GARAGE LOCATION SELECTION FOR RESIDENTIAL HOUSE BY WASPAS-SVNS METHOD

Transcription

1 JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT ISSN / eissn Volume 23(3): GARAGE LOCATION SELECTION FOR RESIDENTIAL HOUSE BY WASPAS-SVNS METHOD Romualdas BAUŠYS, Birutė JUODAGALVIENĖ Departmet of Graphical Systems, Faculty of Fudametal Scieces, Vilius Gedimias Techical Uiversity, Saulėtekio al. 11, Vilius LT-10223, Lithuaia Received 09 Mar 2016; accepted 30 Nov 2016 Abstract. The paper deals with the locatio selectio problem of the garage at the parcel of a sigle-family residetial house. The mathematical model for this real life problem is costructed withi MCDM framework. The sigificace of the chose criteria was evaluated by AHP approach. The formulated MCDM problem is solved applyig WASPAS extesio, amely WASPAS-SVNS. The applied sigle-valued eutrosophic set allows to modelig ucertaity of the iitial iformatio explicitly. A umerical example is cosidered i order to verify the proposed approach. Keywords: garage locatio, residetial house, MCDM, WASPAS, eutrosophic set. Itroductio Huma comfort (well-beig, physical ad metal coditio, security) is closely related to the developmet of fuctioal architectural space i residetial house desig process. The quality of the architectural, fuctioal space desig is ivestigated i the cotext of a residetial house ad a garage. The positio of these residetial house spaces provides physical ad psychological comfort, which results i the achievemet of the mai desig goal. The Committees of the Regios Housig ad Regioal Policy have formed a opiio already some time ago o the quality of the residetial housig (EUR-Lex 2007a). After the restoratio of Lithuaia s idepedece, the situatio with parcel owership has chaged (ow they are iherited, bought, sold, etc.), so i the cities ad suburbs costructios of sigle-family residetial houses have icreased. I 2007, the Miistry of the Eviromet carried out the survey (about 413,000 villages, tows, district ceters ad urba residets were iterviewed) which results showed that most people would choose his ow residetial house (82.6 percet) (AM 2007). Therefore, the selectio of the garage a place is importat problem. Accordig to Europea statistical data (Eurostat 2014), 33.7 percet of the populatio lived i sigle-family dwelligs i 28 coutries i the territory of Europe i The percetage is the highest i Croatia, Sloveia or Hugary, ad although Lithuaia is laggig behid the above-metioed coutries it still exceeds the average of metioed statistics. The Uited Natios Ecoomic Commissio for Europe (UNECE) already i 2006 stressed that the quality of housig plays a crucial role i assessig the health of the populatio (WHO 2006). With the agreemet of WHO (World Health Orgaizatio), the residetial housig is importat, like a separate physical structure ad i a lik betwee the commuity (eighbors), too. Both of these factors ifluece a perso s physical, metal ad social status, so their importace is directly related to the welfare of society. Europea social policy is a itegral part of the housig ecoomic iterest (EUR-Lex 2007b). Garage positio problem is associated with the architectural ad structural coherece, which iflueces housig comfort (Mazao-Agugliaro et al. 2015). Problems of garages of blocks or public buildigs are solved, which are related to their vetilatio, safety ad ecoomy (Pierce et al. 2015; Vasilevska et al. 2015), evaluatio tools are cosidered ad offered for the determiatio of the logterm evirometal ad social impacts i differet dwelligs as separate uits (icludig garages). The situatio of the garages of the sigle-family houses is beig examied as oe of the spatial areas of the house ad overheatig ad vetilatio problems are addressed. Due to cotiuously risig requiremets of EPBD (Eergy Performace of Buildigs Directive), the Belgia scietists aalyze the desig parameters ad coditios, esurig good premises comfort i differet thermal zoes. To this ed, the dwellig is divided ito thermal zoes (the garage is Correspodig author: Romualdas Baušys romualdas.bausys@vgtu.lt 421 Copyright 2017 Vilius Gedimias Techical Uiversity (VGTU) Press

2 422 R. Baušys, B. Juodagalvieė. Garage locatio selectio for residetial house by WASPAS-SVNS method attached to the auxiliary space) ad thus the typical Flemish housig (Claes et al. 2015) is beig simulated. Amog the desig parameters differet garage positio i respect of residetial space is ot cosidered i the study of these scietists. Study of other scietists (Nirva et al. 2012) is associated with the impact of atural vetilatio ad mechaical vetilatio systems for the residetial space cocerig garage istallatio. But the differet positios of the garage are ot cosidered i this case, also. The purpose of our work is to choose a garage positio i respect to of a residetial house with multi-criteria methods searchig for the physical ad psychological comfort. To this ed, firstly there were set 6 most popular object positios. The architects, recommedatios of future sigle-family houses owers, review of projects proposed i Lithuaia are the basis for the choice of this set. It is uderstood that there caot be oe sigle solutio for all the differet cases (i.e. families of differet size ad age ad dwelligs). Oe should ot compare the so-called small houses (up to 80 m 2 ) iteded for 1 or 2 perso family with houses of the much bigger area ad the requiremets for them. Therefore, limits are set for the testig: ecoomic class families with 3 to 5 persos with iteded garage/carport (2 stads) for them ext to the residetial house. Today i most of describig parcel optios the garages are goig to be made for two cars m i size (miimum dimesios of the double garage, accordig to the Lithuaia legal documets is m (STR :2005)). Urbaizatio problems are beig solved with multicriteria methods associated with urba reewal (ad thus the reclaimig of ew parcels) ad may other problems at least partly related to the garage positios i the parcels. I all cases, the selectio of criteria (Azma et al. 2013) is oe of the most importat aspects of the study. These aforemetioed quite complicated decisio problems ca be effectively solved withi multi-criteria decisio makig (MCDM) framework (Ada et al. 2015; Jaskowski et al. 2014; Lee 2014; Vafaeipour et al. 2014). Durig the last decade a lot of the research has bee doe applyig the fuzzy sets i the MCDM problem formulatio (Aliakbari et al. 2015; Mardai et al. 2015). The applicatio of these fuzzy sets allows takig ito accout the ucertaity of the iitial iformatio of the solutio about the real life problems. Despite the fact that the various types of the fuzzy sets have bee defied ad applied to the solutio of the MCDM problems they are ot able to iclude all sorts of the vagueess ito the mathematical model of the cosidered real egieerig problem. The ew eutrosophic sets allow dealig idepedetly with the idetermiacy of the iitial iformatio (Bausys et al. 2015; Smaradache 1999). By the logic of the eutrosophic sets, each criterio of the MCDM problem is represeted by three idepedet fuctios: the degree of the truth (t), a degree of the idetermiacy (i) ad a degree of the falsity (f). The evolutio of WASPAS method, which is applied to the solutio of the cosidered problem, is preseted below. The first extesio of the origial crisp WASPAS method (Chakraborty et al. 2015) that is costructed uder iterval-valued ituitioistic fuzzy set eviromet was performed by Zavadskas et al. (2014). Recetly, a ovel multiple attribute Weighted Sum-Product Assessmet method with the gray attributes scores, amely WASPAS-G, was proposed i Zavadskas et al. (2015a). Turskis et al. (2015) proposed a fuzzy multi-attribute performace measuremet (MAPM) framework, which icorporates the applicatio of the ovel Weighted Aggregated Sum-Product Assessmet method with Fuzzy values (WASPAS-F) ad Aalytical Hierarchy Process (AHP). Zavadskas et al. (2015b) developed a ew extesio of WASPAS method, amely WASPAS-SVNS. The cosidered eutrosophic set provides the meas to represet ad model the vagueess of the iitial iformatio explicitly. Differet locatio selectio problems have bee solved withi the framework of the multi-criteria decisio makig. Dheea ad Moharaj (2011) preseted solutio of the distributio ceter locatio problem. Elevli (2014) performed a evaluatio of locatios for the logistics ceter at Samsu (Turkey). Zavadskas et al. (2015c) solved a decisio problem cocerig the selectio of the locatio for a deep-water port. 1. Problem formulatio for the selectio of garage locatio It is importat to idetify the key factors while plaig the costructio of housig for a residece that determies the quality of huma life. The optimal distributio of fuctioal space has a sigificat impact ot oly i the house itself but i its parcel of lad, also. Accordig to the importace, the factors ifluecig the parcel s selectio ad costructio situatio i it ca be listed as follows: Cardial directios (North, East, South, West); Prevailig wid directio; Etrace locatio of the parcel; Iteded place of the yard; Lookout opeig from the parcel (to the city, forest, river ad so o); Other (high eighbors house, locatio ear the oisy road, specific features of the area ad so o). The factor etrace locatio i the parcel is directly associated with the car parkig place. Accordig to Techical Costructio Regulatio (STR :2005), there are restrictios i this regard: the parcel must have etrace to a private garage ot arrower tha 3.5 m wide, ad the straightest ad most coveiet path for pedestrias from the street towards the mai etrace to the house caot cross or overlap with the auto road. Choosig a uique ad exclusive parcel ad aimig to build the best available house o it with the use of stadard premises ad parkig lot layout plas will fail. However, most parcels do ot have exclusios i specific terrai features, because they are usually rectagular i shape from 6 to

3 Joural of Civil Egieerig ad Maagemet, 2017, 23(3): acres plots adjoiig the street, from which etrace locatio of the parcel should be made. Number of cars i Lithuaia accordig to statistics i 2016 compared with 2010 whe 509 cars fell o 1000 people icreased by 62 percet (Regitra 2016). Thus, today o average a family of 3 to 4 persos has 1 to 2 cars. Today sigle-family houses are ot desiged without car storage space. It is a closed ad a ope type garages or simply a space i the parcel iteded for the car parkig. Selectio of garage type is determied by differet criteria: from the architectural refiemets of the parcel to the ower s wishes (Mazao-Agugliaro et al. 2015). The truth is that exist oe aspect, which sometimes has a great sigificace, ad it is regulated i Lithuaia legal documets. It is the total area (garage-ope shelter is ot couted i the total area of a sigle-family house). Closed type garages usually are desiged ear the buildig (whe oe wall is a partitio betwee the livig space ad garage) ad are itegrated ito the space of the house (whe two walls are partitios betwee the livig space ad garage). Closed type garage as a separate buildig is ormally estimated i the authorig projects whe combiig it with the parcel ad buildig architecture. Ope type garages (awigs) ca be desiged ear the buildig or separately as a separate buildig. The locatio of these parkig lots ca be evaluated accordig to certai criteria i order to reveal the peculiarities of alterative locatios. Whe choosig a garage locatio accordig to the images foud o the Iteret or ay other source of iformatio, usually oe chooses accordig to the aesthetic view of the other house. The importace of practicality ad coveiece, alterative possibilities of positios of the garage ofte are beig reflected later whe the project is already coordiated; it meas too late (Alsaadai, De Souza 2016). Therefore, the ower should firstly decide whether the buildig will have a purely fuctioal purpose or aesthetic highlight of the parcel, ad also about the reovatio prospects i case of a icrease or chages i family compositio, etc. Hece it is importat to decide i advace ad pla whether a garage will be built i cojuctio with a house or away from it. So, the decisio of the task is relevat for idividuals who pla to desig or are already desigig their ow housig i the parcels. The accurate decisio makig i buildig idustry is quite difficult ad complicated problem (Ksiąźek et al. 2015). There ca be umerous ad diverse selectio criteria for garage site: from the orietatio of cardial directios i the parcel to the adjacet eighbor s house height. We have selected four (i the expert opiio) the most importat criteria ( c1 c4 ): c 1 the legth of the foudatio, m; c 2 iteral fuctioal commuicatio, scores; c 3 cotextuality, scores; c 4 aesthetics ad others, scores. Selectio of criterio of foudatio legth is relevat because of the earthwork scope ad costructio cost. Whe the garage is beig desiged ear to oe façade of the house, the legth of the garage foudatio reduces by oe-quarter, ad after garage itegratio ito the house space eve by three-quarters. I both cases, the rates of earthworks are fallig because of excavatio of the oe ad the same dip, equipmet istallatio, etc. I the case of the awig, costructio of idividual foudatios uder the supports could ot be liked with the house foudatio. Iteral fuctioal commuicatio describes the comfort of the use of sigle-family house uits ad compliace with user eeds. Cotextuality is defied as a forecast of optios of zoig of the buildigs i the parcel, depedig from the parcel, orietatio with respect to the cardial directios. The last c criterio 4 icludes aesthetics ad other partially relevat (i expert opiio) aspects: isulatio of residetial premises dwellig (Motuziee et al. 2016; Balyai et al. 2015) because of the uheated garage, performace evaluatio of garage isulatio optio ad costs of other materials (walls ad roof structures). Particular geometric shape houses are desiged ad built traditioally i the metioed rectagular parcels (Fig. 1): square, rectagular, cross- ad L-shaped. The desiged ad istalled garage ca be situated o the frot side of the house, ad also from a facade, i the form of the house ad stad separately. Fig. 1. Shapes of sigle-family houses 5 idepedet experts-desigers ad 2 future owers of the residetial house performed the assigmet of criteria importace. 2. Alteratives For the costructio of the cosidered alteratives, the aalysis of the projects of the residetial houses developed i Lithuaia was performed. The projects are take Fig. 2. Schemes of garage positio i commuicatio to the house

4 424 R. Baušys, B. Juodagalvieė. Garage locatio selectio for residetial house by WASPAS-SVNS method ito cosideratio ivolve oly the houses with a total area of 80 to 300 m 2 (House plas 2016). The aalysis icludes 251 projects that were created i the last 2 3 year period. There were distiguished six garages positios i relatio to the house for the study, show schematically i Figure 2. The aalysis of the above-metioed projects shows that i the projects of the houses with a lowest commo area, garages are usually ot icluded or plaed as ope shelter. Projects where garages are ot provided, we ve assiged to the 6-th scheme. All garages selected i the study are ot isulated because isulatio of 49 m 2 garage would hardly respect the provisios of the Europea Parliamet ad Coucil Directives (Directive 2010/31/EU). I five of them, the garages are i oe or aother way itegrated ito the volume of the residetial house Garage positio accordig to Scheme 1 Accordig to Scheme 1, the garage is desiged ear the mai facade wall of the house (Fig. 3). Fig. 4. Ope shelter ear the mai facade side of the house the lowest, ad the walls of the etire istalled. Commuicatio with the residetial premises is possible from the outside, but usually with a partitio (roof) from the top. If the ope shelter is desiged from the mai facade side of the house, the roof ca be resolved by a extesio of the roof of the residetial house (depedig o the architectural decisio). If the itesity ad the desity of parcel s build-up are relevat to a particular parcel, the i the case of ope shelter the solutio is simple it is ot cosidered as a garage. This scheme covers 14% of the aalyzed the house projects Garage positio accordig to Scheme 3 I the case of Scheme 3, the garage is itegrated ito the house space (Fig. 5). Fig. 3. Garage ear the mai facade side of the house Costructio of the foudatios ad supportig walls of the both buildigs is closely related: the scale of lad works ad foudatio price is a bit smaller because oe wall of the garage is adjacet to the wall of a residetial house. If there is o basemet i the house, usually boiler-room is istalled ear the garage or other auxiliary space i this way the heat is saved, which ca be lost due to the o-heated garage. Iteral coectio with the residetial premises is desiged withi the space of these premises. There will ot be may optios o the premises of the house ad yard zoig by placig the garage o the orther side of the parcel (eve if it is possible i accordace with site deploymet of the parcel i relatio to the cardial directios). It is possible to achieve the desired itegrity of the buildig by selectig the same house fiish as the facade fiish ad the roof structure. This scheme correspods to 26% if the aalyzed the house projects Garage positio accordig to Scheme 2 I the case of Scheme 2, the garage is desiged ear the house s mai facade wall as i the Scheme 1, but the garage is istalled without walls, it meas ope shelter (Fig. 4). The volume of lad works is the smallest because the foudatio for the garage must be detached istalled beeath two colums, the the foudatio price will be Fig. 5. Garage itegrated ito the house space The volume of lad works is the smallest (from the preseted optios), because oe wall of the garage, geerally coicides with the ier supportig, ad beeath the other o-supportig wall ca be istalled, foudatio oly with oe block i height (i the same way as beeath the brick partitio of 12 cm). Itercommuicatio with residetial premises has the most optios because two garage walls are iside the buildig. I this case, work ad guest room or other premises are desiged above the garage so ot oly two walls of the garage but also the overlap should be isulated. Thus, there will be the attic above the first floor (or the secod floor), so the ower will have a additioal ivestmet (overlap, stairs). Depedig o the deploymet of the parcel i relatio to the cardial directios, the zoig of the premises ad yard of the house is see as the worst, because i the worst-case sceario, most rooms of the house ca be directed to the orth. This scheme ivolves 20% of the aalyzed the house projects.

5 Joural of Civil Egieerig ad Maagemet, 2017, 23(3): Garage positio accordig to Scheme 4 I the case of Scheme 4, the garage is partly itegrated ito a housig space (Fig. 6) as stuffed i the corer of the house. Fig. 6. Garage partially itegrated ito the house space Ulike i the case of Scheme 3, all garage walls are load-bearig ad the foudatio is istalled udereath them. Therefore, the legth of the foudatio is oe of the biggest (from selected schemes). Itercommuicatio with residetial premises is oe of the bests because i part two garage walls are iside the buildig. Zoig of the premises of the house ad the yard is see as average. This alterative coforms to 5% of the aalyzed the house projects Garage positio accordig to Scheme 5 I the case of Scheme 5, the garage is divided ito two spaces: closed ad ope (Fig. 5). Fig. 7. The garage is divided ito two spaces: closed ad ope Optios of istallatio of the foudatio ad itercommuicatio with residetial premises are the same as those i Scheme 1, cosiderig the fact that the idividual awigs foudatio istalled at the same time. I this versio, oe wall is shared with accommodatio, so commuicatio with them see quite favorably. Possibility for a variat of a buildig layout i the parcel icreases compared with the istallatio of a garage ext to the facade wall. This alterative coheres with 14% of the aalysed the house projects Garage positio accordig to Scheme 6 I the case of Scheme 6, the garage is a freestadig buildig. Volumes of the lad works ad foudatio price are amog the highest. Cotact with residetial premises is exteral without ay partitios, the worst of all. However, it is possible maximum variace i zoig the buildigs i relatio to the cardial directios. Typically, such solutio of the freestadig garage is take whe the parcel is a bit larger because the 3 m distace should be left util the parcel boudary. This solutio would be more suitable for parcels with exclusive terrai features while choosig a uique combiatio of two buildigs. This alterative goes together with 21% of the aalyzed the house projects. 3. Selectio of the garage locatio by WASPAS- SVNS method Iitially, for the WASPAS-SVNS method, criteria weights are eeded to be determied. The weights of the criteria were calculated by applyig AHP method (Table 1). Table 1. Pairwise compariso of criteria c1 c2 c3 c4 c c c c CI/RI 0.02 q1 q q 2 3 q Iitial decisio matrix for garage locatio problem together with criteria weight is preseted i Table 2. For the solutio of the formulated MCDM problem, the extesio of WASPAS approach, amely WASPAS- SVNS, is applied. Origially WASPAS-SVNS method was applied to solve the site selectio problem of the waste icieratio plat (Zavadskas et al. 2015b). This method is costructed o the basis of the sigle-valued eutrosophic set. The cosidered approach to the solutio Table 2. Criteria ad alteratives to weight ratio matrix Weight A 1 A 2 A 3 A 4 A 5 A 6 The legth of the foudatio, m 1 mi Iteral fuctioal commuicatio, scores, c2 max Cotextuality, scores, c3 max Aesthetics ad other, scores, c4 max

6 426 R. Baušys, B. Juodagalvieė. Garage locatio selectio for residetial house by WASPAS-SVNS method of the garage locatio selectio problem ca be outlied by the descriptio of the separate steps: 1. The iitial iformatio cosists of the evaluatios cocerig the ratigs of the alteratives with respect to the criteria ad the criterio weights. It ca be preseted by the followig data xij, i = 1, 2,..., m; j = 1,2,...,, which i fact is the aggregated expert evaluatio of the i th alterative by the j th criterio. Therefore, the decisio matrix will have the followig form: x 11 x12 x 1 x21 x22 x X 2 =. (1) xm1 xm2 x m 2. At this step, the decisio matrix X is ormalized by vector ormalizatio techique, which ca be expressed as: xij x ij =. (2) m 2 1 ( xij ) i= 3. At the eutrosophicatio step, the obtaied ormalized decisio matrix X ~ i the crisp form is coverted ito the sigle-valued eutrosophic umbers. Therefore, the eutrosophic decisio matrix X ~ is calculated. I order to perform this actio, the relatioships betwee ormalized values of the criteria of the alteratives ad sigle-valued eutrosophic umbers are applied. The relatioships betwee crisp ad eutrosophic values are show i Table 3. Table 3. Crisp to eutrosophic coversio expressios describig the criteria of the alteratives Crisp Normalized Values Sigle-Valued Neutrosophic Numbers Extremely good (EG)/1.0 (1.00, 0.00, 0.00) Very very good (VVG)/0.9 (0.90, 0.10, 0.10) Very good (VG )/0.8 (0.80, 0.15, 0.20) Good (G)/0.7 (0.70, 0.25, 0.30) Medium good (MG)/0.6 (0.60, 0.35, 0.40) Medium (M)/0.5 (0.50, 0.50, 0.50) Medium bad (MB)/0.4 (0.40, 0.65, 0.60) Bad (B)/0.3 (0.30, 0.75, 0.70) Very bad (VB)/0.2 (0.20, 0.85, 0.80) Very very bad (VVB)/0.1 (0.10, 0.90, 0.90) Extremely bad (EB)/0.0 (0.00, 1.00, 1.00) 4. I lie with the WASPAS-SVNS approach, the first decisio compoet is based o the sum of the total relative importace of the alterative i is calculated by the followig equatio: Lmi ( ) (1) L c max i = j 1 + ij + j + = j= 1 ij j Q x w x w, (3) where x + ij ad j criteria to be maximized ad w + values are associated with the ad w j values are x ij associated with the criteria to be miimized. The multiplicatio of the eutrosophic variable ad crisp real weight is calculated applyig the equatio as follows: λ λ λ ( 1 ( 1 t ), i, f ), 0 ~ λn = λ. (4) > Here is ecessary to metio, that sigle valued eutrosophic umber ca be expressed by N 1 = ( t1, i1, f1), t cor- ~ respods to membership degree, i to idetermiacy degree ad t to a o-membership degree. The summatio of two sigle-valued eutrosophic umbers is performed as follows: (,, ) N N = t + t tt ii f f. (5) The secod term of the summatio (Eq (3)) cosists of the complemetary eutrosophic umbers, which are determied by equatio: (,1, ) N f i t. (6) c 1 = The secod term of the optimal alterative i the WASPAS-SVNS methodology is determied by applyig the formulatio of the product total relative importace of the alterative i ad is calculated by the followig equatio: w j Q i x + x = j= j=. (7) ( 2) L w max j Lmi 1 ( + ij ) 1 ( ij ) The meaig of the terms of this equatio is the same as i Eq (4). The multiplicatio of the eutrosophic umbers is govered by the followig equatio: (,, ) N N = tt i + i ii f + f f f. (8) A fial geeralized criterio, which eables to rak the alteratives by the applied WASPAS-SVNS method is calculated as follows: ( 1) ( 2) Q = 0.5Q + 0.5Q. (9) i i i 7. I the fial step, the score fuctio ( i ) S Q is calculated for all rakig alteratives i = 1, 2,, m applyig expressio: 3 ta 2iA fa S( N + A ) = (10) 4 ad the fial rakigs of the alteratives ca be performed by applyig the descedig order of the ( i ) 2,, m. c S Q, i = 1,

7 Joural of Civil Egieerig ad Maagemet, 2017, 23(3): Table 4. The decisio matrix Criteria c 1 mi c 2 max c 3 max c 4 max X ~ after the eutrosophicatio step Alteratives I II III IV V VI (0.4471, , ) (0.3627, , ) (0.3716, , ) (0.3015, , ) (0.3096, , ) (0.2176, , ) (0.2230, , ) (0.6784, , ) (0.3612, , ) (0.6529, , ) (0.0743, , ) (0.0754, , ) (0.4815, , ) (0.5078, , ) (0.2973, , ) (0.3769, , ) (0.2752, , ) (0.3627, , ) (0.5203, , ) (0.5276, , ) (0.5159, , ) (0.0725, , ) (0.6690, , ) (0.1508, , ) Table 5. Numerical results of WASPAS-SVNS ~ (1) Q ~ (2) Q Alteratives I II III IV V VI (0.9581, , ) (0.1516, , ) Q ~ (0.6560, , ) (0.9724, , ) (0.1222, , ) (0.6890, , ) (0.9788, , ) (0.0934, , ) (0.7062, , ) (0.9618, , ) (0.1758, , ) (0.6720, , ) (0.9815, , ) (0.1967, , ) (0.7407, , ) (0.9364, , ) (0.0779, , ) (0.5866, , ) S ( Q ~ ) Rak Numerical example The solutio of the garage locatio problem i the parcel for the residetial house applyig MCDM framework is give below. The obtaied eutrosophic decisio matrix after secod ad third steps of the applied WASPAS- SVNS approach is preseted i Table 4. The umerical results of the WASPAS-SVNS approach, illustratig the employmet of the steps 4 7, are show i Table 5. The fial rakigs of the alteratives show i Table 5 are determied by the applicatio of the score fuctios, which are defied by Eq (11). Accordig to calculatios made by WASPAS-SVNS method ca be cocluded that the best garage locatio is o facade side of the house (Alterative No 5). This solutio ca also be i priciple applied to ay house shape (Fig. 1) ad a square case, eve to all four sides of the house. For this best positio of the garage, coectio with the dwellig rooms ca be orgaized i a iteral or exteral ways as well (or both). The determied alterative provides the best buildig zoig optios amog all those studied alteratives, accordig to the wishes ad eeds of the may opportuities i their ow way to istall a garage appearace (wall fiishes ad roofig). Coclusios The obtaied results ca be applied for the parcels, which do ot have exclusively specific terrai features, they must be approximately rectagular i shape from 6 to 10 acres plots adjoiig the street, from which etrace locatio of the parcel should be made. The garage locatio selectio problem has bee formulated icludig the followig aspects: the price of the foudatio, iteral commuicatio possibility, the orietatio of the buildig layout i the parcel ad aesthetics scores. The experts performed the evaluatio of the criteria for the selectio of the garage locatio. Processig this iformatio by AHP method, there was determied that the most importat criterio is a iteral commuicatio possibility. To the solutio of the aforemetioed MCDM problem, the extesio of the origial crisp WASPAS method by the eutrosophic sets has bee applied. Based o calculated results, the most appropriate locatio for the garage withi residetial parcel has bee chose. The best alterative is the case No 5. Comparig the two best alteratives is easy to observe that the presece of the best optios of the alterative No 5 was govered by cotextual-

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9 Joural of Civil Egieerig ad Maagemet, 2017, 23(3): Vasilevska, L.; Milaovic, D.; Nikolic, M.; Vraic, P.; Milojkovic, A Garage capitalism as a form ad process of post-socialist urba chages: Its pace, itesity ad structural characteristics. A case study of Nis, Serbia, Habitat Iteratioal 48: WHO Housig-health regulatio i Europe [olie], [cited 21 July 2016]. Available from Iteret: /e89278.pdf Zavadskas, E. K.; Atuchevicieė, J.; Seyed, H. R. H.; Shide, S. H Extesio of weighted aggregated sum product assessmet with iterval-valued ituitioistic fuzzy umbers (WASPAS-IVIF), Applied Soft Computig 24: Zavadskas, E. K.; Turskis, Z.; Atucheviciee, J. 2015a. Selectig a cotractor by usig a ovel method for multiple attribute aalysis: Weighted Aggregated Sum Product Assessmet with grey values (WASPAS-G), Studies i Iformatics ad Cotrol 24(2): Zavadskas, E. K.; Baušys, R.; Lazauskas, M. 2015b. Sustaiable assessmet of alterative sites for the costructio of a waste icieratio plat by applyig WASPAS method with sigle-valued eutrosophic set, Sustaiability 7(12): Zavadskas, E. K.; Turskis, Z.; Bagocius, V. 2015c. Multi-criteria selectio of a deep-water port i the Easter Baltic Sea, Applied Soft Computig 26: Romualdas BAUŠYS. Habil. Dr, Professor at the Departmet of Graphical Systems, Vilius Gedimias Techical Uiversity (VGTU), Faculty of Fudametal Scieces, Lithuaia. Research iterests: multimedia processig, multi-criteria decisio makig, iformatio techologies. Birutė JUODAGALVIENĖ. Lecturer at the Departmet of Graphical Systems, Vilius Gedimias Techical Uiversity (VGTU), Faculty of Fudametal Scieces, Lithuaia. Research iterests: egieerig graphics i buildig desig, buildig desig, iformatio techologies.