Consequently, the ccurcy of fuzzy GM(,) model is higher thn the other two kinds method, which prove our method is pplicble. Fig. 0. Trend of ctul vlue nd forecst vlues (unit:ton). TABLE II: THE RESULT OF CONTRAST ANALYSIS Prediction method MAE Movingvergemethod.9 GM(,) model.6 Fuzzy GM(,) model. D. Countermesures nd Suggestions In view of these circumstnces which led to the increse of emissions, pproprite mesures must be tken to reduce the CO emissions. Firstly, it is importnt to control increment, nd optimize the industry structure. In ddition, it is lso necessry to control the gs-guzzling nd high pollution industries should be prevented from growing rpidly. Wht's more, incresing the investment nd implementing the key projects fully. We should speed up the implementtion on the ten mjor energy conservtion projects nd wter sving projects. Secondly, relying on science nd technology to ccelerte technologicl development nd generliztion is fesible. Besides, in order to ly solid foundtion the od energy sving mngement nd emission reduction should be enhnced. Thirdly, it is essentil to improve the legl system, nd strengthen the supervision, inspection nd enforcement. At the sme time, we should py more ttention to perfection of the policies nd the formtion of the incentive nd restrint mechnisms. Finlly, in order to strengthen the publicity, nd enhnce the consciousness of ntionl citizen. Such ctivities re prcticble. IV. CONCLUSION In this study, fuzzy grey method is employed to mke prediction bsed on the dte of CO emissions in the pst yers of Leshn city, the CO emissions dte of the nest eight yers re obtined. Fuzzy possibility check nd contrsted nlysis show the ccurcy of the model is quite high, providing scientific bsis for policy mkers. In word, the estblished fuzzy grey predict modeling cn ccurtely predict the CO emissions dte, giving support for policy mkers in Leshn city nd other the world nturl nd culturl heritge res. 9

7 Interntionl Journl of Mchine Lerning nd Computing, Vol. 5, No., Februry 05 ACKNOWLEDGMENT This reserch ws supported by the Key Progrm of NSFC (Grnt No ), nd the Key Project of Chin Petroleum nd Chemicl Corportion (Grnt No. GJ ). REFERENCES [] Y. Fn, Q. M. Ling, Y. M. Wei, nd N. Okd, A model for Chin's energy requirements nd CO emissions nlysis, Environmentl Modelling & Softwre, vol., no., pp. 78-9, 007. [] J. I. Arr nd D. Southgte, Vluting CO reduction strtegies in the US, Ecologicl Modelling, vol. 0, no. 4, pp, , 009. [] M. A. L. Cetno, D. F. M. Gherrdi, nd T. Yoneym, Optiml resource mngement control for CO emission nd reduction of the greenhouse effect, Ecologicl Modelling, vol., no., pp. 9-6, 008. [4] A. W. King, R. V. O'Neill, nd D. L. DeAngelis, Using ecosystem models to predict regionl CO exchnge between the tmosphere nd the terrestril biosphere, Globl Biogeochemicl Cycles, vol., no. 4, pp. 7-6, 989. [5] R. B. Bcstow nd C. D. Keeling, Models to predict future tmospheric CO concentrtions, in Proc. Workshop on the Globl Effects of Crbon Dioxide from Fossil Fuels, pp.7-90, 979. [6] J. W. Rich nd C. S. Potter, Globl ptterns of crbon dioxide emissions from soils, Globl Biogeochemicl Cycles, vol. 9, no., pp. -6, 995 [7] Y. S. Kim, W. Y. Choi, J. H. Jng, K. P. Yoo, nd C. S. Lee, Solubility mesurement nd prediction of crbon dioxide in ionic liquids, Fluid Phse Equilibri, vol. 8, pp , 005. [8] S. H. Prk, K. B. Lee, J. C. Hyun, nd S. H. Kim, Correltion nd prediction of the solubility of crbon dioxide in queous lknolmine nd mixed lknolmine solutions, Industril & Engineering Chemistry Reserch, vol. 4, no. 6, pp , 00. [9] J. L. Deng, Introduction to grey system theory, The Journl of Grey System, vol., no., pp. -4, 989. [0] H. J. Zimmermnn, Fuzzy Set Theory nd Its Applictions, Springer Netherlnds, 00. [] L. A. Zdeh, Fuzzy sets, Informtion nd Control, vol. 8, no., pp. 8-5, 965. [] J. P. Xu nd X. Zhou, Fuzzy-like multiple objective decision mking, Studies in Fuzziness nd Soft Computing, vol. 6, Springer-Verlg Berlin Heidelberg, 0. Zhiyi Meng ws born in 987. He received his M.S. degree in Sichun University. He is currently Ph.D. cndidte t Sichun University. His reserch interests include systems engineering nd informtion system. 0