A Valid Scheme to Evaluate Fuzzy Definite Integrals by Applying the CADNA Library

Theaimofthispaperistoestimatethevalueofafuzzyintegralandtofindtheoptimalstepsizeand nodesviathestochasticarithmetic.Forthispurpose,thefuzzyRombergintegrationruleisconsidered as an integration rule, then the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs)methodisappliedwhichisamethodtodescribethediscretestochasticarithmetic.Also,in ordertoimplementthismethod,theCADNA(ControlofAccuracyandDebuggingforNumerical Applications)isappliedwhichisalibrarytoperformtheCESTACmethodautomatically.Atheorem isprovedtoshowtheaccuracyoftheresultsbymeansoftheconceptofcommonsignificantdigits. Then,analgorithmisgiventoperformtheproposedideaonsamplefuzzyintegralsbycomputingthe Hausdorffdistancebetweentwofuzzysequentialresultswhichisconsideredtobeaninformatical zerointheterminationcriterion.Threesamplefuzzyintegralsareevaluatedbasedontheproposed algorithmtofindtheoptimalnumberofpointsandvalidatetheresults. KEywoRDS CADNA Library, CESTAC Method, Discrete Stochastic Arithmetic, Fuzzy Number, Fuzzy Romberg Integration Rule

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