COMPARATIVE ANALYSIS AND SELECTION OF THE BEST METHOD HIGHWAY ROUTE

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1 Orgnal Scentfc paper UDC: : DOI: /afts B COBISS.RS-ID COMPARATIVE ANALYSIS AND SELECTION OF THE BEST METHOD HIGHWAY ROUTE Bašć Zahd 1, Džananovć Amr 1 1 Unversty of Tuzla, Faculty of Mnng, Geology and Cvl Engneerng, Bosna and Herzegovna, e-mal: mdo_basc@hotmal.co.uk SUMMARY The man objectve of ths study was to revew the methods used n the process of selectng the optmal route of the hghway, the way n whch these methods are used, hghlghtng the advantages and dsadvantages of each method, and comparng the partcular case make the favored one of the offered methods. In addton to mutual comparson crtera optmzaton work are detaled methods and presents a concrete example, whch can be very useful to researchers n ths feld. Comparson of the already complex valuaton methods wth a large number of nfluental factors s a partcular challenge to the author. It s extremely dffcult to make a comparson method whch the authors used a completely dfferent mathematcal approach. Some of the crtera optmzaton are ncurred n order to concrete problems (ar transport of passengers, the annual predcton of accdents, etc.) and as such are not prmarly been desgned for the selecton of the optmal route of the hghway. After much thought and research crtera optmzaton, ths paper appled the mathematcal approach n comparson method, as follows: Spearman's and Pearson's correlaton coeffcent and Kendall's coeffcent of correlaton. Keywords: road, hghway, multdscplnary optmzaton, comparson, methods INTRODUCTION Road Desgn s a complex research process whch s consderng a large number of parameters to fnd an optmal soluton. It nvolves analyss of a large number of parameters, fndng the weght of these parameters and applyng approprate methods n order to reach an objectve assessment of project solutons. Snce many elements nfluence the selecton of the route tmes requre access to a maxmum fund nformaton and objectve analyss of all the nput parameters. It s clear that when selectng the optmal route of the hghway nvolved a large number of crtera and the relatve weght of these crtera s not the same (for example, the prce of buldng the hghway and rde comfort). In addton, certan crtera are mutually conflctng (cost of road constructon should be as small as possble, but at the same tme amng for the greater stablty of the hghway or drvng Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

2 comfort). To all of these crtera and weght of each crtera consdered necessary the applcaton of approprate methods that are called multcrtera method or methods of mult-crtera optmzaton (MCA- mult crtera analyss, MCDA - mult-crtera decson analyss) [1,2,3,4]. MCA s a formal approach used to assst n the process of complex decson-makng the last few decades (Anand Raj and Kumar, 1996; Cho and Park, 2001; Davd and Ducksten, 1976; Flug and others, 2000; Hajeeh and Al-Othman, 2005; Hobbs et al, 1992; and Mohsen Jaber, 2001; and Fahmy Khereldn, 2001; and Rjsberman Rdgley, 1994). MCA s wdely used because t facltates the partcpaton of a large number of partcpants and jont decson-makng, does not requre the assgnment of a monetary value to envronmental or socal crtera and to consder a number of crtera wth ncommensurable unts (eg. A combnaton of quanttatve and qualtatve crtera) (Hajkowcz, 2000) [3,4,5]. METHOD MULTI-CRITERIA OPTIMIZATION - THEORETICAL BASIS Choosng among several varants hghway route represents part of the overall problem of managng the constructon of transport networks. The selecton represents a scentfc analyss of the solutons wth the help of subjectve methods (ntuton), and wth the help of exact methods. Admnstraton methods for mult-crtera analyss represent one of the methods that are used n the selecton of the optmal route of the hghway. Results obtaned usng the method of mult-crtera analyss of the ranks who often gve a dfferent order. Reducng the dfference between the output result of the method can be acheved usng the same lnear normalzaton, other than the AHP method formng ts matrx and makng t not requre normalzaton [6,7,8]. You can use two categores of weghts that wll help n the analyss of the same methods and determne the mpact of weght coeffcents n the fnal rankngs. Dfferences dscrepances between the dfferent methods are the bass for a comparatve analyss and selecton of the most sutable method for rankng. INTERCONNECTION RESULTS METHODS OF MULTI-CRITERIA ANALYSIS The results of other methods ranked alternatves or optmal algnment of the hghway, and there s the problem of so-called. conflct ranks. In order to statstcally analyze the conflcts must be good enough sample dfferent evaluaton of alternatves, as n practce hard to accomplsh. One possblty s the use of Spearman's coeffcent, whch s on a smaller sample reported correlaton of ranks obtaned by dfferent methods. Another way s to use Kendall's coeffcent consent. Usng these statstcal methods can demonstrate the nterconnecton results methods of mult-crtera analyss, and the dependence of certan methods of weght coeffcents. Ths wll be used and Pearson's correlaton that s normally appled to the results of the method, on ther rankng. not SPEARMAN'S CORRELATION COEFFICIENT "Spearman rank correlaton coeffcent measures the degree and drecton of assocaton between two events presented doubles rankng varables" [9]. Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

3 In ths correlaton coeffcent f the varables NUMERICAL need to be transformed nto varable shapes rank. The bascs of ths coeffcent couples modaltes rankng varables and wth the help of them to account correlaton. Spearman's correlaton coeffcent s [3,5]. n 2 6 d = 1 s = 3 = r 1 ; d r( x ) r( y ) n n where s: d dfference between the two sets whch are compared n total number of unts sets that are compared The value of the results of ths rato can vary between theoretcal value of -1 and 1. When approachng 1, an ndcaton that the ranks of smlar or the same, when the value s less than zero and s approachng -1, ranks are reversed or negatvely correlated. Wth the help of Spearman correlaton coeffcent wll be calculated degree of correlaton between the rankng lst of the optmal route of the hghway for a varety of methods. Calculatng ths rato can be done wth the help of SPSS Inc. Statstcs n KENDALL'S COEFFICIENT OF CORRELATION Besdes Spearman's rank correlaton coeffcent s very often used and Kendall rank correlaton coeffcent. The method of calculatng the correlaton coeffcent s dfferent from calculatng the Spearman correlaton coeffcent. In ts applcaton, t s assumed that each varable rankng takes the value from the set of the frst n natural numbers. In the performance of ths rato s based frst on the assumpton that there s a concdence n the rankng. Kendall's coeffcent of correlaton takes values from 0 to 1. The mnmum value of the coeffcent represents the total dsagreement varatons varable rankng and t s 0, and 1 represents the largest total agreement rankngs varables rank [3,9]. The form for calculatng Kendall's coeffcent of correlaton s: ( ) m m n S n S S ρ = 4 12 n n where s: m Number of observed phenomena; n Number of data occurs; S The sum of the values of ranks by type Kendall's coeffcent of correlaton has the advantage of usng t can be counted and partal correlaton. Wth the help of the same parameters as the Spearman-ovkoefcjent consent calculated Kendall's correlaton coeffcent wth the help of SPSS INC. Statstcs THE SELECTION OF THE MOST SUITABLE METHOD FOR RANKING THE HIGHWAY ROUTE By usng Spearman's and Kendall's correlaton coeffcent are comparable rankngs optmal hghway route obtaned usng the mult-crtera analyss. In order for the analyss to be complete except rankngs route by ndvdual multobjectve t s necessary to calculate the devaton of the results of Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

4 these methods. Ths s done by usng Pearson's correlaton coeffcent. Pearson's correlaton coeffcent s used n cases where a model varables observed a lnear relatonshp and contnuous normal dstrbuton. He calculates the correlaton between the two varables. Its results can range from 1 (perfect postve correlaton) to-1 (perfect negatve correlaton) [1,9]. The coeffcent us to the drecton of correlaton - whether postve or negatve, but we are not suggestng the strength of correlaton. Pearson correlaton coeffcent based on a comparson of the actual mpact of the observed varables to one another n relaton to the maxmum possble mpact of two varables. Indcates the small Latn letters r. To calculate the orrelaton coeffcent requres three dfferent sums of squares (SS): sum of squared varables, sum of squares and the sum of the products of varables and varables. The sum of squares of varables equal to the sum of the squares of the value of the varable from ts average value: xx n 2 ( ), = 1 SS = x x 1 n x n = 1 x = The sum of squares of varables equal to the sum of the squares of the value of the varable from ts average value: yy n 2 ( ), = 1 SS = y y 1 n y n = 1 y = The sum of the products of varables and equal to the sum of the products of devatons from the values of varables and ther average: SS = ( x x)( y y) xy The correlaton coeffcent equal to the rato: r = SS SS xx xy SS yy In the case of the varables of a lnear relatonshp, can perform the approprate transformaton of the values of the varables whch are reduced to the lnear model. Pearson's correlaton coeffcent s calculated only under the followng condtons: data both studed varables followng an nterval or rato scale, data for at least one varable are normal, e. symmetrcally dstrbuted, t s preferred that the test sample s hgh (N> 35) satsfes the condton of lnear connecton. It should be noted that VIKOR method ranks the value of the worst to the best, whle other methods value ranked vce versa, and the result of the correlaton s necessary to multply by "-1" to make unform results [10] COMPARATIVE ANALYSIS By applyng the methods of mult-crtera optmzaton receved the same order for all methods. The queston s whether all methods are good enough for use n selecton of the optmal route of the hghway or need certan methods to avod. On the other hand, t s necessary to look further specfc crtera and the possblty of gvng preference to certan subjectve crtera. If the decson maker make a subjectve preference for a partcular crteron (such as, for example, the prce of buldng the hghway) then ths crteron can be a cause to whch the applcaton of the methods of mult-crtera optmzaton certan routes has an advantage over other more expensve route. To compare specfc crtera and thus analyze appled methods used are dfferent correlaton coeffcents. In the frst place t s the Pearson correlaton coeffcent, then Spearman coeffcent of correlaton [5]. Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

5 DATA NORMALIZATION To be used any correlaton coeffcent t s necessary to normalze the ntal decson matrx. Normalzaton of data s done to make the data unform and comparable. One process of normalzaton of the ntal decson matrx s shown as part of the AHP method and requres normalzaton before the fnal budget-level varants. Ths method of normalzaton s recommended Saaty, one of the authors of ths method. Meanng recommended normalzaton s that the value of each crteron dvded by the sum of the values for each crteron. Belton and Gear have suggested that the normalzaton of the matrx s performed so that certan crtera to share wth the hghest value-for certan crtera. Methods Vkor, electre and Topss requre that the normalzaton of the ntal decson matrx done usng the followng equaton [3,5,10]. xj r = j n k = 1 In Promethee method s not necessary to normalze the ntal value because of the method by adoptng the tool preferences gves the correspondng values for the fnal decson-makng matrx. Gven that there are more functons preferences, ths method provdes the most possblty of the decson-maker to choose a partcular functon preferences. In addton, the decson maker can choose dfferent functons preferences for dfferent crtera when t consdered the correct decson [7]. No matter whch way the normalzaton that s used most often to obtan a value of crtera between 0:01 or possbly between -1 and 1 to smpler decson there. Below s the frst analyss, used way of normalzaton that recommended Belton and Gear, and normalzaton s done so that each crteron s dvded by the hghest value for that crteron. In ths way, all the values of the ntal decson matrx gven a value between 0 and 1. The maxmum value for each crteron s gven a value of 1, and mnmum values for each crteron obtan the closest value s 0. In the second readng adopted the way of normalzaton that s commonly used n the method Vkor, Electre and Topss, and that s that the value of each crteron s dvded by the square root of the sum of squares value for ths crteron [3,5,12]. For both normalzed matrx beng calculated and Spearman and Pearson correlaton coeffcent between all decson-makng crtera. x 2 kj The followng are crtera that are consdered prevous methods, and n the case of desgnng route of the hghway Tuzla-Orasje (Table 1). [13]. the K1 Investment value ( ) K2 length of the route (km) K3 length of brdges and vaducts (km) K4 tunnel length (km) K5 bend characterstcs (cty / km) K6 mddle longtudnal nclnaton (%) K7 hlly (% / km) K8 wave (m / km) Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

6 K9 total length parts of the route wth a slope of more than 3% f they are longer than 500 meters (yards) K10 length of the route wth an alttude of more than 300 meters (yards) K11 mark the route wth a geologcal pont of vew n relaton to the explotaton and mantenance K12 ratng mpact on creatng opportuntes for the development of the area K13 length of the route on whch there s a possblty of endangerng (km) K14 length of the route on whch appears the possblty of conflct (km) crtera Table 1. Home stencl makng secton /varant A B C D Object ve funct on Weght am K mn 0,286 K 2 49,256 46,562 47,461 49,326 mn 0,043 K 3 2,48 1,421 1,431 7,167 mn 0,042 K 4 5,99 3,67 3,67 10,34 mn 0,063 K 5 26,476 31,147 33,068 22,879 mn 0,027 K 6 1,831 1,967 1,931 1,080 mn 0,028 K 7 0,603 0,683 0,640 0,369 mn 0,023 K 8 10,222 10,962 10,719 10,042 mn 0,023 K 9 13,471 15,307 15,373 15,407 mn 0,018 K 10 19,566 15,703 15,703 20,068 mn 0,042 K 11 3,311 3,597 3,623 2,000 max 0,077 K 12 2,467 3,525 4,281 3,408 max 0,116 K 13 18,00 17,50 13,00 11,50 mn 0,116 K 14 18,00 15,60 11,10 19,00 mn 0,097 SPEARMAN AND PEARSON'S COEFFICIENT The frst step s to calculate the Spearman and Pearson correlaton coeffcent normalzed matrx s derved from the value of each crteron s dvded by the maxmum value for ths crteron (Table 2). In the rght part of the table provdes a rankng of varants accordng to ndvdual crtera. Where the same value crtera and could not be executed rankng each varant are gven the arthmetc mean. Such a case s seen wth crtera K4 and K10 where there s 1:02 place than the varants B and C gve the mean value, or the value of 1.5 [13]. In order to determne the connectvty rankng shall be appled Spearman and Pearson correlaton coeffcent. The value of the results of the correlaton coeffcent can range between -1 and 1. Lookng at the table above t can be concluded that the Spearman and Pearson correlaton coeffcent behave smlarly when t comes to relatons between the crtera. Where there s a strong lnk certan crtera both coeffcents have hgh value and vce versa. (Table 3). Lookng Spearman and Pearson correlaton coeffcent was appled to the prevous normalzaton can be concluded that there s a strong or medum strong correlaton for most of the observed crtera, except for the crteron K9 and K13. For crteron K9 (total length parts of the route wth a slope of more than 3% f they are longer than 500 m, expressed n km) absolute value of the correlaton coeffcent s the mostly movng from 0.20 to 0.40, whle the absolute value of the Pearson coeffcent ranges from 0, from 02 to 0.85 [13]. Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

7 Table 2. Matrx normalzed wth the maxmum values for each crteron, rankng lst for each crteron separately crtera Ranked accordng to certan Secton/ varant Objectve crtera functon A B C D A B C D K 1 0,9329 0,7646 0,7603 1,0000 mn K 2 0,9986 0,9440 0,9622 1,0000 mn K 3 0,3460 0,1983 0,1997 1,0000 mn K 4 0,5793 0,3549 0,3549 1,0000 mn 3 1,5 1,5 4 K 5 0,8007 0,9419 1,0000 0,6919 mn K 6 0,9309 1,0000 0,9817 0,5491 mn K 7 0,8829 1,0000 0,9370 0,5403 mn K 8 0,9325 1,0000 0,9778 0,9161 mn K 9 0,8743 0,9935 0,9978 1,0000 mn K 10 0,9750 0,7825 0,7825 1,0000 mn 3 1,5 1,5 4 K 11 0,9139 0,9928 1,0000 0,5520 max K 12 0,5763 0,8234 1,0000 0,7961 max K 13 1,0000 0,9722 0,7222 0,6389 mn K 14 0,9474 0,8211 0,5842 1,0000 mn Table 3. Values of Spearman coeffcent (above) and the Pearson coeffcent (below) K 1 K 2 K 3 K 4 K 5 K 6 K 7 K 8 K 9 K 10 K 11 K 12 K 13 K 14 K 1 1,00 0,80 0,80 0,95-1,00-0,80-0,80-0,80 0,20 0,95 1,00 0,80-0,20 1,00 K 2 0,94 1,00 1,00 0,95-0,80-1,00-0,90-0,90 0,40 0,95 0,80 0,60-0,40 0,80 K 3 0,86 0,70 1,00 0,95-0,80-1,00-1,00-1,00 0,40 0,95 0,80 1,00-0,40 0,80 K 4 0,93 0,81 0,99 1,00-0,85-0,85-0,85-0,85 0,35 1,00 0,95 0,75-0,25 0,95 K 5-0,98-0,86-0,89-0,95 1,00 0,80 0,80 0,80-0,20-0,85-1,00-0,80 0,20-1,00 K 6-0,83-0,68-1,00-0,97 0,86 1,00 1,00 1,00-0,40-0,85-0,80-0,60 0,40-0,80 K 7-0,86-0,74-0,99-0,98 0,87 0,99 1,00 1,00-0,40-0,85-0,80-0,60 0,40-0,80 K 8-0,97-0,99-0,81-0,89 0,91 0,79 0,84 1,00-0,40-0,85-0,80-0,60 0,40-0,80 K 9-0,35-0,50 0,19 0,02 0,38-0,24-0,18 0,38 1,00 0,35 0,20-0,40-1,00 0,20 K 10 0,99 0,96 0,77 0,87-0,96-0,74-0,78-0,97-0,48 1,00 0,95 0,75-0,25 0,95 K 11-0,86-0,70-1,00-0,99 0,89 1,00 0,99 0,80-0,19-0,77 1,00 0,80-0,20 1,00 K 12-0,62-0,60-0,18-0,33 0,60 0,12 0,14 0,53 0,85-0,70 0,18 1,00 0,40 0,80 K 13-0,26-0,25-0,64-0,54 0,25 0,68 0,69 0,36-0,65-0,16 0,63-0,59 1,00-0,20 K 14 0,86 0,68 0,68 0,76-0,91-0,64-0,62-0,71-0,38 0,85-0,69-0,79 0,13 1,00 For crteron K13 (length of the route on whch there s a possblty of endangerng (km)) absolute value Spearman correlaton coeffcents are predomnantly movng from 0.20 to 0.40, whle the absolute value of Pearson coeffcent ranges from 0.13 to In addton to these two crtera, we can extract the crteron K12 (ratng mpact on creatng opportuntes for the development of the area) whose coeffcents consent mlder correlaton wth certan crtera but also a slght correlaton wth the four crtera (Pearson coeffcents less than 0.20). What s also nterestng n the above table (Table 4). s the fact that the crtera that have lttle correlaton wth other crtera, mlder or strong correlaton between them (correlaton coeffcent between crtera K9 and K13 s Spearman, or Pearson) [13]. Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

8 Table 4. Table showng the strength of correlaton between varables The absolute value of the correlaton coeffcent r = 1 The strength of the assocaton between varables full correlaton 0.80 r < 1 strong correlaton 0.50 r < 0.80 Medum strong correlaton 0.20 r < 0.50 Relatvely low correlaton 0.00 r < 0.20 nsgnfcant correlaton r = 0 The complete absence of correlaton Gven the fact that there are dfferent forms of normalzaton ntal decson matrx below wll apply normalzaton whch s commonly used n the method Vkor, Electre and Topss recommendng that the normalzaton of the ntal decson matrx done usng the followng equaton (Table 5). [10,12]. xj r = j n k = 1 Table 5. Matrx normalzed by the root sum of squares for each crteron, rankng lst for each crteron separately x 2 kj crtera Secton/varant Objectv Ranked accordng to certan e crtera A B C D functon A B C D K 1 K 2 0, ,020 K 3 9 0,499 K 4 9 0,418 K 5 7 0,536 K 6 5 0,151 K 7 4 0,244 K 8 7 0,613 K 9 8 0,998 K ,081 K ,516 K ,354 K ,654 K , ,6871 0,6996 0,0000 mn ,8287 0,5592 0,0000 mn ,6129 0,0000 0,0000 mn ,6421 0,6421 0,0000 mn 2 3,5 3,5 1 0,1563 0,0000 0,8298 mn ,0000 0,0400 0,9876 mn ,0000 0,1315 0,9606 mn ,0000 0,2015 0,7632 mn ,0515 0,0175 0,0000 mn ,7047 0,7047 0,0000 mn 2 3,5 3,5 1 0,5615 0,5656 0,3122 max ,5064 0,6150 0,4896 max ,0000 0,4534 0,6045 mn ,3926 0,9124 0,0000 mn Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

9 Table 6. Values of Spearman coeffcent (above) and the Pearson coeffcent (below) K 1 K 2 K 3 K 4 K 5 K 6 K 7 K 8 K 9 K 10 K 11 K 12 K 13 K 14 K 1 1,00 0,80-0,10 0,95-1,00-0,80-0,80-0,80 0,20 0,95-1,00-0,80-0,60 1,00 K 2 0,94 1,00 0,50 0,95-0,80-1,00-0,90-0,90 0,40 0,95-0,80-0,60-0,80 0,80 K 3 0,23 0,32 1,00 0,25-0,30-0,90-0,90-0,90 0,70 0,25-0,30 1,00-0,50-0,10 K 4 0,93 0,81 0,44 1,00-0,85-0,85-0,85-0,85 0,35 1,00-0,85-0,65-0,65 0,95 K 5-0,98-0,86-0,16-0,95 1,00 0,80 0,80 0,80-0,20-0,85 1,00 0,80 0,60-1,00 K 6-0,83-0,68-0,56-0,97 0,86 1,00 1,00 1,00-0,40-0,85 0,80 0,60 0,80-0,80 K 7-0,86-0,74-0,60-0,98 0,87 0,99 1,00 1,00-0,40-0,85 0,80 0,60 0,80-0,80 K 8-0,97-0,99-0,38-0,89 0,91 0,79 0,84 1,00-0,40-0,85 0,80 0,60 0,80-0,80 K 9-0,35-0,50 0,49 0,02 0,38-0,24-0,18 0,38 1,00 0,35-0,20 0,40 0,20 0,20 K 10 0,99 0,96 0,15 0,87-0,96-0,74-0,78-0,97-0,48 1,00-0,85-0,65-0,65 0,95 K 11 0,86 0,70 0,50 0,99-0,89-1,00-0,99-0,80 0,19 0,77 1,00 0,80 0,60-1,00 K 12 0,62 0,60-0,57 0,33-0,60-0,12-0,14-0,53-0,85 0,70 0,18 1,00 0,80-0,80 K 13-0,74-0,92-0,51-0,61 0,60 0,50 0,59 0,88 0,47-0,77-0,50-0,36 1,00-0,60 K 14 0,86 0,68-0,24 0,76-0,91-0,64-0,62-0,71-0,38 0,85 0,69 0,79-0,33 1,00 Lookng Spearman and Pearson correlaton coeffcent was appled to the prevous normalzaton can be concluded that there s a strong or medum strong correlaton for most of the observed crtera, except for the crteron K9, K13, and ths tme the crtera K3 (Table 6).. For crteron K9 (total length parts of the route wth a slope of more than 3% f they are longer than 500 m, expressed n km) absolute value of the correlaton coeffcent s the mostly movng from 0.20 to 0.40, whle the absolute value of the Pearson coeffcent ranges from 0, from 02 to 0.85 [13]. For crteron K13 (length of the route on whch there s a possblty of endangerng (km)) absolute value Spearman correlaton coeffcents are predomnantly movng from 0.20 to 0.80, whle the absolute value of Pearson coeffcent ranges from 0.33 to For crteron K3 (length of brdges and vaducts (km)) absolute value Spearman correlaton coeffcents are predomnantly movng from 0.10 to 0.90, whle the absolute value of Pearson oeffcent ranges from 0.15 to In addton to these two crtera, we can extract the crteron K12 (ratng mpact on creatng opportuntes for the development of the area) whose coeffcents consent mlder correlaton wth certan crtera but also a slght correlaton wth the three crtera (Pearson coeffcents less than 0.20) [13] The above analyss leads to the concluson that n both ways used normalzaton correlaton coeffcents between certan crtera are mnor or neglgble. It s essentally the same crtera for both normalzaton. CONCLUSION Choosng among several varants hghway route represents part of the overall problem of managng the constructon of transport networks. Results obtaned usng the method of mult-crtera analyss of the ranks who often gve a dfferent order. Reducng the dfference between the output method may be acheved by usng the same lnear normalzaton, other than the AHP method formng ts matrx and makng t not requre normalzaton. Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N

10 One possblty s the use of Spearman's coeffcent, whch s on a smaller sample reported correlaton of ranks obtaned by dfferent methods. Another way s to use Kendall's coeffcent consent. Usng these statstcal methods can demonstrate the nterconnecton results methods of mult-crtera analyss, and the dependence of certan methods of weght coeffcents. By usng Spearman's and Kendall's correlaton coeffcent are comparable rankngs optmal hghway route obtaned usng the mult-crtera analyss. In order for the analyss to be complete except rankngs route by ndvdual multobjectve t s necessary to calculate the devaton of the results of these methods. Ths s done by usng Pearson's correlaton coeffcent. To be used any correlaton coeffcent t s necessary to normalze the ntal decson matrx. Normalzaton of data s done to make the data unform and comparable. REFERENCES (Receved February 2017, accepted March 2017) [1] Hyde, K.. M., Maer, H. R., Colby, C. B. (2005). A dstance-based uncertanty analyss approach to mult-crtera decson analyss for water resource decson-makng. Journal of envronmental management, v.77(4). [2] Radojčć, M., Vesć, J. (2003). One approach to modelng and preference n Mult-crtera optmzaton, publshed n the Proceedngs of: management n the ndustry. [3] Srđevć, B., Srđevć, Z., Zoranovć, T. (2002). Promethee, topss and CP n multcrtera decson makng n agrculture. [4] Belton, S. and Stewart, T.S., (2002). Multple Crtera Decson Analyss. An Integrated Approach, Kluwer Academc Publshers, Massachusetts. [5] Pavlčć, D. (2002). Cconsstency of the method attrbute analyss. Faculty of Economcs. [6] Kablan, M.M., (2004). Decson support for energy conservaton promoton: an analytc herarchy process approach, Energy Polcy 32, [7] Wnston, W., Albrght C. (2008). Practcal management scence. Revsed Thrd Edton, London, Thomson South-Western [8] Saaty, T. L, (1990). How to make a decson. The Analytc Herarchy Process, European Journal of Operatonal Research 48. [9] Šošć, I. (2004). Appled Statstcs, Zagreb. School book. [10] Oprecovć, S., Tzeng, G.H. (2004). Compromse soluton by MCDM methods. Acomparatve analyss of Vkor and Topss. European Journal of Operatonal Research 156, [11] Srđevć, B., Bajčetć, R. (2007). Mult-crtera analyss of alternatves for the reconstructon of regonal water supply system method Promethee, Water Management 39. [12] Buchanan, J., Sheppard P., Vanderpooten, D. (1999). Project rankng usng Electre III. Journal of Mult- Crtera Decson Analyss 11 (4-5). [13] Mnng, Geology and Cvl Engneerng, Unversty of Tuzla, Tuzla, Lneal doo. Marbor, IRGO consultng doo, Marbor, Grads Desgn Centre d.o.o. Traffc study for the hghway Orašje (The Sava Rver) Tuzla (Šćk Brod), Marbor, Techncal Insttute Bjeljna, Archves for Techncal Scences. Year IX N