Polycystic Ovarian Syndrome a Threat to Infertility in Women

AdvancesinMathematics:ScientificJournal 9 (2020),no.5,3067–3073 ISSN:1857-8365(printed);1857-8438(electronic) https://doi.org/10.37418/amsj.9.5.66

POLYCYSTICOVARIANSYNDROMEATHREAT TOINFERTILITYINWOMEN-DIAGNOSISBY NEUTROSOPHICLINGUISTICFUZZYMATRICES

H.MUMTAJBEGUM1 ,M.UMADEVI,V.P.M.SENTHILNAYAKI,ANDN.MARTIN

ABSTRACT.Inrecenttimes,theproblemofinfertilityinwomenisclimbing thealtitude.ExtensiveresearchonthisissuehaslabelledPolycysticOvarian Syndrome(PCOS)isoneoftheprimecausesofinfertility.PCOSareofvarious kindsandthesymptomsarequitesimilar.Theprocessofdiagnosisisfilled withuncertaintyasthesymptomofdifferenttypesofPCOSandotherhormonal imbalancesarelike.Tohandlesuchinstancesofimprecisenessandambiguity, thenotionoffuzzymatricescanbeusedtorepresentthesymptomsandthe typesofPCOS.ThisarticlepresentsvariouskindsofPCOSanditssymptoms. TheassociationbetweensymptomsandPCOSandtheaffectedarerepresented asneutrosophicfuzzymatrices.Theproposedmethodofdiagnosisdiffersfrom theearliermodelsbytherepresentationandcomputationalprocedure.The diagnosisbyneutrosophiclinguisticfuzzymatricesisaninnovativeinitiative anditcanbeextendedtootherkindsoffuzzyrepresentations.

1.INTRODUCTION

Theconceptoffuzzyhasintenseapplicationsinthefieldofmedicine;especiallythenotionofFuzzymatricesisextensivelyusedbythemedicalexpertsin diagnosingthediseasesofthepatients.Fuzzyrepresentationsofdataarethe channeltohandletheimprecisenessandvaguenessindecisionmaking.The

1correspondingauthor 2010 MathematicsSubjectClassification. 15B15,97M60. Keywordsandphrases. PolycysticOvariansyndrome,Neutrosophicfuzzymatrices,optimal decision. 3067

fuzzysetsareextendedtointuitionisticfuzzysetswithmembershipandnonmembershipfunctions.TheconceptofindeterminacyisintroducedbyFlorentineanditisrepresentedtogetherwithtruthandfalsemembershipfunctions. Therepresentationoffuzzymatriceswithintervalvaluedrepresentationsand softsetsarealsousedtomakethedecisionmakingfeasible.Basedonthese earlierworks,adecisionmakingmodelusingfuzzymatrixwithneutrosophic linguisticrepresentationsisproposedtomakeoptimaldiagnosisofpolycystic ovariansyndrome(PCOS).

TheoccurrenceofdisordersrelatedtoPCOSistheresultantofthemalfunctioningoftheinternalsystemofhumananditispredominantlyfoundin women,[1].Thefertilityofwomenisgreatlyaffectedbytheimbalanceof hormonescausedbyexternalandinternalfactors.Theproblemoffertilityis gainingmoreconcernamidstthemedicalresearchers,asmanywomensubject themselvestotreatmentforchildbearing.TherearemanycausesofinfertilityinwomenbutoneoftheprimecausesinPCOSandtherecordofinfertility casesduetoPCOSisclimbinghigh.ThecontributingfactorsofPCOSandits symptomshavecategorizedPCOStomanykinds.Initiallyintheprocessofdiagnosis,itisquitedifficulttoidentifythevictimwiththecommonsymptoms, thustheprevalenceofuncertaintydragsthediagnosistonextstageasproper treatmentcanbeadministeredonlyafteridentifyingthekindofPCOtheperson isaffectedby.AlsointhisscenariothesymptomsofthevariouskindsofPCOS arequitesimilar.Thismakesthedecisionmakingmorecomplicated.Toresolve suchcrisisthefuzzymatrixwithneutrosophiclinguisticrepresentationcanbe usedtomodelthisdecisionmakingcircumstance.Inthisproposeddecision makingmodel,fourkindsofPCOSsuchasInsulinResistant,Pillinduced,Lean typeandHiddenPCOSandthesymptomslikeAnovulation,obesity,Androgenic Alopecia,HirsutismandAcneareconsideredforthestudy.Alsotheelementsof therelationmatrixarerepresentedbylinguisticneutrosophicsets.Theserepresentationsaregivenbythemedicalexpertsinthefieldofgynecology.The relationmatricesbetweenthesymptomscumkindsofPCOSandpatientscum symptomsareformulatedrespectivelywithneutrosophiclinguisticrepresentations.Thetruth,indeterminacyandfalsemembershipvaluesarerepresentedby linguisticvariablesratherthannumericalvalues[2–4].Thedegreeofindeterminacyisessentialas,itreflectsthedifficultyofthemedicalexpertsindrawing

POLYCYSTICOVARIANSYNDROME...3069 conclusionsfromtheavailabledata.Theproposedmodelisvalidatedwiththe primarydataofthepatientssufferingfrominfertilityproblems.

Thepaperisstructuredasfollows:section2comprisesofthemethodology; section3presentsthevalidationoftheproposedmodel;section4discussesthe resultsandthelastsectionconcludestheresearchworkwiththescopeofmodel extension.

2.METHODOLOGY

Fuzzymatrixinmedicaldiagnosishasvariousillustrations,forinstanceSophia Porchelviin[5]hasusedtriangularrepresentationsoffuzzymatrixinwhichthe victimsofthediseasesaredetermined.Byadoptingthesameprocedureinthe constructionofrelationmatrix,thefollowingstepsoftheproposedmethodology arelistedasfollows.

Step1:Constructthesymptom-diseaseneutrosophiclinguisticmatrix Zd.

Step2:Formulatethepatient-symptomneutrosophiclinguisticmatrix Zp.

Step3:Convertthelinguisticfuzzyrepresentationstotriangularfuzzynumbers.

Step4:Compute R1 ,where R1 = Zp and Zd[operator max(min),min(max),min(max)]

Step5:Calculate R2 ,where R2 = Zp. H Zd(H =∼ Zd).

Step6:Determine R3 ,where R3 = W Zp. Zd(W =∼ Zp).

Step7:Find R4 = Max{R2 , R3 }[(Max,min,min)].

Step8:Obtain R5 = R1 R4 .

Step9:Thedecisionmakerfirmlyconfirmsthekindofdiseaseordisorderthe personissufferingfrom.

3.VALIDATIONOFTHEPROPOSEDMODEL

Theproposeddecisionmakingmodelisvalidatedwiththeprimarydataof thepeoplesufferingPCOSproblem.Therelationmatrix Zp ispresentedbelow. TheabovematricesrepresenttheoptimaldiagnosisofthekindsofPCOSto thepatients.

FIGURE 1.Therelationmatrix Zd

FIGURE 2.Therelationmatrix R1

FIGURE 3.Therelationmatrix R2

FIGURE 4.Therelationmatrix R3

FIGURE 5.Therelationmatrix R4

4.RESULTSAND DISCUSSION

Figure3clearlypresentsthepatientsandthekindofPCOStheyaresuffering from.Theproposeddecisionmakingmodelplaysavitalroleindiagnosing thediseasesorthedisorderswhicharecloselyrelatedanddonotdiffermuch. Therepresentationofthedataintheformoflinguisticneutrosophicsetsisthe significantaspectofthemodel.ThekindsofPCOSarecharacterizedbysimilar symptomsbutstillthetreatmentdiffers,tohandlethesecrisisthesedecision makingmodelscanbeappliedformedicaldiagnosis.

5.CONCLUSION

Theproposedmodelishighlycompatibleandfeasible,asitreflectstheexpert’sopinioninamorepragmaticmanner.Therealexistingscenarioisprojectedintheformofneutrosophiclinguisticrepresentationsandtheapplication offuzzymatrixindeterminingtheoptimaldiagnosismakesthedecisionmakingprocesseasier.Theformulatedmodelcanbeextendedwithotherfuzzysets representation.

REFERENCES

[1] C.C.DENNETT,J.SIMON: TheRoleofPolycysticOvarySyndromeinReproductiveand MetabolicHealth:OverviewandApproachesforTreatment,DiabetesSpectrum, 28(2)(2015), 116–120.

[2] F.SMARANDACHE: DefinitionofNeutrosophicLogic-AGeneralizationoftheIntuitionistic FuzzyLogic,ProceedingsoftheThirdConferenceoftheEuropeanSocietyforFuzzyLogic andTechnology,EUSFLAT,Zittau,Germany,2003,141–146.

[3] F.SMARANDACHE: AUnifyingFieldinLogics:NeutrosophicLogic,inMultipleValuedLogic, AnInternationalJournal, 8(3)(2002),385–438.

[4] F.SMARANDACHE: Neutrosophy,ANewBranchofPhilosophy,inMultiple-ValuedLogic,An InternationalJournal, 8(3)(2002),297–384.

[5] R.S.PORCHELVI,P.SELVAVATHI,R.VANITHA: AnApplicationofFuzzyMatricesinMedical Diagnosis,Intern.J.FuzzyMathematicalArchive, 9(2)(2015),211–216.

DEPARTMENTOF MATHEMATICS

PSNACET

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DEPARTMENTOF MATHEMATICS PSNACET

DINDIGUL

DEPARTMENTOF MATHEMATICS PSNACET

DINDIGUL

DEPARTMENTOF MATHEMATICS

ARUL ANANDAR COLLEGE (AUTONOMOUS)

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