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JakubBrzostowski,TomaszWachowicz
ofuncertaintyweproposetomodelthelevel(orchance)ofbelongingtothe
surfacebyusingthenotionofprobability.Moreprecisely9weproposetobuild
acharacteristicofanindifferencesurfaceintheformofprobabilitydistribution.
Suchafunctionwillassigntoeachalternativealevelofbelongingtothe
particularindifferencesurface.
Afterthesurfaceshavebeenspecifiedandtheutilitydegreeshavebeen
assigned9theNegoManagesystemperformsitsmostimportanttask9namely
thecomputationofprobabilitydistributionsforallspecifiedsurfacesthat
willbefurtherusedtobuildaglobalscoringsystem.Theprobabilityassigned
toaparticularpointoftheindifferencesurfacecanbeinterpretedasachance
ofactualassignmentofthispointtotheindifferenceset.Tobuildthe
characteristicofasurfaceweusethefollowingstraightforwardpostulate:
Thecloseranalternativeunderconsiderationislocatedtothe
onethatfullybelongstotheindifferencesurface,thehigher
isthelevelofprobabilitythatweassigntothisalternative.
Inotherwords9foranalternativelocatedintheneighborhoodofafully
classifiedalternativewefirstcomputethedistancetotheclassifiedalternative
andmapitintoasimilaritydegree.Thesimilaritydegreeoftheconsidered
alternativetothefullyclassifiedalternativeisregardedastheprobability
ofbelongingtothesurface.Basedonourpostulateweproposetobuildpeaks
aroundtheclassifiedalternativesasapreliminarystepofbuildingthe
probabilitydistribution.Suchpeaksmayhaveabellshapeofthenormal
distributioncurves9andsuchapeakshapeisconsideredatthecurrentstage
ofresearch.However9therearenosubstantialorexperimentallyprovedreasons
forusingthistypeofprobabilitydistributionsinourapproach.Wesimplyuse
thenormaldistributionfunctionsasthemostcommonlyusedsolutioninthe
selectionofthepredefinedshapeoftheprobabilityfunctionsincewelack
therelevantinformationthatwouldallowustouseothertypesofprobability
distributionfunctions.Inthenextstepsuchpeaksarefusedtogethertoforman
overallmulti-modaldistributionwhichistreatedastheindifferencesurface’s
characteristictogetherwithutilitylevelsassignedtothesurfacesbythene-
gotiator.Thisinformationabouteachindifferencesetisabasisfordetermining
thescoreofanyfeasiblealternativeunderevaluationlateronintheactual
negotiationphase9whenthenegotiatorsfacetheproblemofscoringtheoffers
presentedbytheircounterpartasthenegotiationcompromiseproposals.