INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCES Volume 7, No 4, Copyright by the authors - Licensee IPA- Under Creative Commons license 3.

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1 INTERNATIONAL JOURNAL OF ENVIRONMENTAL SCIENCES Volume 7, No 4, 2017 Copyrght by the authors - Lcensee IPA- Under Creatve Commons lcense 3.0 Research artcle ISSN An applcaton of TOPSIS method to rank the US states based on recent toxc release of prorty chemcals Department of Mathematcs, DePauw Unversty, Indana 46135, USA kayanca_2017@depauw.edu do: /es.7024 ABSTRACT Keepng the balance between ndustral development and envronmental protecton s always a challenge for every country around the world. Thus, there s an ncreased nterest n envronmental assessment based on chemcal polluton. The 33/50 program addresses 17 toxc chemcals whose release can cause serous human dsease and envronmental polluton. In ths artcle, we focus on the extent of ar, land and water polluton n each US state. From a practcal pont of vew, t s unlkely that a sngle state can be optmum under all selected crtera. Therefore, an advanced statstcal technque needs to be used n the evaluaton process. Our goal n ths paper s to rank the US states based on the recent toxc Toxc Release Inventory data, by applyng a specfc multple crtera decson-makng procedure called Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS) method. Due to the varatons among the sources under each evaluaton crteron, entropy weghts of these three crtera were obtaned and then ncorporated nto the TOPSIS technque to calculate an overall composte ndex for the US states to arrve at ther ndvdual rankngs. Keywords: Multple crtera decson makng, technque for order preference by smlarty to deal soluton, entropy method, polluton, 33/50 program. 1. Introducton Progress n our socety has always come wth ndustral development snce the 18 th century. As a result of ncreasng output, today s ndustres have produced a sgnfcant amount of toxc chemcal waste that s found to cause adverse effects on human health and the envronment. Therefore, envronmental evaluaton such as rankng dfferent regons based on the extent of polluton plays an mportant role n envronmental polcy makng. In 1991, Wllam Relly, an Admnstrator for the Unted States Envronmental Protecton Agency (EPA), establshed a voluntary polluton reducton program called the 33/50 program (Arora and Cason, 1995). Rather than punshng regulaton noncomplance, ths program provded ncentves to encourage the reducton of polluton. Instead of tryng to reduce thousands of chemcals wastes, the 33/50 program targeted the reducton of 17 prorty toxc chemcals due to ther hgh rsk to human health and the envronment and ther hgh volume of use. The 17 toxc chemcals are: 1. Benzene 2. Cadmum and cadmum compounds 3. Carbon tetrachlorde 4. Chloroform Receved on June 2016 Publshed on January

2 5. Chromum and chromum compounds 6. Cyande compounds and hydrogen cyande 7. Dchloromethane (methylene chlorde) 8. Lead and lead compounds 9. Mercury and mercury compounds 10. Methyl ethyl ketone 11. Methyl sobutyl ketone 12. Nckel and nckel compounds 13. Tetrachloroethylene 14. Toluene 15. 1,1,1 trchloroethane 16. Trchloroethylene 17. Xylene The overall goal of ths program was to acheve a natonal nterm reducton of 33 percent by 1992 of drect envronmental releases and off-ste transfers of 17 prorty toxc chemcals and an ultmate 50 percent reducton by1995, based on releases and transfers reported to the Toxcs Release Inventory (TRI) n 1988 (NEPIS, 1992). TRI s a database of envronmental releases and off-ste transfers of approxmately 600 chemcals mantaned by the US EPA. The TRI database started n 1987, and companes usng chemcals lsted n the TRI are requred by law to report ther annual release and transfer of each chemcal so that communtes can be nformed about the pollutants enterng ther envronment (EPA, 1989). In 1991, a letter was sent by EPA to the chef executve, presdent, and other hgh rankng offcers of the parent companes of over 16,000 facltes nvtng them to partcpate n the 33/50 program (NEPIS, 1992). These facltes were dentfed because they had reported the release or transfer of at least one of the 17 targeted chemcals to the EPA n recent years. More than 60 percent of these facltes had elected to partcpate n the program. Ths program was very successful. In 1991, the 33/50 program acheved ts nterm goal one year ahead of schedule by reducng over 500 mllon pounds of the 17 prorty chemcals. By 1994, the program brought total reductons from the 1988 levels by over 750 mllon pounds, whch exceeded ts overall goal of 50 percent reducton (Zatz and Harbour, 1999). Based on the recent TRI dataset released by the EPA, the goal of ths paper s to rank all 50 states wth respect to the volume of the 17 chemcals reported n 33/50 program n order to determne whch state s the best and the worst n toxc chemcal polluton. Dfferent crtera (for example, ar, land and water) are always consdered when assessng the envronmental stuatons. Under these crtera, t s dffcult to compare the performance of dfferent states. Therefore, a mathematcal approach called Multple Crtera Decson Makng (MCDM) s ntroduced to deal wth ths stuaton. The applcatons of the MCDM methods for envronmental studes can be found n the lterature (see, for example, Snha and Shah, 2003; Lertprapa and Tensuwan, 2009). The MCDM method s a technque used for a meanngful ntegraton of component ndces to an overall ndex n order to rank the number of alternatves from the best to worst (Hwang and Yoon, 1981; Zeleny, 1982; Yoon and Hwang, 1995). In problems dealng wth MCDM, 271

3 all gven alternatves (n ths case 50 dfferent states) generally show no obvous domnance over one another wth respect to the crtera (for example, three release stes here). There s always a trade-off n selectng one alternatve over the other. To ad n ths complex decsonmakng, a more advanced MCDM method called the Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS) was ntroduced. The man reason for choosng the TOPSIS method from other smple MCDM methods s that the decsons made by TOPSIS maxmze the beneft and mnmze the harm, just lke wse busness solutons (Pakpour et al., 2013). The TOPSIS method, developed by Hwang and Yoon n 1981, utlzes the concept that the chosen alternatve should have the shortest dstance from the postve-deal soluton and the longest dstance from the negatve-deal soluton (Hwang and Yoon, 1981; Oprcovc and Tzeng, 2004). Consderng that data s measured mprecsely, decson makers would wegh, rather than a raw data wth uncertanty. Therefore, pror to the TOPSIS method, decson weghts, whch essentally ndcate the measurement of relatve mportance among the dfferent proportons, need to be calculated (Lertprapa, 2013). Among those decson weght assgnment technques appled n MCDM method, the entropy method s one of the most objectve and effcent approaches because ts weght values are not affected by the decson-maker s subjectve judgments (Lotf and Fallahnejad, 2010). The concept of Shannon s entropy (Shannon, 1948) s often used n general measurement of uncertanty, or the degree of randomness. In the entropy method, the weght values of ndvdual ndcators are determned by means of statstcal formulaton. A smaller value of entropy correspondng to a specfc crteron mples a greater crtera s weght. The greater the weght, the more the dscrmnate power among the proportons for that crteron n the process of decson makng (Q et al., 2010). The mathematcal procedures of the entropy and TOPSIS method wll be dscussed n Secton 2. The paper s organzed as follows. In Secton 2, we wll ntroduce the dataset and provde a step-by-step of the computatonal algorthm underlyng the entropy method and TOPSIS method n a theoretcal framework. Our fndngs are based on the analyses shown n Secton 3. Fnally, we summarze the paper wth concludng statements n Secton Materal and methods 2.1 Data All the data used n ths paper was extracted from the EPA. We used the latest 2014 TRI database that was released n March As mentoned earler, the TRI database ncludes nformaton for approxmately 600 chemcals. Therefore, the total sum of the annual dataset for each state n the TRI database cannot be used drectly because the tem we are lookng for (that s, sum of chemcal release) contans a large amount of redundant data. In order to gather data for only the 17 hgh prorty chemcals addressed n 33/50 program, we extracted these target chemcals from the 600 chemcals for each state. Snce water, ar and land are the three major stes for determnng the extent of polluton, we consdered only these three stes for the 17 target chemcals n each state. By summng up, n pounds, the 17 chemcals released at each ste, we gathered the data for each state as dsplayed n Table

4 Table 1: Total release of 17 chemcals n each state under three evaluaton crtera. State Ar emsson (n pounds) Water dscharge (n pounds) Land dsposal (n pounds) Alabama Alaska Arzona Arkansas Calforna Colorado Connectcut Delaware Florda Georga Hawa Idaho Illnos Indana Iowa Kansas Kentucky Lousana Mane Maryland Massachusetts Mchgan Mnnesota Msssspp Mssour Montana Nebraska Nevada New Hampshre New Jersey New Mexco New York North Carolna North Dakota Oho Oklahoma Oregon Pennsylvana Rhode Island South Carolna South Dakota Tennessee Texas Utah Vermont Vrgna Washngton West Vrgna

5 Wsconsn Wyomng The entropy weght and TOPSIS method We denote the data representng n Table 1 by X x )) the postve-valued score matrx (or the decson matrx) of order m n representng the states as rows of the matrx X and the evaluaton crtera (ar, water and land) as the columns of the matrx X. In order that each state s judged the best wth respect to a specfc evaluaton crteron, t s tactly assumed that the score for each partcular state should not exceed those of all other states n the lst. The objectve of the study s to arrve at an over-all rankng of the states, by takng nto account ther performance across all the evaluaton crtera. Addtonally, one has to ensure that all the scores for each evaluaton crteron have the same nterpretaton n terms of mn-to-max along wth best-to-worst. In general, the TOPSIS method evaluates the followng decson matrx shown n Table 2 whch contans m alternatves A 1, A2,, Am assocated wth n attrbutes or crtera C 1, C2,, Cn, x s the numercal outcome of the th alternatve wth respect to the j th crteron, and w s the weght of crteron C, ndcatng the relatve mportance of the evaluaton crtera. j (( Table 2: Decson matrx n MCDM j We consder the followng steps n calculatng the entropy weght: Step 1. Transferrng the decson matrx to the normalzed mode: In order to compute the entropy measure for the j th crteron, the related values n the decson matrx are frst normalzed as: p x m 1 x for 1,2,3,..., m and j 1,2,3,..., n (1) Step 2. Calculatng the entropy of dataset for each crteron: In ths step, the entropy of the j th crteron, e j, s calculated as follows: j m e p ln p for j 1,2,3,..., n (2) 1 274

6 where, represents a constant: a =1 ln(m), whch guarantees that 0 e j 1. Next, the operaton of subtracton s used to measure the degree of dversty relatve to the correspondng anchor value (unty), d j, usng the followng formula: d j =1- e j for j =1,2,3,...,n (3) Step 3. Defnng crtera weghts: The entropy weght W w, w,, w ) s calculated usng w j = n j=1 d j å d j ( 1 2 n for j =1,2,3,...,n (4) Once the weghts are chosen usng the entropy method, these weghts are then ncorporated nto the so-called TOPSIS method to calculate an overall score. The algorthm of ths technque s summarzed as follows: ) Construct the normalzed decson matrx R: r = x m å =1 x 2 for =1,2,3,...,m and j =1,2,3,...,n (5) ) Construct the weghted the normalzed decson matrx V: v = r w j for =1,2,3,...,m and j =1,2,3,...,n (6) ) Determne the Postve-deal Row (IDR) that one wth the smallest observed value for each column: IDR ( mnv1,mn v2,,mnvn ) ( v1, v2,, vn ) for =1,2,3,...,m (7a) Smlarly, the Negatve-deal Row (NIDR) that one wth the largest observed value for each column: NIDR ( maxv1,maxv 2,,maxvn ) ( v1, v2,, vn ) for =1,2,3,...,m (7b) v) Measure the dstance, deal one: d for =1,2,3,...,m, of each alternatve from the postve 275

7 n ( ) 2 d + + = å v - v j for =1,2,3...,m (8a) j=1 Smlarly, measure the dstance, negatve deal one: n ( ) 2 d for =1,2,3,...,m, of each alternatve from the - d ī = å v - v j for =1,2,3...,m (8b) j=1 The dstance measures used n equatons 8a and 8b are referred to as Eucldan dstance or Eucldan Norm, denoted by L 2. v) Calculate the relatve closeness of alternatves to deal soluton by computng what s known as Composte Index [CI] : CI = d + d - + d + for =1,2,3,...,m (9) Where 0 CI 1. These composte ndces are used for the fnal rankng of each state, the rule beng: mn to max for ranks 1 to m. 3. Results The release of 17 toxc chemcals under the crtera ar, water and land for each state s dsplayed n Table 1. We consder ths as a gven decson matrx to the MCDM method where we can apply the TOPSIS-MCDM technque. Before applyng the TOPSIS method, we calculate the entropy weghts for all three crtera. After normalzng the decson matrx usng equaton (1), we calculate the ndces e j and d j usng formulas provded n equatons (2) and (3), respectvely. Fnally, we use these ndces to calculate the entropy weghts for all crtera usng equaton (4). Table 3 summarzes the results of all necessary ndces ncludng the weghts for all three crtera. Table 3: Calculatng the entropy ( e j ), degree of dversty ( d j ) and crtera weght ( w j ) for each decson crteron of 17 chemcals release Indces Ar emsson Water dscharge Land dsposal e j d j w j Note: The total 17 chemcals released n water s zero n Vermont. Therefore, t wll make the P*lnP ndetermnate form snce ln(x) s defned only for x>0. In order to mnmze the 276

8 effect of ths data pont, we evaluated ths value by usng the L Hosptal s rule (Rogawsk, 2012), gvng the result of 0. Table 4: Summary of the postve d + and negatve dstance d -, the fnal TOPSIS scores, and the ranks for the states State d d CI Alabama Alaska Arzona Arkansas Calforna Colorado Connectcut Delaware Florda Georga Hawa Idaho Illnos Indana Iowa Kansas Kentucky Lousana Mane Maryland Massachusetts Mchgan Mnnesota Msssspp Mssour Montana Nebraska Nevada New Hampshre New Jersey New Mexco New York North Carolna North Dakota Oho Oklahoma Oregon Pennsylvana Rhode Island South Carolna South Dakota Tennessee Texas Utah Vermont E-05 1 Vrgna Rank 277

9 Washngton West Vrgna Wsconsn Wyomng The weghts n Table 3 obtaned by the entropy method are then ncorporated nto the TOPSIS technque (equatons 5-9) to calculate an overall score for each state. The fnal rankngs of all 50 states are then arranged n ascendng order of ther TOPSIS score CI, whch s shown n the last column of Table 4. Based on the result, Vermont ranked frst, whle Alaska ranked last. The lower the amount of chemcal release on land, water and ar, the better the rank s for that specfc state. Therefore, the result ndcates that Vermont s expected to be the best n terms of toxc chemcals polluton, whle Alaska s expected to be the worst. 4. Concluson Ths paper demonstrates an evaluaton of the best to worst performng states n terms of toxc chemcal release at three polluton stes by applyng TOPSIS-MCDM method. Generally speakng, under one set of crtera, state A may perform better than state B under ar emsson crteron, but worse under land dsposal crteron. Therefore, we need to take the combnaton of all three crtera nto consderaton before makng a decson. The TOPSIS- MCDM method helps us to calculate an overall score and hence rank each state. Our fndngs reveal that, based on the latest 2014 chemcal release data, Vermont performs better than any other state, and Alaska perform worse, whch ndcates that changes are requred for the Alaska State Government to reduce ths chemcal polluton n order to mprove human health and reduce envronment destructon. Not only Alaska, but the 10 lowest rankng states should take the responsblty of lmtng chemcal polluton and advocatng the concept of waste treatments. Note that the study presented n ths artcle consders the latest TRI dataset only. To gan more nformaton about the envronmental mpact, more data s needed to be collected and further nvestgatons are requred. For example, rank may be dfferent by usng dfferent MCDM methods or by usng dfferent weghts. Furthermore, comparng the rank based on the data over a span of tme would gve nterestng results. 5. References 1. Arora, S. and Cason, T.N., (1995), An experment n voluntary envronmental regulaton: Partcpaton n EPA s 33/50 program. Journal of envronmental economcs and management, 28(3), pp EPA. Envronmental Protecton Agency (1989), EPA Releases Toxc Inventory Data. 3. Hwang, C. and Yoon, K., (1981), Multple attrbute decson makng. Berln: Sprnger-Verlag. 4. Lertprapa, S. and Tensuwan, M., (2009), An applcaton of multple crtera decson makng n combnng envronmental ndces of fve ar polluton ndcators. Thaland statstcan, 7(2), pp Lertprapa, S., (2013), Revew: Multple crtera decson makng method wth applcatons. In nternatonal mathematcal forum, 8(7), pp

10 6. Lotf, F.H. and Fallahnejad, R., (2010), Imprecse Shannon s entropy and mult attrbute decson makng, Entropy, 12(1), pp Oprcovc, S. and Tzeng, G.H., (2004), Compromse soluton by MCDM methods: A comparatve analyss of VIKOR and Topss, European journal of operatonal research, 156(2), pp NEPIS (1992), 33/50 Program: Fact Sheets on the 17 Target Chemcals, avalable at accessed at Web. 27 June Pakpour, S., Olshevska, S.V., Prasher, S.O., Mlan, A.S. and Chéner, M.R., (2013), DNA extracton method selecton for agrcultural sol usng TOPSIS multple crtera decson-makng model. Amercan journal of molecular bology, 3(4), pp Q, Y., Wen, F., Wang, K., L, L. and Sngh, S., (2010), A fuzzy comprehensve evaluaton and entropy weght decson-makng based method for power network structure assessment. Internatonal journal of engneerng, Scence and technology, 2(5), pp Rogawsk, J., (2012), Calculus. New York: W.H. Freeman., 2 nd edton. 12. Shannon, C.E., (1948), A mathematcal theory of communcaton, The bell system techncal journal, 27(3), pp Snha B,K., and Shah K.R., (2003), On some aspects of data ntegraton technques wth envronmental applcatons, Envronmetrcs, 14(4), pp Yoon, K. and Hwang, C., (1995), Multple attrbute decson makng: An ntroducton. Thousand Oaks, CA: Sage Publcatons. 15. Zatz, M. and Harbour, S., (1999), The Unted States envronmental protecton agency's 33/50 program: The anatomy of a successful voluntary polluton reducton program. Journal of cleaner producton, 7(1), pp Zeleny, M., (1982), Multple Crtera Decson Makng, New York: McGraw-Hll. 279