Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant

SustainableAssessmentofAlternativeSitesforthe

ConstructionofaWasteIncinerationPlantby ApplyingWASPASMethodwithSingle-Valued NeutrosophicSet

EdmundasKazimierasZavadskas 1,*,RomualdasBaušys 2,† andMariusLazauskas 1,†

Received:24September2015;Accepted:23November2015;Published:1December2015

AcademicEditors:FaustoCavallaroandMarcA.Rosen

1 ResearchInstituteofSmartBuildingTechnologies,VilniusGediminasTechnicalUniversitySauletekioave.11, VilniusLT-10223,Lithuania;marius.lazauskas@gmail.com

2 DepartmentofGraphicalSystems,VilniusGediminasTechnicalUniversitySauletekioave.11, VilniusLT-10223,Lithuania;romualdas.bausys@vgtu.lt

* Correspondence:edmundas.zavadskas@vgtu.lt;Tel.:+3-705-274-4910

†Theseauthorscontributedequallytothiswork.

Abstract: Theprinciplesofsustainabilityhavebecomeparticularlyimportantintheconstruction, realestatemaintenancesector,andallareasoflifeinrecentyears.Theoneofthemajorproblemof urbanterritoriesthatdomesticandconstructionwasteofgeneratedproductscannotberemoved automatically.Theabovenecessityinducesthedemandofsystemsandtechnologiesforwaste lifecycleandproperdisposaldevelopment.Sitingofthewasteincinerationplantisacomplex process,whichincludesallfactorsofsustainabilityprinciples.Theselectionoftheconstruction areaisacomplexproblemduetotheexistenceofdifferenttangibleandintangiblefactorsand themultiplealternativesavailable.Multicriteriadecision-makingmethods(MCDM)present powerfulandflexibletechniquesforthesolutionofmanysustainabilityproblems.Inthispaper, weproposeanewextensionofWASPASmethod,namelyWASPAS-SVNS.Thisextensionisrealized intheframeworkofthesingle-valuedneutrosophicsetthatenablestorepresentandmodelthe indeterminacyexplicitlyandthefunctionsofthetruth-membership,theindeterminacy-membership andthefalsity-membershiparenotrelatedtoeachother.Thepaperdealswiththesolutionofthe wasteincinerationplantsitingproblemduetotherequirementsofsustainabilityfactors.

Keywords: sustainabilityassessment;wasteincineration;MCDM;WASPAS-SVNS;neutrosophicset

1.Introduction

Recently,EuropeanCommissionannouncedanewstrategyconcerningcirculareconomic systems,whichwouldenableimprovedresourceproductivitybyusingtheproductsrepeatedly withoutturningthemintowaste[1].Thiscirculareconomicstrategywillrequirethetransitionto newbusinessandthesocialmanagementmodels.

Duringthelastdecadetheapplicationofthesustainabilityprincipleshasbecomeanessential requirementofthemodernurbaninfrastructureprojects[2–6].Turningthewasteintoresourcesis oneoftheelementswithintheframeworkofthecirculareconomicsystem.Thus,particularattention mustbedirectedtoinnovationinrecycling,therepetitiveuseoftheproducts,andotheraspects ofthewastemanagement.Theholisticapproachtosolvetheseproblemsiscalledintegratedsolid wastemanagement(ISWM).Thisstrategyincorporatesallaspectsofwastemanagement,suchas prevention,recycling,composting,anddisposal.Wecandistinguishthefollowingoptionsin wastemanagement:sourcereduction,recycling,composting,wastetoenergy,andlandfillingwaste.

Sustainability 2015, 7,15923–15936;doi:10.3390/su71215792www.mdpi.com/journal/sustainability

ApplyingISWM,themosteffectivewastemanagementactionscanbechosentakingintoaccountlocal urban,socialandenvironmentalconditions[7,8].InLithuaniancitiesmunicipalwastemanagement isanissueofprimaryconcernduetotheenvironmentalhazardsofgreatsignificance.Allofthese processesmustbebalancedfromasustainablepointofview.Solidwastemanagementisofthe utmostimportance,especiallyinthecities,wherethiskeyserviceofcitymanagementcanprovide theframework,bywhichpublichealthanddevelopmentofacitycanbeachieved.

Nowadays,wastemanagementhasreachedahightechnologicallevelandnumerouselements, suchassophisticatedcollectionsystems,togetherwithefficientseparationprocedures,allowthe achievementofahighdegreeofrecoveryandrecycling.Thesemeasuresenablealargeamountof municipalsolidwastetobetreated,applyingwastetoenergytechnologies[9].Margallo etal.[10] studiedtheeffectsoftheenvironmentalsustainabilityassessmentmethodologyonthecomplexityof lifecycleassessmentandthepossibilitiestoapplyitinthedecision-makingprocess.

Thenumerousstudiesconcerningefficientintegratedsolidwastemanagementhavebeen performedinthecasesthehigh-incomecountriesandonlyafewanalyseshavebeendirectedtoware thecasesofdevelopingcountries.Theproposedframeworksofsustainablewastemanagement envelopedthedifferentcriteriadescribingwastepreventionactivities,zerowastemanagement systems,and3R(reduce,reuse,recycle)policiesthatenabledmakingtheconversionfrom wastemanagementtoresourcemanagement,seekinganacknowledgmentwithEuropeanUnion requirements[11].Currently,thestrategyofintegratedsustainablewastemanagementoutlinesthe paradigmfortheassessmentofthesustainabilityofwastemanagementalliances.Theessenceof thisstrategyconsistsofthenecessitytoexaminenotonlytechnicalorfinancial-economicaspects, butalsoenvironmental,institutional,andotherissuesthathaveanimpactonsustainabilityofwaste management[12].

Thewasteincinerationplantsitingprocessinvolvesdifferentenvironmental,social,and politicalcriteria,whicharederivedapplyinglocalrequirements.Theframeworkforthechoice ofanappropriate,wholesomestrategyforcontaminatedsitescanbeconsideredamulti-criteria decision-makingproblemwhichincludestechnical,environmental,safety,stakeholderpreferences, andtheothercriteria[13].Allstakeholdersneedtobededicated,engaged,andcollaborateto identifypossiblecompromisesofwastegenerationandconsequentlyintervenetominimizethewaste amounts[14].Thedifferentaspectsofthewastemanagementproblemshadbeenconsideredapplying thegeneralframeworkofmulti-criteriadecision-making[15–17].

Multi-criteriadecision-making,ingeneral,establishesalternativesamongdifferentoptions bymakingreferencetoasetofobjectivesthatthedecision-makingtopichasalreadyidentified. MCDMputsanaccentontheassessmentofthedecision-makingtopic,oncontributingcriteria, ondeterminingrelativeweightsand,toanextent,oncalculatingtheperformanceofeachoption againsteachsatisfactioncriterion.Decision-makinginthisparticularproblemofthesustainability assessmentofwasteincinerationplantconstructionsiteselectionconsistsofevaluatingalternatives withrespecttomultipleconflictingcriteriaandselectingthe“best”alternativeconsideringthe resultsobtainedbyevaluationapproach.Therehavebeenproposedahugevarietyofmulti-criteria decision-makingmethodstosolvesuchtypesofproblems[18–22].MCDMmethodsareoftheutmost significancesincetheycanevaluatedifferentalternativesnotonlytakingintoaccountthedataof variouscriteria,butalsotheformatofthepresentation,suchascrisp,fuzzy,andothers.

Differentsustainabilityproblemshavebeensolvedapplyingtheframeworkofthemulti-criteria decision-making.Theassessmentoftheaffordabilityofdifferentlocations,applyingcriteriareflecting variousaspectsofthesustainabilitywasperformedbytheCOPRASmethodofmulti-criteria decision-makingin[23].Theproblemofthegreensupplierofthethermalpowerequipmentfor powerplantsinChinawasconsideredandsolvedbytheTOPSISapproachunderatriangularfuzzy numberenvironment[24].Asustainabilityassessmentoftheenergysystemsbytheapplicationof MCDMstrategy,namelytheSWARAapproach,waspresentedin[25].Modernfuzzyapproaches havebeenimplementedtosolveinvestmentstrategiesintheprivatesectorofIran[26]andtoperform

environmentalimpactassessment(EIA)processesforevaluationofthepossibleimpactofmine developmentandoperationsontheenvironment,includingthenatural,social,andeconomicaspects waspresentedin[27].

Therearealotofproblemsanditisverydifficultintherealworldtoextractprecisedatareferring totheestimationfactorssinceallhumanselectionsareinclinedtoadegreeofuncertainty.Duringthe lastdecadethevariousformulationsofthefuzzysetshavebeendevelopedanddifferentMCDM problemshavebeensolved[28–31].However,theyusuallycannottakeintoaccountallpatternsof uncertaintiesthatareusuallymetinthemodelsoftherealworldproblems.

InrecentyearsdifferentapproachesareproposedtoextendthecrispMCDMmethodsintoa fuzzyenvironmentinordertodealwithuncertaininformation[20,27–30].

Recently,newneutrosophicsetshavebeenproposedbySmarandache[32]andthese neutrosophicsetsallowdealingwith“knowledgeofneutralthought”andthis“neutral”component distinguishesthissetfromtheotherapproachesthatmodeluncertainphenomenaofinformation. Infact,theneutrosophicsetsareageneralizationofthe“fuzzy”and“intuitionisticfuzzy”sets. Nowadaystheresearchproposessomeapplicationsoftheneutrosophicsetsforthesolution multi-criteriadecision-makingproblems.Recently,Peng etal. [33]havestudiedthecomputational aspects,applyingsingle-valuedneutrosophicsetsinmulti-criteriadecision-makingapproaches. ZhangandWu[34]developedanovelmethodforthesolutionofthesingle-valuedneutrosophic multi-criteriadecision-makingproblemsundertheassumptionoftheincompleteweightinformation. Thispaperfocusesonwasteincinerationplantconstructionsiteplanningtakingintoaccountthe ecological,technological,andurbanaspects.Thearticleaimstoshowhowthemulti-criteriadecision methods(MCDM)canbeappliedtosolvepracticalproblemofthesitingofthewasteincineration plant,includingnotonlytechnical,butalsosustainabilityrequirements.Theapplicabilityand usefulnessofajointmethodasacombinationoftwocriteriaofoptimality,namelyWSM (WeightedSumModel)andWPM(WeightedProductModel),namelyaWeightedAggregatedSum ProductAssessment(WASPAS)[28],isexploredsolvingsitingwasteincinerationplantconstruction sites.ForthesolutionweproposedanewextensionoftheoriginalWASPASmethod,namely WASPAS-SVNS,whichisgovernedbyasingle-valuedneutrosophicset.

2.WasteManagementStrategies

Continuouspopulationgrowthaffectstheincreaseintheconsumptionofgoodsandservices. However,theincreaseintheconsumptionhaspositive,aswellasnegative,outcomes.Theincrease indemandnecessitatesmoreenergy,firstly,fortheproductionofcertainrawmaterialsrequiredfor themanufactureofgoodsand,then,fortheproduction,packaging,andlogisticsofmanufactured goods.Indirectinvestmentsaremadeintothemarketingofproducts,whichalsorequirescertain materialresources.Thereisapersistingglobalissueregardingthere-useorutilizationofnolonger requiredmaterials, i.e.,waste.Notonlydoesthisissueconcernregionsthathousethelargest economiesbutalsosmallstates,suchasLithuania.ThesituationontheLithuanianmarketof constructionandmunicipalwasteseemsgrave.Regionalmunicipalwastelandfillsareoverflowing duetothelackofinfrastructureforwastesortingandfullre-useofalltypesofnon-hazardouswaste. Attheendof2014,theoverflowingregionallandfillofVilniusCountyresultedinproblemswiththe collectionofconstructionwaste.Theseproblemswereunearthedbecauseofthelackofasystem forsorting,re-use,andfinalutilizationofwaste.Asimilarsituationprevailsontheglobalscale, whichnecessitatesagreaterfocusontheimprovementofwastemanagement,re-use,andutilization systems,strategicplanning,andthedevelopmentofthemodelforasustainablesystem.

Municipalwastemanagementsystemsmustbeorganizedtoensurethatcities,townships, andvillageshave(a)meansforthecollectionandremovalofwaste;(b)meansforwastesorting attheplaceofitsorigin;(c)meansforseparatecollectionofdifferentmunicipalwasteflows,such asconstructionanddemolitionwastesfromhouseholds,bulkywaste(furniture, etc.),discarded

electricalandelectronicequipment,end-of-lifetires, etc.;and(d)meansforseparatecollectionof hazardouswastesfromhouseholds(exceptforbatteriesandaccumulators).

Accordingtotheanalysisofpossiblewastemanagementstrategies,allnewwastemanagement facilitiesmustbeconstructedasaninseparablepartofthealready-functioningregionalwaste managementsystemandtheimprovementofthissystemmustconsiderprinciplesofsustainable development.Selectionofsitesforwastemanagementandincinerationfacilitiesdependsona numberofimportantfactors,includingthemostadvancedengineeringinfrastructurerequiredfor suchfacilitiesandavailableintheterritoryofcities,aswellascloseproximitytotheconsumerof energy,whichisplannedtobegenerated(heatandelectricity).

In2000,130thousandtonsofbiodegradablewaste(approx.50%ofthetotalquantityofall municipalandsimilarwastes)wasdisposedofinVilniusCountylandfills.Consideringthetargets setoutintheCouncilDirective99/31/EConthelandfillofwaste,nomorethan97.5tonsof biodegradablewastehadtobedisposedofintheregionallandfillofVilniusCountysince2010, nomorethan65thousandtons—since2013,andnomorethan45thousandtons—since2020.Thereal wastedisposalsituationwaspresentedin[35].

ConsideringthesituationofthecityofVilniusandbasedonthereportoftheonthereport ontheEconomicAnalysisofOptionsforManagingBiodegradableMunicipalWaste[36],thereare fourpossiblescenariosforfurtherwastemanagement(Table 1).

Thefirstalternativeanticipatesthemaximumseparatecollectionofsecondaryrawmaterials (andpackagingwaste),gardenwastes,andbiodegradablewastes(includingtheproductionofbiogas anditspreparation),aseparatetreatmentofsuchwastes(ensuringapossiblyhigherqualityofthe resultantproduct),andthefinancialassistancefortheintroductionandoperationofhomecomposting sites(VilniusCountyhasapprox.73,000privatehomes).Tomaximizetherecoveredamountsof secondaryrawmaterialsandpackagingwastefitforrecyclingfromthemunicipalwasteflows,this alternativeenvisagesawastesortingplant,whichwouldalsoensurethequalitativecomposition ofincineratedwastes.Onlysortedwastes,whichareunsuitableforrecycling,areincinerated.The producedelectricandheatenergyissoldtocompensatesomeofthewastemanagementcosts.

Thesecondandthirdalternativesgeneratesignificantwasteflowstothelandfill.Theanticipated taxfortheenvironmentalpollutionbywastewouldincreasethegeneralwastemanagementcostsby approx.25%.Post2020,thesealternativeswillrequiresystematicchangesandadditionalinvestments.

Table1. OptionsforthewastemanagementstrategyofthecityofVilnius.

TechnologicalProcesses

I IIIIIIV

Strategies

Secondarycollectionofsecondaryrawmaterials + +++

Secondarycollectionandcompostingofgardenwastes + +++ Homecomposting + +-+

Mechanicalbiologicaltreatment - -++

Collectionandseparatetreatmentofa biodegradablefraction + +-+

Separationofabiodegradablefractionand productionofbiogas - -+-

Mechanicalwastesortingplant(productionof secondaryrawmaterials) + +++

Preparationofwasteforincinerationandincineration + --+ Disposalofwastebylandfill + +++

Thefourthalternativedoesnotprovideaseparatecollectionofbiodegradablewaste.However, itemphasisesthecentralizedtreatmentofcollectedmixedmunicipalwaste,theuseoftechnological meanstoseparatesecondaryrawmaterials,andpackagingwaste,whicharesuitableforrecycling, andshreddingtheremainingwaste,whichisthensenttoabiologicaldryingfacility,wherewastesare aeratedanddried.Thisresultsinsmalleramounts(20%less)ofwaste,whichhasagreaterthermal value(20%more).Thewastebecomesstabilizedandcanbewarehousedforalongerperiodpriorto

Sustainability 2015, 7,15923–15936

incineration(thelevelofmoistureofsuchwasteis10%–20%dependingonthedurationoftreatment). Thisalternativeprovidesincinerationoffuelproducedfromwasteinawasteincinerationfacility[37]. Assessmentofthesealternativesfromthepointofviewofsustainabledevelopmentresultsin thechoiceofthestrategythatbringsthemostvaluetothewastemanagementsystem,ensuringthe liquidityofwasteandtheproductionofelectricandheatenergy, i.e.,choosingthewasteturnover systemwithanincinerationoption.Itisthisstrategy,whichservesasthebasisforthesolutionofthe problemthatseekstoidentifythemostappropriatesitefortheprojectimplementationinthecityof Vilnius,consideringopinionsofmoststakeholdergroups.

3.PossibleAlternatives

Incinerationplantsareassessedbasedonawiderangeofcriteriajustifiedbyrequirementssetfor theenvironmentalprotectionandecologyaswellasbysocialattitudes,economicbenefit,theneedfor financingandplannedreturn,architecturalculturalnormsofthecity,andtechnologicalcapabilities forprojectimplementation[30].Solvingtheproblemconcerningtheselectionoftheconstruction siteforawasteincinerationplant,theauthorschosesevenpotentialalternativesfortheproject implementation.Toidentifyasuitablesiteforawasteincinerationplant,itisimportanttoconsider therequirementsofallstakeholdergroupsandfindanalternativesolution.Therefore,thisproblem isaddressedbyassessingengineering,social,economicandenvironmentalfactors(Table 2).

Engineeringfactors(x1–x3)coverapartofinvestmentsrequiredfortheprojectdevelopment. Residential,office,industrial,andpublicsectorbuildingscannotfunctionwithoutengineering communications.Theanalysisofindustrialstructuresingeneral,andheatandelectricpower productionfacilities,inparticular,revealedspecificrequirements,suchastheneedtobeconnected toelectricpowertransmissiongridorothersystemstosupplyproducedheatorpowertoend-users. Suchsupplyalsorequirespipelinesandelectriclines.Additionally,localsurfacerunoffcannotbe directedtothecitysewageasrainwaterwouldmixwithwastewater,andthemixturewouldputa strainonwastewatertreatmentfacilitiesofthecity.

Thedistancefromawastesortingbasetoawasteincinerationplant(x2)determines solutionstologisticsproblems.Clearly,awastesortingbasemustbelocatedfurtherawayfrom densely-populatedterritoriesasthewastesortingtechnologyalsoincludeswastewarehousing, whichofteninvolvesopen-airstorage.Suchfacilitiesareopentoenvironmentalprocessesand usuallyemitodorstosurroundingterritories.Certainly,open-airwarehousingofwastealsoresults inthevisualpollutionofresidentialareas.

Table2. Factorsofalternativeassessment.

EngineeringFactors:

Distancetoahigh-pressure(12bar)gaspipe,inkm;

Distanceto110kWpowertransmissiongrid,inkm;

Distancetothewatersupplynetwork,inkm;

Distancetoindustrialanddomesticwastewaternetworks,inkm;

Distancetothesurfacewaterdrain,inkm;

Distancetoacomplexofwastesortingbases,inkm.

Numberofinstallationsconstructedonthesite,inunits; EnvironmentalFactors:

DistancetothecenterofthecityofVilnius,inkm;

Impactonair,inpoints;

Levelofnoise,inpoints;

Impactonentrailsoftheearth(soil)andgroundwaterincaseofanaccident,inpoints.

SocialFactors:

Levelofsatisfactionamongresidentsinrelationtothesiteselection,inpoints;

Meanpopulationper1km2 intheterritoryoftheanalyzedalternative,inunits; EconomicFactors:

Usefulfloorareaofresidentialdwellingssituatedinthelocalityoftheplannedproject,inm2 *Valuesofpoints:0—theworst,10—thebest.

Thenumberofinstallationsconstructedonthesite(x3)describesapossibilitytoinstallthe plannedwastemanagement/incinerationinstallations—awasteincinerationplant,and/orwaste sortingplant,and/orbiodegradablewastetreatmentplant,whichrequire2.5ha,2.0ha,and1.0hain area,respectively—ataspecificalternativesite.

Environmentalfactors(x4–x7)characterizethepositionoftheincinerationplantintermsof urbandevelopmentandenvironmentaleffects.Thedistancetothecenterofthecity(x4)assesses thelocationoftheincinerationplantanditspossibleimpactonurbanarchitecture,asacity centerandsurroundingquartersusuallyhaveaculturally-distinctstyleofarchitecture.Thus,such plannedfacilitiesshouldbekeptawayfromculturally-importantsitesandlocatedfurtherawayfrom residentialareas.Suchconclusionsaredeterminedbythepowerproductiontechnology,whichmay inconvenienceresidentsofadjacentareasbynoise,odorsoraestheticsoftheview.

Theeffectonair(x5),soil(x6),andthelevelofnoise(x7)determinetheimpactofthe wasteincinerationplantonthesurroundingenvironment.Theeffectonairandsoilresults fromwarehousingofwasteandbyproductsthatemergeeithernaturallyorduringtheprocessof incineration;meanwhile,thelevelofnoiseisduetotheintensifiedflowoftransporttotheplant. TheintensifiedflowoftransportresultsfromdeliveryofwastefromtheentireVilniusCounty.

Socialfactorsofthelevelofsatisfactionamongresidents(x8)andthemeanpopulationper1km2 intheterritoryoftheanalyzedalternative(x9)fortheconstructionofthewasteincineration plantconsiderthenumberofresidentslivingnexttothepowerproductionplant.Appropriate implementationoftechnologicalsolutionsduringtheconstructionofthewasteincinerationplant willpreventharmfuleffectsandunpleasantodorsduringtheexploitationoftheplant.However, thenegativestanceofthepubliccanbringtheprojectimplementationplanstoastandstill. Assessmentoftheprojectfromthepointofviewofpublicneedsshowsthatthesiteoftheproject implementationshouldbechosenintheleastdenselypopulatedterritories.Assessmentoftheproject onthelevelofthestateoraprivateinvestordemonstratesthatitisrationaltoconstructthepower productionplantindenselypopulatedareastoensurethedemand.

Theeconomicfactorregardingtheusefulfloorareaofresidentialdwellingssituatedinthe localityoftheplannedproject(x10)determinesthefloorareaofbuildingstobesuppliedwithenergy fromthefuturepowerproductionplant.Thisfactorisusefulfromthesocialpointofviewaswell asintermsoftheplantdesign:theknowledgeoftheusefulfloorareaofbuildingsfacilitatesthe planningoftheplantcapacityrequiredtosupplythepowertoallaccessibleconsumers.

Table3. Theindicatorsofwasteincinerationplantsitealternatives.

Criteria Optimum

Alternatives

A1 A2 A3 A4 A5 A6 A7

1.503.500.804.805.500.600.30 0.601.200.501.201.000.700.40 2.504.503.001.601.602.002.00 1.370.500.102.000.300.600.60 1.250.500.100.500.500.600.50 1.311.002.901.500.500.500.50 řx1 8.5311.207.4011.609.405.004.30 x2 min 1.514.513.56.213.11514.5 x3 max 3311321 x4 max 9.268.646.4411.195.96.095.72 x5 max 4558522 x6 max 6658532 x7 max 8664644 x8 max 109610821 x9 min 3188.6497.524842676.5329164905946.7 x10 max 55,269932750,79856,20666,80713,2136123,314

x1 min

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Consideringtheassessedfactors,alternativesitesforthewasteincinerationplantareprovided withcalculatedandassesseddesignvalues(Table 3).

Selectingthesiteforthewasteincinerationplant,whichwouldbebasedonprinciplesof sustainabledevelopment,itisimportanttocarefully,minutely,responsibly,andpurposefullychoose alternatives,aswellasevaluatetheselectedqualitativeandquantitativeindicators.Oncethe designvaluesaredeterminedfortheexistingfactors,alternativesareevaluatedusingthenew WASPAS-SVNSmethod.

4.SustainableAssessmentofWasteIncinerationPlantConstructionSiteAlternativesbyMCDM

4.1.AnExtensionoftheWASPASMethodwithSingle-ValuedNeutrosophicSet(WASPAS-SVNS)

Originally,aweightedaggregatedsumproductassessment(WASPAS)approachforthe solutionofthemulticriteriadecision-makingproblemshasbeenproposedbyZavadskas etal. [28]. Theproposedextensionofthismethod,namelyWASPAS-SVNS,isdevelopedapplyingthe frameworkofthesingle-valuedneutrosophicset.Thealgebraofthesingle-valuedneutrosophicset ispresentedinthesectionofthesupplementarymaterials.Theproposedapproachforthesolution oftheformulatedmulticiteriadecision-makingproblemcanbeoutlinedasfollows.

Step1. Inthisstep,theevaluationsconcerningtheratingsofthealternativeswith respecttotheattributesandtheattributeweightsarepresented.Itcanbeexpressedby xij, i “ 1,2,..., m; j “ 1,2,..., n,whichistheaggregatedexpertsevaluationofthe ith alternativeby the jth criterion.Thus,theaggregateddecisionmatrixcanbeconstructed:

Step2. Normalizationofthedecision X isperformedapplyingvectornormalizationapproach applyingdivisionbythenormasfollows: xij “ xij břm i“1 `xij˘2 (2)

Infact,thisnormalizationtechniquediffersfromthenormalizationapproachappliedinthecrisp WASPASmethod.Thischangeisnecessaryinordertotakeintoaccountthespecificcomputational aspectsoftheneutrosophicalgebra.

Step3. Neutrosophicationofthenormalizatedaggregateddecisionmatrix r X andtheaggregated weightvector w isperformed.Intheneutrosophicationstepweperformconversionofallcrispinitial informationintothesinglevaluedneutrosophicset.Inthisstep,theneutrosophicaggregateddecision matrix r Xn isdetermined.Forthispurposeweapplyrelationshipsbetweennormalizedtermsofthe alternativesandsingle-valuedneutrosophicnumbers.Thisevaluationisexpressedinlinguisticterms presentedintheTable 4.

Table4. Neutrosophicconversiontermstorateimportanceofthealternatives.

CrispNormalizedTermsSingle-ValuedNeutrosophicNumbers

Extremelygood(EG)/1.0(1.00,0.00,0.00) Veryverygood(VVG)/0.9(0.90,0.10,0.10) Verygood(VG)/0.8(0.80,0.15,0.20) Good(G)/0.7(0.70,0.25,0.30)

Mediumgood(MG)/0.6(0.60,0.35,0.40) Medium(M)/0.5(0.50,0.50,0.50) Mediumbad(MB)/0.4(0.40,0.65,0.60) Bad(B)/0.3(0.30,0.75,0.70) Verybad(VB)/0.2(0.20,0.85,0.80) Veryverybad(VVB)/0.1(0.10,0.90,0.90) Extremelybad(EB)/0.0(0.00,1.00,1.00)

Step4. FollowingtheWASPAS-SVNSapproach,thesumofthetotalrelativeimportanceofthe alternative i iscalculatedbythefollowingequation:

r Qp1q i “ ÿLmax j“1 r xn `ij wn `j ` ´ÿLmin j“1 r xn ij wn j¯c (3) where r xn `ij and wn `j valuescorrespondtothecriteriatobemaximizedand r xn ij and wn j values correspondtothecriteriatobeminimized.Thesecondtermofthesummationconsistsofthe complementaryneutrosophicnumbers,whicharedeterminedbyEquation(S6).

Step.5. ThesecondcriteriaoftheWASPAS-SVNSmethodologyisdeterminedbyapplying theframeworkoftheproducttotalrelativeimportanceofthealternative i andiscalculatedbythe followingequation:

r Qp2q i “ źLmax j“1 ´r xn `ij¯wn `j ¨ ˆźLmin j“1 ´r xn ij¯wn j ˙c (4)

Thedescriptionofthetermsofthisequationcorrespondstothedefinitionpresentedatthe previousstep. Step6. AjointgeneralizedcriteriafortherankingalternativesbytheproposedWASPAS-SVNS approachisdeterminedasfollows: r Qi “ 0.5 r Qp1q i ` 0.5 r Qp2q i (5)

Step7. Inthelaststep,thescorefunction S ´ r Qi¯ isdeterminedfor i = 1,2, ,m applying Equation(S7)andthefinalrankingsofthealternativesarecalculatedconsideringthedescending orderofthe r Qi, i = 1,2, ... ,m.

4.2.NumericalExample

ThenumericalillustrationoftheproposedMCDMapproach,namelyWASPAS-SVNS, forthesolutionoftheconsideredproblemisgivenbelow.Theaggregateddecisionmatrixafter normalizationandneutrosophicationstepsispresentedintheTable 5

Thenumericalresults,representingtheapplicationofthesteps4–7,areshowninTable 6 TherankingsofthealternativesrepresentedinTable 6 arecalculatedbyapplyingthescorefunctions ofWASPAS-SVNS(Equation(S7)).Itcanbeconcludedthatthemostpreferredalternativeis A1. Ifanalysisoftheaggregateddecisionmatrixisperformed,itisnotdifficulttoobservethatalternative A1 possessesthebestresultsforC2,C3,C7,C8, andreasonablygoodresultsforC4,C6.Comparing A1 and A3 (theyarethefirstandthesecondonesintherankingqueue)westatethatthealternative A1 isbetterforthecriteriaC2,C3,C4,C6,C7,C8,andC10.

Forthesakeofthecomparisontheconsideredproblemhasbeensolvedapplyingdifferent MCDMapproaches:crispWASPASandCOPRASmethodsandthefuzzyARAS-Fapproach[30].The resultsoftheapplicationoftheoriginalWASPASmethodunderthecrispinformationrepresentation environmentarepresentedinTable 7.

Table5. Theaggregateddecisionmatrix Xn aftertheneutrosophicationstep.

Criteria

Alternatives IIIIIIIVVVIVII

C1 min (0.3743, 0.6757, 0.6257)

C2 min (0.0465, 0.9535, 0.9535)

C3 max (0.5145, 0.4783, 0.4855)

C4 max (0.4457, 0.5815, 0.5543)

C5 max (0.3133, 0.7367, 0.6867)

C6 max (0.4253, 0.6120, 0.5747)

C7 max (0.5394, 0.4410, 0.4606)

C8 max (0.5090, 0.4865, 0.4910)

C9 min (0.3012, 0.7488, 0.6988)

C10 max (0.2577, 0.7923, 0.7423)

(0.4914, 0.5128, 0.5086)

(0.4496, 0.5756, 0.5504)

(0.5145, 0.4783, 0.4855)

(0.4158, 0.6262, 0.5842)

(0.3916, 0.6584, 0.6084)

(0.4253, 0.6120, 0.5747)

(0.4045, 0.6432, 0.5955)

(0.4581, 0.5629, 0.5419)

(0.0470, 0.9530, 0.9530)

(0.0435, 0.9565, 0.9565)

(0.3247, 0.7253, 0.6753)

(0.4186, 0.6221, 0.5814)

(0.1715, 0.8643, 0.8285)

(0.3100, 0.7400, 0.6900)

(0.3916, 0.6584, 0.6084)

(0.3544, 0.6956, 0.6456)

(0.4045, 0.6432, 0.5955)

(0.3054, 0.7446, 0.6946)

(0.2347, 0.8153, 0.7653)

(0.2368, 0.8132, 0.7632)

(0.5090, 0.4865, 0.4910)

(0.1922, 0.8539, 0.8078)

(0.1715, 0.8643, 0.8285)

(0.5386, 0.4422, 0.4614)

(0.6266, 0.3234, 0.3734)

(0.5671, 0.3993, 0.4329)

(0.2697, 0.7803, 0.7303)

(0.5090, 0.4865, 0.4910)

(0.2528, 0.7972, 0.7472)

(0.2620, 0.7880, 0.7380)

(0.4125, 0.6313, 0.5875)

(0.4062, 0.6407, 0.5938)

(0.5145, 0.4783, 0.4855)

(0.2840, 0.7660, 0.7160)

(0.3916, 0.6584, 0.6084)

(0.3544, 0.6956, 0.6456)

(0.4045, 0.6432, 0.5955)

(0.4072, 0.6392, 0.5928)

(0.3109, 0.7391, 0.6891)

(0.3115, 0.7385, 0.6885)

Table6. NumericalresultsofWASPAS-SVNS.

Alternatives

(0.2194, 0.8306, 0.7806)

(0.4651, 0.5523, 0.5349)

(0.3430, 0.7070, 0.6570)

(0.2931, 0.7569, 0.7069)

(0.1567, 0.8717, 0.8433)

(0.2127, 0.8373, 0.7873)

(0.2697, 0.7803, 0.7303)

(0.1018, 0.8991, 0.8982)

(0.6131, 0.3369, 0.3869)

(0.6160, 0.3340, 0.3840)

(0.1887, 0.8557, 0.8113)

(0.4496, 0.5756, 0..5504)

(0.1715, 0.8643, 0.8285)

(0.2753, 0.7747, 0.7247)

(0.1567, 0.8717, 0.8433)

(0.1418, 0.8791, 0.8582)

(0.2697, 0.7803, 0.7303)

(0.0509, 0.9491, 0.9491)

(0.5618, 0.4074, 0.4382)

(0.5749, 0.3877, 0.4251)

IIIIIIIVVVIVII

r Qp1q (0.9603, 0.0375, 0.449)

r Qp2q (0.1108, 0.8959, 0.8892)

r Q (0.6500, 0.3459, 0.3441)

(0.9423, 0.0603, 0.0619)

(0.0923, 0.9157, 0.9077)

(0.6029, 0.4049, 0.4025)

(0.9508, 0.0491, 0.0594)

(0.0865, 0.9260, 0.9135)

(0.6198, 0.3837, 0.3800)

(0.9416, 0.0549, 0,0581)

(0.1081, 0.8964, 0.8919)

(0.6062, 0.3879, 0.3865)

(0.9431, 0.0570, 0.0666)

(0.1006, 0.9114, 0.8994)

(0.6071, 0.3967, 0.3931)

(0.9186, 0.0910, 0.0894)

(0.0591, 0.9486, 0.9409)

(0.5485, 0.4695, 0.4669)

(0.9239, 0.0821, 0.0836)

(0.0482, 0.9577, 0.9518)

(0.5539, 0.4582, 0.4563)

S ´ r Q¯ 0.65350.59760.61810.61100.60520.53560.5453 Rank1523476

Sustainability 2015, 7,15923–15936

Table7. NumericalresultsoftheoriginalcrispWASPASmethod.

Alternatives

IIIIIIIVVVIVII

r Qp1q 0.75500.70230.58160.70250.64160.46250.4238

r Qp2q 0.65780.57800.50770.59800.55780.34110.2874

r Q 0.70640.64020.54460.65020.59970.40280.3556 Rank1352467

ThefinalrankingsofthealternativesobtainedbydifferentMCDMapproachesarepresentedin Table 8.Itisnotdifficulttoobservethatdifferentcrispmethods,suchasWASPASandCOPRAS providedexactlythesameresults.Ontheotherhand,thefuzzyapproachARAS-Fandtheproposed methodWASPAS-SVNStookintoaccountthedifferentcomponentsoftheuncertaintyoftheinitial informationsothefinalrankingofthealternativesslightlydiffersfromtheresultsobtainedbycrisp methods.However,thebestalternativeisthesameapplyingdifferentMCDMapproachesandthis factsupportstheconclusionthatthefirstalternativeisthebestcandidateforthewasteincineration plantconstructionsite.

Table8. ComparisonoftheresultsobtainedbysolutionwithdifferentMCDMapproaches.

Method

Alternatives IIIIIIIVVVIVII

OriginalcrispWASPAS1352467 ProposedWASPAS-SVNS1523476 ARAS-F1253467 COPRAS1352467

Ontheotherhand,itisnecessarytopointoutthatmigrationofthealternativesobtainedby differentMCDMmethodsdonotexceedthegroupingofthealternativesinthreelocalizedzones: twozonesaresituatedinterritoriesallocatedfortheindustrialdevelopmentofthecity(A4, A1 and A2, A3, A5)andonezoneindenselypopulatedpartsofthecity(A6, A7).

5.Conclusions

Determiningthesiteforawasteincinerationplantisacomplicatedprocessthathasmany social,economic,political,andtechnologicalfactors.Implementationofsuchprojectsinvolvesmany differentstakeholdergroupswhoseneedsmustbeconsideredtoachievesuccess.Inthesearchforthe bestsolutionsitis,therefore,rationaltodrawonmethodsdevelopedbyscientiststhatcanencompass andassesslargequantitiesofinformation.

Sevenalternativeswereanalyzedtoselectthesiteofthewasteincinerationplantinthecityof Vilnius.Alternativesaredistributedinzonesintendedfortheindustrialdevelopmentofthecityand denselypopulatedareas.Accordingtotheassessmentofthelocationofalternativesintheterritory ofthecity,theanalyzedrationalsitesforthewasteincinerationplantcomprisethreelocalizedzones. Twozonesaresituatedinterritoriesallocatedfortheindustrialdevelopmentofthecity(A4, A1 and A2, A3, A5)andonezoneindenselypopulatedpartsofthecity(A6, A7).

Thezonewithalternatives A2, A3,and A5 havechallengesrelatedtotheconnectionto engineeringcommunicationsandconstructionofaccessroads.TheairportofVilniusisthekey challengeforthedesignoftheflue-gasstackoftheincinerationplantinthisparticularzone. Thus,fromthepointofviewofrationaldevelopment,requirementsofstakeholdergroupscanbe satisfiedbychoosingthealternative a1,whichisselectedbasedoncalculatedresults.Thissiteis technologicallyfitfortheconstructionofwasteincineration,wastesorting,andbiodegradablewaste treatmentplants.

Sustainability 2015, 7,15923–15936

WithintheMCDMframeworkwehavedevelopedanewextensionoftheoriginalcrispWASPAS method.Theproposednewextension,namelyWASPAS-SVNS,appliestheframeworkofthe single-valuedneutrosophicset.ComparisonoftheresultsobtainedbyotherMCDMapproaches hasbeenperformed.Basedoncalculatedresults,themostappropriatesitefortheconstructionofthe plantforincinerationofnon-hazardouswastesinthecityofVilniusisGariunaiDistrict.Considering theresults,itcanbeconcludedthatthisterritoryissuitablefortheimplementationoftheprojectfor theconstructionofawasteincinerationplant.

Multiplecriteriamethodsfacilitatethebestdecision-makingand,therefore,theyshouldbeused toensurebalancedwastemanagement.Basedonprinciplesofsustainabledevelopment,awaste managementsystemhelpstobalanceregionalwasteflowsandtheirfurtherappropriateutilization.

AuthorContributions: EdmundasKazimierasZavadskasdiscussedthemainideaoftheresearch.Romualdas BausysandMariusLazauskasdealtwiththemainresearch,analyzedtheobtainedresultsandperformedthe developmentofthepaper.Allauthorshavereadandapprovedthefinalmanuscript.

ConflictsofInterest: Theauthorsdeclarenoconflictofinterest.

Appendix

NeutrosophicSets

Smarandache[32]originallyproposedtheconceptofaneutrosophicsetfromphilosophicalpoint ofviewandwepresentabriefreviewofgeneralconceptsofneutrosophicset.

Definition1. Let X bespaceoftheobjectsand x P X.Aneutrosophicset A in X isdefinedbythreefunctions:truth-membershipfunction TA pxq,anindeterminacy-membership function IA pxq andfalsity-membershipfunction FA pxq.Thesefunctions TA pxq, IA pxq and FA pxq aredefinedonrealstandardorrealnon-standardsubsetsof s0 ,1`r.Thatis TA pxq : X Ñs0 ,1`r , IA pxq : X Ñs0 ,1`r and FA pxq : X Ñs0 ,1`r .Wehavenoanyrestrictiononthesumof TA pxq, IA pxq and FA pxq,so0 ď supTA pxq` supIA pxq` supFA pxqď 3`

Definition2. Asingle-valuedneutrosophicset(SVNS)hasbeendefinedasdescribedin Wang etal.,scientificwork[38].Let X beauniversalspaceoftheobjectsand x P X.Asingle-valued neutrosophicset(SVNS) r N Ă X canbeexpressedas

r N “ !Ax, TN pxq , IN pxq , FN pxqE : x P X) (S1)

where TN pxq : X Ñr0,1s , IN pxq : X Ñr0,1s and FN pxq : X Ñr0,1s with0 ď TN pxq` IN pxq` FN pxqď 3forall x P X.Thevalues TN pxq, IN pxq and FN pxq correspondtotruth-membershipdegree, theindeterminacy-membershipdegreeandthefalsity-membershipdegreeof x to r N,respectively. Forthecasewhen X consistsofthesingleelement, r N iscalledasingle-valuedneutrosophic number[33].Forthesakeofthesimplicity,asinglevaluedneutrosophicnumberisexpressedby r NA “ptA, iA, f Aq where tA, iA, f A Pr0,1s and0 ď tA ` iA ` f A ď 3.

Definition3. If r N1 “pt1, i1, f1q and r N2 “pt2, i2, f2q aretwosingle-valuedneutrosophicnumbers (SVNN),thenthesummationbetween r N1 and r N2 canbeexpressedasfollows

r N1 ‘ r N2 “pt1 ` t2 t1t2, i1i2, f1 f2q (S2)

Definition4. If r N1 “pt1, i1, f1q and r N2 “pt2, i2, f2q aretwosingle-valuedneutrosophicnumbers, thenmultiplicationbetween r N1 and r N2 canbeexpressedasfollows

r N1 b r N2 “pt1t2, i1 ` i2 i1i2, f1 ` f2 f1 f2q (S3)

Sustainability 2015, 7,15923–15936

Definition5. If r N1 “pt1, i1, f1q isasingle-valuedneutrosophicnumberand λ P isanarbitrary positiverealnumberthen

λ r N1 “ ´1 ´p1 t1qλ , iλ 1 , f λ 1 ¯ , λ ą 0(S4)

Definition6. If r N1 “pt1, i1, f1q isasingle-valuedneutrosophicnumberand λ P isanarbitrary positiverealnumberthen

r Nλ 1 “ ´tλ 1 ,1 ´p1 i1qλ ,1 ´p1 f1qλ¯ , λ ą 0(S5)

Definition7. If r N1 “ pt1, i1, f1q isasingle-valuedneutrosophicnumberthenthecomplementary componentofthissinglevaluedneutrosophicnumberisdeterminedasfollows

r Nc 1 “p f1,1 i1, t1q (S6)

Definition8. If r NA “ptA, iA, f Aq isasingle-valuedneutrosophicnumber,ascorefunctionis mapped r NA intothesinglecrispoutput S ´ r NA¯ asfollows S ´ r NA¯ “ 3 ` tA 2iA f A 4 (S7) where S ´ r NA¯ Pr0,1s.Thisscorefunctionisthemodificationofthescorefunctionproposedby SahinandKucuk[39]andallowsustohavetheresultsinthesameintervalaswedealwithsingle valuedneutrosophicnumbers.

Definition9. Let r N1 and r N2 beanytwoSVNNs.Therefore,if S ´ r N1¯ ă S ´ r N2¯ then r N1 is smallerthan r N2, r N1 ă r N2

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