MCDM METHODS WASPAS AND MULTIMOORA: VERIFICATION OF ROBUSTNESS OF METHODS WHEN ASSESSING ALTERNATIVE SOLUTIONS

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1 Professor Edmudas Kazmeras ZAVADSKAS, Dr. Sc. E-mal: Jurgta ANTUCHEVICIENE*, PhD E-mal: (*correspodg author) Joas SAPARAUSKAS, PhD E-mal: Professor Zeoas TURSKIS, Dr. Sc. E-mal: MCDM METHODS WASPAS AND MULTIMOORA: VERIFICATION OF ROBUSTNESS OF METHODS WHEN ASSESSING ALTERNATIVE SOLUTIONS Abstract. The paper employs a couple of Multple Crtera Decso Makg (MCDM) methods: ovatve, ewly developed WASPAS (Weghted Aggregated Sum Product ASsessmet), reputed MOORA (Multple Obectve Optmsato o the bass of Rato Aalyss) method cosstg of the Rato System ad the Referece Pot approach, also MULTIMOORA (MOORA plus Full Multplcatve Form). Developmet of WASPAS as a aggregated method of two crtera of optmalty, amely WSM (Weghted Sum Model) ad WPM (Weghted Product Model) s shortly troduced wth refereces to prevous researches of the authors. Applcato of the method s preseted for multple crtera assessmet of alteratve buldg desgs. Crtera represetg ecoomy of decsos, performace parameters, evrometal mpact, structural ad physcal propertes of structures are volved for rakg of alteratves ad selectg the optmal oe. Net, to verfy the decso ad to valdate robustess of the ewly developed method, the rather kow ad reputed MOORA ad MULTIMOORA are appled ad rakg of alteratves s performed. Coclusos as cocers partal coformty of the methods depedg o the weghts of both crtera of optmalty the aggregated fucto are preseted. Key words: MCDM, WASPAS, MOORA, MULTIMOORA, robustess, buldg desg. JEL Classfcato: C0, C44, C5, C53, C61, C Itroducto Multple obectve optmzato ad multple crtera decso makg problems are creasgly mportat ecoomcs. There are a lot of methods employed ad case studes avalable whe comple decsos are eeded. I a paper of Zavadskas ad Tursks (011) a comple overvew of MCDM methods ecoomcs s preseted, startg from backgroud approaches ad the earlest

2 Edmudas K. Zavadskas, Jurgta Atuchevcee, Joas Saparauskas, Zeoas Tursks applcatos ad edg by later developmets ad applcatos. Several mportat ew cocepts ad treds for solvg actual multple crtera problems are cosdered by Lou ad Tzeg (01). Also ew developmets of MCDM methods as well as ther applcatos costructo ecoomcs are preseted by Kaplsk ad Tupeate (011). The further the more developmets of decso makg methodology appear ad ther applcatos become more advaced. The usual methods are modfed, adaptg them for vague or ucerta evromet. Broad revew of fuzzy multple crtera decso makg s preseted publcatos of El-Wahed (008), Chu ad L (009). The revew study of Bragge et al. (01) shows that the area of research keeps growg. Hybrd ad modular crsp as well as fuzzfed methods are umerously developed, whe a couple of methods are tegrated. Further a short revew of recet papers o ew theoretcal developmets of tegrated methods ad ther applcatos to dfferet problems ecoomy s provded. The frst group of papers represets tegrato of old, classc methods, usually AHP (Aalytc Herarchy Process) or ANP (Aalytc Network Process) wth TOPSIS (the Techque for the Order Preferece by Smlarty to Ideal Soluto), VIKOR ( Serba VIsekrterumska optmzaca I KOmpromso Resee, whch meas Multcrtera Optmzato ad Compromse Soluto), SAW (Smple Addtve Weghtg) ad alke. Applcato of the latter developmets for persoal dgtal assstat selecto s preseted by Büyüközka et al. (01). Also Büyüközka ad Çfç (01) apply a ovel hybrd approach to evaluate supplers. Portfolo selecto s eplored by Tzeg ad Tsa (011), Ho et al. (011). Importat problems such as marketg or trade decsos are supported by research of Wag (01), Wag ad Tzeg (01). Also the latter developmets are appled for etrepreeurshp polcy evaluato (Tsa ad Kuo, 011), for evaluato of staff or equpmet (Wu et al., 01; Lashgar et al., 011), for effectve selectg the best team member (Hashemkha Zolfa ad Atuchevcee, 01). The secod group of papers s composed of researches cocerg tegrated classc MCDM methods wth ew oes, cludg COPRAS (COmple PRoportoal Assessmet), MOORA (Multple Obectve Optmsato o the bass of Rato Aalyss), MULTIMOORA ad the other methods. Medeckee ad Börk (011) demostrate usg AHP for determg crtera weghts ad several MCDM methods for calculatos o the effects of a umber of reovato measures. COPRAS ad AHP uder fuzzy evromet are appled for measurg performace of sttutos Ida (Das et al., 01). AHP ad COPRAS wth grey umbers are used for selectg compay suppler Ira (Hashemkha Zolfa et al., 01). Kosareva ad Krylovas (013) aalyze applcato of terval ad tragular tutostc fuzzy umbers for decso makg a ucerta evromet together wth COPRAS, TOPSIS ad VIKOR methods. Although a great varety of rakg methods are developed, the cotual problem of proper choce remas uder cosderato. How to select the best oe? Whch method s the most robust ad what assessmet s the most accurate?

3 MCDM Methods WASPAS ad MULTIMOORA: Verfcato of Robustess of Methods whe Assessg Alteratve Solutos Accordgly, comparatve aalyss of MCDM methods ad evaluato of rakg results are preseted a umber of publcatos. Oprcovc ad Tzeg (004) provded a famous paper o comparatve aalyss of VIKOR ad TOPSIS methods. Podvezko (011) performed comparatve aalyss of classc SAW ad more moder COPRAS. Kou et al. (01) aalyses dsagreemets amog methods rakgs. The paper proposes a approach to resolve dsagreemets based o rak correlato ad fve MCDM methods are eamed. The smlar methodology s appled for fuzzfed methods by Atuchevcee et al. (011, 01), aalyss of rakg results s performed ad ther cogruece (cogruece) s measured. Balezets et al. (01b) appled several fuzzy MCDM methods for assessmet of ecoomc sectors of a coutry. The paper of Chatteree ad Chakraborty (01) focuses o the applcato of four MCDM methods for materal selecto ad comparso of rakg results, whle the paper of Karade ad Chakraborty (01) employs much more techques for the same problem ad evaluates the performace of the methods ad ther relatos by calculatg rak correlatos. Performace of methods ca also be measured by evaluatg robustess of the method. Meag of robustess s dscussed a umber of papers. Brauers ad Zavadskas (01) summarze deftos of robustess ad codtos of robustess, cludg researches publshed several decades ago ad recet works (Chakraborty, 011). Robustess of MOORA ad MULTIMOORA s also proved (Brauers ad Zavadskas, 009; Brauers ad Zavadskas, 01). The problem of robustess of certa mult-crtera decso makg method s stll uder cosderato. Accordg to codtos or robustess, the use of two dfferet methods of multple crtera optmzato s more robust tha the use of a sgle method; the use of three methods s more robust tha the use of two, etc. (Brauers ad Zavadskas, 01). Accordgly, the authors of the curret research propose a ot method as a combato of two crtera of optmalty, amely WSM (Weghted Sum Model) ad WPM (Weghted Product Model). Moreover, t s suggested to select the most approprate multple crtera decso makg method based o ts accuracy of measuremet ad a combato of two methods s proposed to crease the rakg accuracy. Optmzato of aggregato s held ad Weghted Aggregated Sum Product Assessmet (WASPAS) method for rakg of alteratves s proposed (Zavadskas et al., 01). The et step s to verfy performace of the approach ad to valdate robustess of the ewly developed method. Therefore the well-kow ad reputed MOORA method cosstg of the Rato System ad the Referece Pot approach (Brauers ad Zavadskas, 006) as well as the Full Multplcatve Form ad MULTIMOORA (Brauers ad Zavadskas, 010) are volved the research. A case study of multple crtera assessmet of alteratve buldg desgs, cosderg ecoomy of decsos, performace parameters, evrometal mpact, structural ad physcal propertes of structures, s performed. Coclusos as cocers partal coformty of the methods depedg o the weghts of both crtera of optmalty the aggregated fucto are preseted.

4 Edmudas K. Zavadskas, Jurgta Atuchevcee, Joas Saparauskas, Zeoas Tursks. Weghted Aggregated Sum Product Assessmet (WASPAS) Two crtera of optmalty were the tal source for developmet of the thrd ot crtero of optmalty ad the WASPAS method afterwards. The frst crtero of optmalty,.e. crtero of a mea-weghted success s smlar to the well-kow Weghted Sum Model (WSM). Ths s a method for multple crtera decso makg,.e. t s appled for evaluatg a umber of alteratves terms of a umber of decso crtera. Suppose that problem s defed o m alteratves ad decso crtera. The relatve sgfcace (weght) of the crtero s deoted by w. Varable stads for the performace value of alteratve whe t s evaluated terms of crtero. The relatve mportace of alteratve, deoted as (MacCrmo, 1968; Trataphyllou ad Ma, 1989): 1 Q, s defed as follows Q 1 w, (1) where lear ormalzato of tal crtera values s appled,.e. ma, () f ma value s preferable or m, (3) f m value s preferable. The secod crtero of optmalty, amely multplcatve epoetal geeralzed crtero, geeral cocdes wth Weghted Product Model (WPM). The relatve mportace of alteratve, deoted as Q, s defed as follows (Mller ad Starr, 1969; Trataphyllou ad Ma, 1989): Q w. (4) The thrd ot geeralzed crtero of weghted aggregato of addtve ad multplcatve methods was proposed by Saparauskas et al. (011):

5 MCDM Methods WASPAS ad MULTIMOORA: Verfcato of Robustess of Methods whe Assessg Alteratve Solutos Q 0.5Q 1 0.5Q 0.5 w 0.5 w. (5) Supposg the crease of rakg accuracy ad the effectveess of decsos, methodology for optmzato of weghted aggregated fucto was proposed ad the Weghted Aggregated Sum Product Assessmet (WASPAS) method for rakg of alteratves was preseted (Zavadskas et al., 01): Q w 1 w, 0,...,1. (6) Optmal values of ca be foud whe searchg the etreme of the fucto: Q 1 Q Q. (7) The varaces 1 Q ad Q should be calculated as: Q 1 w, (8) Q w w w 1 w. (9) I the case of ormal dstrbuto of tal data wth the credblty q=0.05, estmates of varaces of ormalzed crtera values are calculated as follows: (10) Please, see Zavadskas et al. (01) for detaled eplaato of Eq. (7 10). The smplfed applcato of WASPAS for ecologcal-ecoomcal assessmet of houses moderzato ca be foud Stauas et al. (013). 3. Multple Obectve Optmsato o the bass of Rato Aalyss (MOORA ad MULTIMOORA) The MOORA method cossts of the Rato System ad the Referece Pot approach (Brauers ad Zavadskas, 006).

6 Edmudas K. Zavadskas, Jurgta Atuchevcee, Joas Saparauskas, Zeoas Tursks I the Rato System each respose of a alteratve to the obectve s ormalzed as follows:, (11) m 1 where respose of alteratve to obectve ; = 1,,, m; m the umber of alteratves; = 1,,, ; the umber of obectves (decso crtera); a dmesoless umber represetg the ormalsed respose of alteratve to obectve. Net, for optmsato, a case of mamsato the resposes (weghted ormalzed crtera) are added ad, a case of mmsato, weghted ormalzed crtera are subtracted, respectvely: g y w w, (1) g 1 where = 1,,, g are mamsed decso crtera; = g + 1, g +,, g + are mmsed decso crtera; w s the relatve sgfcace (weght) of the crtero; y stads for the calculated relatve mportace of alteratve wth respect to all obectves accordg to the Rato System approach. A ordal rakg of y shows the fal preferece of alteratves. Accordg to the secod part of the MOORA, the mamal obectve Referece Pot approach s used. The desrable deal alteratve wth coordates r s formed selectg data from every decso alteratve uder cosderato, cosderg optmzato drecto of every partcular crtero. Net, ormalzato accordg to Eq. (11) s performed. Havg ormalsed respose of alteratve to obectve ad the relatve sgfcace (weght) of the crtero w, the M Ma metrc of Tchebycheff (Karl ad Studde, 1966) s appled for rakg of alteratves: the M ma r w. (13) Brauers ad Zavadskas (010) proposed MOORA to be updated by the Full Multplcatve Form. The Full Multplcatve Form s appled as follows: A U, (14) B

7 MCDM Methods WASPAS ad MULTIMOORA: Verfcato of Robustess of Methods whe Assessg Alteratve Solutos where U deotes overall utlty of alteratve. g A w, (15) B w, (16) g 1 where = 1,,, g are mamsed decso crtera; = g + 1, g +,, g + are mmsed decso crtera. The MULTIMOORA summarzes MOORA ad the Full Multplcatve Form based o the theory of domace (Brauers ad Zavadskas, 010). The MOORA ad MULTIMOORA are wdely appled, ad especally ecoomcs. The ecoomy of regos s tested ad regoal developmet cosderg multple obectves s evaluated by Brauers et al. (010). Ecoomc rakg of Europea Uo member states s performed (Brauers et al., 01a). Some more recet applcatos ca be metoed, as persoel selecto (Balezets et al., 01a) or calculatos for eergy savgs buldgs (Brauers et al., 01b). Balezets ad Zeg (013) propose a eteso of techque for group decso makg based upo terval-valued fuzzy umbers ad provde a applcato for persoel selecto. 4. Multple crtera assessmet of alteratve buldg desg solutos 4.1. Cosdered alteratve solutos Assessmet of alteratve buldg desgs s far from beg etrely a techologcal questo. Harmoy betwee ecoomy, evromet, qualty of lvg evromet, ad requred techologcal parameters should be supported ad sustaable decso should be made. To choose the best buldg s desg alteratve usually several dfferet solutos are beg cosdered. I the preseted case study facade s alteratves for publc or commercal buldg are assessed. Four buldg facades alteratves are evaluated, amely cellular cocrete masory covered by Rockwool plates ad decoratve plaster surface, sadwch facade paels, gas slcate masory covered by Rockwool ad Mert facade plates, ad alumum-glazg facade (Povlavcus, 007). There are some advatages ad dsadvatages of structures metoed (see Table 1).

8 Edmudas K. Zavadskas, Jurgta Atuchevcee, Joas Saparauskas, Zeoas Tursks Table 1. Advatages ad dsadvatages of dfferet facades Type of facade Advatages Dsadvatages Cellular cocrete masory covered by Rockwool plates ad decoratve plaster surface The relatvely low prce Vulerable; Stubbor stas; Requres care; Breach threates facade structures; It s dffcult to fd defects Sadwch facade paels Gas slcate masory covered by Rockwool ad Mert facade plates Alumum-glazg facade Resstat to shock ad corroso; Easy to remove drt Resstat to water; Resstat to chemcals; Easly removed drt, grafft Ca be easly observed structural damage; Easy to remove drt Volato dffcult to sort out The relatvely hgh prce Threat of volato of costructo ad facade; Hgh prce Potetal alteratves are evaluated terms of a umber of quattatve ad qualtatve crtera. Twelve crtera are appled that represet ecoomy of decsos (stallato cost ad labour testy), performace parameters (user fredless, durablty ad warraty), evrometal mpact of partcular facades systems (evrometal fredless, recovery or utlzato, aesthetcs), structural propertes (weght ad thckess of structure) ad physcal propertes of structures (soud solato ad fre resstace). 4.. Rakg of alteratves applyg WASPAS A smlar problem was aalysed prevous researches of the authors. Three crtera of optmalty were appled ad alteratve decsos were raked by Saparauskas et al. (011). Two crtera of optmalty dcated the most preferable alteratve; however the thrd crtero dcated the other alteratve as the best oe. Accordgly, the questo remaed usolved. Soluto of the problem s cotued the curret research ad a ot method of the latter crtera of optmalty called WASPAS s appled for rakg of facades. The problem s defed o m alteratves (m=4 the curret case) ad decso crtera (=1 the curret case). Varable stads for the performace value of alteratve a (=1,,4) whe t s evaluated terms of crtero (=1,,1). Crtera uder cosderato are stallato cost, Lt/m ( 1 ); labour testy by assemblg, days ( ); user fredless, pots ( 3 ); durablty, pots ( 4 ); warraty, pots ( 5 ); evrometal fredless, pots ( 6 ); recovery (utlzato), pots ( 7 ); aesthetcs, pots ( 8 ); weght of structure, kg/m ( 9 ); thckess of

9 MCDM Methods WASPAS ad MULTIMOORA: Verfcato of Robustess of Methods whe Assessg Alteratve Solutos structure, mm ( 10 ); soud solato, pots ( 11 ); fre resstace, pots ( 1 ). Crtera 1,, 9 ad 10 are mmzed, whle the remag 3 8, 11 ad 1 are mamzed a process of optmzato. Four buldg facades alteratves are evaluated cosderg the above crtera ad raked, amely cellular cocrete masory covered by Rockwool plates ad decoratve plaster surface (a 1 ), sadwch facade paels (a ), gas slcate masory, covered by Rockwool ad Mert facade plates (a 3 ) ad alumum-glazg facade (a 4 ). Relatve sgfcaces (weghts) of the crtera are deoted by w (=1,,1) ad are determed by meas of Etropy method (Shao, 1948). Calculatos of relatve sgfcaces for the curret case study were preseted Saparauskas et al. (011). Ital decso makg matr for descrpto of alteratves terms of partcular crtera s preseted Table. Table. Ital decso makg matr: tal crtera values ad weghts Crtera Weghts w Alteratves a a 1 a a 3 a Rakg of alteratves s performed applyg Weghted Aggregated Sum Product Assessmet, Eq. (1 4) ad Eq. (6) whe λ=0, 0.1,,1. Establshed relatve sgfcaces of alteratves are preseted Table 3.

10 Edmudas K. Zavadskas, Jurgta Atuchevcee, Joas Saparauskas, Zeoas Tursks Table 3. Rakg of alteratves applyg WASPAS Relatve sgfcaces Q ad raks of alteratves Alteratve a 1 Alteratve a Alteratve a 3 Alteratve a 4 Q 1 Rak Q Rak Q 3 Rak Q 4 Rak Oe ca observe from calculato results that the most preferable alteratve depeds o value whe applyg WASPAS. Alteratve a ( sadwch facade paels) s raked as the best ad alteratve a 4 (alumum-glazg facade) remas the secod place several cases amog aalyzed eleve varats wth dfferet values. Whle rakg order of the partcular alteratves chages several other cases ad a 4 s preferred. Accordgly, the questo of selecto of the best alteratve desgs remas ot completely solved. Therefore, MOORA method ad the Full Multplcatve Form are appled to valdate the decso as well as robustess of the ewly developed method Rakg of alteratves applyg MOORA, the Full Multplcatve Form ad MULTIMOORA methods Four alteratves cosderg twelve crtera (Table ) are raked applyg the Rato System, Eq. (11 1); the Referece Pot approach, Eq. (11), Eq. (13); the Full Multplcatve Form, Eq. (14 16) ad MULTIMOORA. Establshed relatve sgfcaces of alteratves, also rakg order of alteratves are preseted Table 4.

11 MCDM Methods WASPAS ad MULTIMOORA: Verfcato of Robustess of Methods whe Assessg Alteratve Solutos Table 4. Rakg of alteratves applyg the Rato System, the Referece Pot approach, the Full Multplcatve Form ad MULTIMOORA a Rato System MOORA Referece Pot y Rak ma r w Rak U Full Multplcatve Form Rak MULTIMOORA Rak based o domace a , 4.9E a E a , E a E-05 Sadwch facade paels are selected as the most preferable alteratve whe applyg the Rato System, the Referece Pot approach, the Full Multplcatve Form ad MULTIMOORA Verfcato of rakg results Whe applyg MOORA method cosstg of the Rato System ad the Referece Pot approaches as well as the Full Multplcatve Form ad MULTIMOORA, the best raked alteratve decsos cocde all cases ad sadwch facade paels (a ) are preferred the aalysed case study. Whle appled aggregated crtera of success (Eq. 1 6) produce partly dfferet rakg results. The case study proves that the most preferable alteratve depeds o λ value whe applyg a ot weghted method WASPAS. Alteratve a ( sadwch facade paels) s raked as the best ad alteratve a 4 (alumumglazg facade) remas the secod place whe λ=0, 0.1,,0.4. Whle rakg order of the partcular alteratves chages ther places ad alumum-glazg facade (a 4 ) s preferred whe λ=0.5, 0.6,, 1. The robustess of MOORA ad MULTIMOORA methods s proved by Brauers ad Zavadskas (009, 01). Accordgly, the calculato results applyg the latter methods are relable ad applcable. Rakg order applyg WASPAS method cocdes wth the well-kow, reputed ad robust approach whe λ s less tha 0.5. The above detfed terval of λ less tha 0.5 s cosstet wth the proposed approach to calculate optmal values of λ (Zavadskas et al. 01). Calculato results whe searchg optmal λ coformty wth Eq. (7 10) are preseted Table 5. Calculated relatve sgfcaces of alteratves Q * (Eq. 6) usg the establshed optmal λ values are also preseted Table 5. Oe ca observe from the Table 5 that calculated optmal λ values really are less tha 0.5. Also, whe calculatg stadard devatos the case of ormal dstrbuto of tal data wth the credblty q=0.05, the hgher rakg accuracy

12 Edmudas K. Zavadskas, Jurgta Atuchevcee, Joas Saparauskas, Zeoas Tursks s reached whe applyg weghted aggregated fucto as compared to accuracy of WSM or WPM dvdually. It meas that oe of the codtos of robustess as cocers the use of two dfferet methods of multple crtera optmzato stead of a sgle oe s ot oly a presumpto. The codto was proved by calculatos. Therefore, the cocluso that ewly developed WASPAS method appears to be robust ca be approved ad valdato of the ovatve method for real lfe applcatos ca be made. Table 5. Optmal λ ad relatve sgfcaces of alteratves Relatve sgfcaces of Alteratves a Optmal λ alteratves Q a a a a Coclusos The paper employs ovatve, ewly developed WASPAS (Weghted Aggregated Sum Product ASsessmet) method ad reputed MOORA (Multple Obectve Optmsato o the bass of Rato Aalyss) method cosstg of the Rato System ad the Referece Pot approach as well as the Full Multplcatve Form ad MULTIMOORA. A case study of multple crtera assessmet of four alteratve buldg desg solutos cosderg ecoomy of decsos, performace parameters, evrometal mpact ad physcal propertes of structures s performed applyg the above methods. It s assessed that the most preferable alteratve depeds o λ value whe applyg a ot weghted method WASPAS. Alteratve a ( sadwch facade paels) s raked as the best ad alteratve a 4 (alumum-glazg facade) remas the secod place whe λ=0, 0.1,,0.4 a curret case. Whle rakg order of the partcular alteratves chages ad alumum-glazg facade s preferred whe λ=0.5, 0.6,,1. Whereas the best raked alteratve cocdes whe applyg all approaches of MOORA ad MULTIMOORA ad sadwch paels (a ) are preferred. Robustess of the MOORA ad MULTIMOORA methods were tested prevous researches. Accordgly, calculato results of the latter methods ca be cosdered as relable. It s estmated that prorty order of alteratves by applyg WASPAS method cocdes wth the above reputed approaches a case whe λ s less tha 0.5.

13 MCDM Methods WASPAS ad MULTIMOORA: Verfcato of Robustess of Methods whe Assessg Alteratve Solutos It s proved that the hgher rakg accuracy s reached whe applyg weghted aggregated fucto as compared to accuracy of WSM or WPM dvdually,.e. a partcular codto of robustess s fulflled. Supposg the crease of rakg accuracy ad applyg the proposed methodology for optmzato of weghted aggregated fucto, optmal λ values are calculated. Optmal λ values vary from 0.3 to 0.49 ad are also less tha 0.5 the curret case. Based o the results of the research, the cocluso that ewly developed WASPAS method appears to be robust ca be approved. Valdato of the method for real lfe applcatos ca be made. REFERENCES [1] Atuchevcee, J., Zakarevcus, A., Zavadskas, E. K. (011), Measurg Cogruece of Rakg Results Applyg Partcular MCDM Methods. Iformatca (3), ; [] Atuchevcee, J., Zavadskas, E. K., Zakarevcus, A. (01), Rakg Redevelopmet Decsos of Derelct Buldgs ad Aalyss of Rakg Results. Ecoomc Computato ad Ecoomc Cyberetcs Studes ad Research 46(), 37 6, ASE Publshg; [3] Balezets, A., Balezets, T., Brauers, W. K. M. (01a), MULIMOORA FG: A Mult obectve Decso Makg Method for Lgustc Reasog wth a Applcato to Persoel Selecto. Iformatca 3(), ; [4] Balezets, A., Balezets, T., Msuas, A. (01b), A Itegrated Assessmet of Lthuaa Ecoomc Sectors Based o Facal Ratos ad Fuzzy MCDM Methods. Techologcal ad Ecoomc Developmet of Ecoomy 18(1), 34-53; [5] Balezets, T., Zeg, Sh. (013), Group Mult-crtera Decso Makg Based upo Iterval-valued Fuzzy Numbers: A Eteso of the MULTIMOORA Method. Epert Systems wth Applcatos 40(), ; [6] Bragge, J., Korhoe, P., Walleus, H., Walleus, J. (01). Scholarly Commutes of Research Multple Crtera Decso Makg: A Bblometrc Research Proflg Study. Iteratoal Joural of Iformato Techology & Decso Makg 11(), ; [7] Brauers, W. K. M., Balezets, A., Balezets, T. (01a), Europea Uo Member States Preparg for EUROPE 00. A applcato of the MULTIMOORA method. Techologcal ad Ecoomc Developmet of Ecoomy 18(4), ;

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