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Definition 1.3 ( ( )) is Nano Penta topological space and .Let ⁄ * +be all decision classes induced by decision attribute and is divided into a set of condition attributes, obtain Nano Penta degree of dependence is , - | |,| ( )| | ( )|-. Definition 1.4 [8] Let betheuniverseset,anyfiveequivalencerelations on , where and ∑ ( ) { ∑ ∑ ( ) ∑ ( )}, ∑ ( ) ∐ {, - ( ) ( ) ( ) ( ) ( ) }, ∑ ( ) ∐ {, - ( ) ( ) ( ) ( ) ( ) }and ∑ ( ) ∑ ( ) ∑ ( ) 25 29,99 34,99 3999 40≤
Rana B. Yaseen1 , Mizal H. Alobaidi2 , Ali A. Shihabc3
Key Words: Nano Penta topology, Multi Granular Nano Penta topology , Childhood Obesity 1.
International Research Journal of Engineering and Technology (IRJET) e ISSN: 2395 0056 Volume: 09 Issue: 02 | Feb 2022 www.irjet.net p ISSN: 2395 0072
Definition 1.2[8] Let be a non_ empty universe set, ( ) ( ) ( ) ( )and ( ) are Nano topologieson withrespectto .Thenasubset issaid to be Nano Penta open ( open)set, if ( ( ) ( ) ( ) ( ) ( )) and complement is _closed set and the set with five topologies called ( ( ))Nano Penta topological space( topology), =1,2,3,4,5,sothese opensetssatisfyall theaxiomsofNanotopology .
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1,2Professor, Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq.
kg 3 Mediumobesity 35
kg 4 Severeobesity
kg 2 Lowobesity 30
The data used in this study were collected from the research presented by Asmaa et.al[1] in 2021 as the most important factors causing obesity in children from the age of 5 years to14 years old, that revealed the presence of 5 main factors that had a clear influence on overweight and obesity in children Inthepastyears,Nanotopologicalspaceknownby ThivagarandRichard[4]hasbeenusedincivilianlife,asin[4]. In2021Yaseen[9]studiedthepropertiesof Pentaopensets inPentatopologicalintroducedbyKhan [6] in2018 Definition 1.1 [5] ( ( )) Nano topological space & .Let ⁄ * +be all decision classes inducedbydecisionattribute and isdividedintoaset of condition attributes, obtain Nano degree of dependenceisdefinedas [ , ] | |,| ( )| | ( )|-. The potential factors of childhood obesity were studied and investigated using the concept of the Nano Penta topologyconceptwhichintroducedbyYaseen,R.etal.
INTRODUCTION AND PRELIMINARIES
Application of Childhood Obesity in Nano Penta Topological Spaces
3Professor, Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit, Iraq. ***
Table 1:Tableof informationonobesitymeasures
The difference and methods for calculating Nano Penta degree of decision traits in the practical application of childhood obesity have been studied in Nano Penta and Multi Granular Nano Penta topologies. It was found that the use of Multi Granular Nano Penta topology becomes better than the Nano Penta topology.
Obesity is an increase in the percentage of fat and it is accumulationundertheskinandaroundbodytissuesthatare differ from the normal limits. The diagnosis of obesity is based on the body mass index (BMI). According to the followingequation:BMI=bodyweightinkilograms/square height in meters [7] and the world health organization has defined obesity indicators according to the following classifications[3].
No. Obesityindicators 1 Overweight
Abstract
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3.TheThirdFactor:(theeconomicFactor) Thethirdfactorofvariablesrepresentedby(achild's expensesmorethan1000,Thewaytogotoschoolis bycar,Thegotoschoolisbywalking)
Thus, ∑ ( )formsatopologyon calledasthe Multi GranularNanoPentatopologyon with respectto .( ∑ ( ))calledtheMulti GranularNanoPentatopologicalspaces. Inthisresearch,NanoPentadegreeiscalculatedto findNanoPentaandMulti GranularNanotopological spacesaccuracythroughthepracticalapplicationof childhoodobesity.
Table 2:informationonobesityvariable
2.TheSecondFactor:(socialfactors) Thevariablessecondfactorare(Mother'smarital status,livingwithhisparents).
Asampleof10malechildrenaged8yearswith overweightandobesitywhichidentifiedfromastudy theresearcherAsmaaet.alin2021,itwasfoundthere arefivefactorsthathavedirectimpacton children's weightgain,namely: 1.TheFirstFactor:(badhealthhabit) Thevariablesofthefirstfactorrepresentedby(late bedtime,sittingforlonghoursonanytablet,fastfood, consumingartificialjuicesandsoftdrinks)
={Mother'smaritalstatusmarried(MM),livingwith one ofhisparents(LP)} ={child'sexpensesmorethan1000(CE),thewaytogoto schoolisbycar(SC),thegotoschoolisbywalking(SW)} = {heredity(H),arrangementofthechildinfamily(first, middle,last(CA1,CA2,CA3)} = {childengaginginphysicalactivity(PA),childnot engaginginphysicalactivity(NPA)}
Cacase 1 : Here * , , , , , , , , , }the set of children, * + and a set of decision attribute. Let ** + * + * + * + * + * ⁄++
4.TheforthFactor:(familyhistory) Thefourthfactoris(heredity,child'sarrangementin 5.Thefamily)fifthFactor(physicalactivity) thisfactorcontainsonevariablethatmainly contributestoitsformation,whichis(physicalactivity)anda set ofdecisionattribute.Take , , , , and will standfor(badhealthhabit,socialfactors,theeconomicfactor, familyhistory,physicalactivity,decision). Thedomainsareasfollows ={latebedtime(BT),sittingforlonghoursonany tablet(ST),fastfood(FF),consumingartificialjuicesandsoft drinks(AJ)}.
De Decision 1 1: Obese Children with respect to . Then the correspondingupper,lowerapproximationandtheboundary reregionof ⁄ ( ) 3,4,5=1,2, ( ) ( ) ( ) * + * + * + { * ++ * + * + * + { * +} * + * + * + { * ++ * + * + * + { * +} * + * + * + * * ++ Then ( ) { * },{ + * },* + * +}, so ( ) * ,* +}. Phase 1 1 1: The attribute when (late bed time) was removedfrom , ( ⁄) ** + * + * + * ++,weobtain ( ) ( ) { ,* },* +,* },{ +}, so ( ) ={ ,{ }}isbasisfor ( ) ( ), then ( ) ( ) ( ) Phase1-1- 2:Theattributewhen(sittingforlonghourson anytablet)wasremovedfrom , Children ghWeit Length (Group1 ) Group2( ) Group3( ) Group4 ( ) Group5 ( ) Decision 55 132 { ,FFST,BT,AJ} {LP} W}{CE,S 1}{H,CA {PA} sityObe 48 128 { ,FFST,BT,AJ} {MM} W}{CE,S 2}{H,CA {PA} sityObe 43 128 { AJST,} {MM} }{CE,SC {CA3} {PA} ightrweOve 50 125 { AJSTBT,,} {MM} }{CE,SC 2}{H,CA {PA} sityObe 44 130 {FF} {MM} {SC} {CA1} NPA}{ ightrweOve 45 128 { AJSTBT,,} {MM} {SW} {CA1} {PA} ightrweOve 55 128 { FFST,} {MM} {SC} 2}{H,CA {PA} sityObe 50 129 { FFST,BT,} {MM} {SW} {CA2} {PA} ightrweOve 42 129 { FFST,BT,} {MM} }{CE,SC 2}{H,CA {NPA} sityObe 45 130 { ,FFST,BT,AJ} {MM} W}{CE,S {CA2} NPA}{ ightrweOve
2. PROBLEM
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 966 ( ⁄) ** + * + * + * + * ++,weobtain ( ) ( ) { ,{ +,* },{ +,{ },{ +},so theset ( ) ={ ,{ +}isbasisfor ( ) ( ), then ( ) ( ) ( )
Note: The condition attributes are the variables from , therefore , the variables CORE ={ +. Which is minimal Case 2 :Here * , , , , , , , , , }thesetofchildren, * +and a set of decision attribute. Let ⁄ {* +,* ++ Decision 2 1:ObeseChildrenwithrespect to Then ( ) * * +,* ++ ( )isbasis for ( ) Phase 2 1 1: The attribute when (the marital status of the mother married)was removed from , ( ⁄) * +, we obtain ( ) ( ) * * ++, so ( ) ( ) ={ { }, }, basis for ( ) ( ), then ( ) ( ) ( ).
( ) * * + * +{ + * + * ++. So ( )={ * ++isthebasisfor ( ) Theattributewhen(latebedtime)wasremoved1-2-1:Phase from ( ⁄) ** + * + * + * ++ ( ) ( ) * * + * + * + * ++, so ( ) ={ ,{ +}is basis for ( ) ( ) ( ) ( ) ( ) Phase 1 2 2: The attribute when (sitting for long hours on any tablet)wasremovedfrom , ( ⁄) ** + * + * + * + * ++,weobtain ( ) ( ) { ,{ +,* },{ +,* },* +}, so ( ) ={ ,{ +}is basis for ( ) ( ), so ( ) ( ) ( ) Phase 1 2 3: The attribute when (fast food)is removed from , ( ⁄) ** + * + * + * ++,then ( ) ( ) { ,{ + * }}, so ={ ,{ }}is basis for ( ) ( ), then ( ) ( ) ( )
Phase 1-1-3:Theattributewhen(fastfood)wasremovedfrom , ( ⁄) ** + * + * + * ++,weobtain ( ) ( ) { ,{ +,{ +,* +},sotheset ={ * +}isbasisfor ( ) ( ),then ( ) ( ) ( ) Phase 1 1 4:Theattributewhen(consumingartificialjuices andsoftdrinks)wasremovedfrom , ( ⁄) ** + * + * + * + * },* ++,weobtain ( ) ( ) * * + * + * + * +},so theset ( ) ={ * ++isthebasic for ( ) ( ),then ( ) ( ) ( )
Phase 1-2-4: The attribute when (consuming artificial juices and soft drinks) was removed from , ( ⁄) ** + * + * + * + * },* ++ , ( ) ( ) * * + * + * + * + * ++ ( ) ={ * ++ is basis for ( ) ( ),so ( ) ( ) ( ).
Phase 2-1-2: The attribute when(living with one of his parents)wasremovedfrom , ( ⁄) * ++,weobtain ( ) ( ) * * }}= ( ) ={ , * }}is basis for ( ) ( ), so that ( ) ( ) ( )
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* * *++*+ + * + * * *++*+ + * +
* *++}*+ + * + * * *++*+ + * + { * *++*+ + * +
Note: the condition attributes are the variables from ,therefore,thevariablesCORE={ +. Decision 1 2:Childrenwhoareoverweightwithrespectto , Then=1,2,3,4,5
Note :thevariablesareindependentoneachother Decision 2 2:Childrenwhoareoverweight with respect to .Weget ( ) * ,* ++= ( )isthebasisfor ( ). Phase 2-2-1:Theattributewhen(maritalstatusof the mothermarried)isremovedfrom , ( ⁄) * +,weobtain ( ) ( ) * +,so ( ) ( )={ }isbasis for ( ) ( ),then ( ) ( ) ( ) Note:Theconditionattributes arethevariablesfrom , therefore,thevariablesareindependentofeachother.CORE ={ +.Whichisminimal. Case 3 :Here * , , , , , , , , , }thesetofchildren, * +andaset ofdecisionattribute.Let ⁄ {* +,* + * },* }}. Decision 3 1:ObeseChildrenwithrespect to , ( ()()() ) ⁄) {
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Then ( ) * * +,* +,* + * +,* +}, so ( )={ , * }}isbasisfor ( ). Phase 3 1 1:Theattributewhen(child'sexpensesmore than1000)wasremovedfrom , ( ⁄) ** + ,* +},weget ( ) ( ) * * + * + * ++= ( ) ( )isbasis for ( ) ( ),then ( ) ( ) ( ). thewaytogotoschoolisbyTheattributewhen(:21Phase 3 usingacar)isremovedfrom , ( ⁄) ** +,{ },{ ++,weobtain ( ) ( ) * * + * +,* ++,so ( ) ( ) ={ * +}isthebasisfor ( ) ( ),then )()(( ) : Theattributewhen(thewaytogotoschoolis31Phase 3 bywalking)isremovedfrom , ( ⁄) { +,{ },{ }},weobtain ( ) ( ) * * + * + * +},so ( ) ( )={ * +}isbasisfor ( ) ( ), then ( ) ( ) ( ). Note :thevariablesareindependentoneachother. Decision 3-2:Childrenwhoareoverweight withrespect to Then ( ) { * + * + * + * + * +}, so ( )={ * ++isbasisfor . Phase 3 2 1: The attribute when (child's expenses more than1000) was removed from , ( ⁄) ** +,{ }},weobtain ( ) ( ) * * ++= ( ) ( )is basis for ( ) ( ), then ( ) ( ) ( ) Phase 3 2 2:Theattributewhen(thewaytogotoschoolisby usingacar)isremovedfrom , ( ⁄) ** +,{ },{ ++,weobtain ( ) ( ) * * + * + * ++, so ( ) ( ) ={ * + * +}is basis for ( ) ( ), then ( ) ( ) ( ). : Theattributewhen(thewaytogotoschoolisby-2-3Phase 3 walking)isremovedfrom , ( ⁄) {* +,{ },{ +},weobtain ( ) ( ) { * +} ( ) ( )isbasis for ( ) ( ),then ( ) ( ) ( ) Note :thevariablesareindependentoneachother. }thesetof,,,,,,,,,*ere:HCase 4 children, * + andaset ofdecisionattribute.Let ⁄ {* + * +,* + * },{ }}. De Decision 4 1:ObeseChildrenwithrespect to , Then ( ) * * + * + * + * + * + * ++, so ( )={ ,{ + * }}isbasisfor ( ) )isremovedfromheredityTheattributewhen(:11Phase 4 , ( ⁄) {* + * + * +}, ( ) ( ) { ,* + * +}, so ( ) ={ * }}for ( ) ( ), then ( ) ( ) ( ) Phase 4 1 2: The attribute when (the child's arrangement in the family)was removed from , ( ⁄) * +,weobtain ( ) ( ) { ,* +}= ( ) is basis for ( ) ( ), then ( ) ( ) ( ) Note :thevariablesareindependentoneachother. Decision 4 2:Childrenwhoareoverweight withrespect to Then. ( ) * ,{ + * + * + * + * ++,so ={ * }}isthebasisfor ( ) )isremovedheredityTheattributewhen(:12Phase 4 from , ( ⁄) {* + * + * +},weobtain ( ) ( ) { ,* },,* + * ++ So theset ( ) ={ * }}isbasis for ( ) ( ),then ( ) ( ) ( ) :Theattributewhen(thechild's22Phase 4 arrangementinthefamily)isremovedfrom ( ⁄) * +,weobtain ( ) ( )={ + ( ) isbasisfor ( ) ( ),then ( ) ( ) ( ) Note :thevariablesareindependentoneachother Case 5 :Here * , , , , , , , , , }, * +andaset ofdecisionattribute.Let ⁄ {* },* ++ Decision 5 1: Obese Children with respect to , Then ( ) * * },* +}, so ( ) =* +isbasisfor ( ). Childengagingin: Theattributewhen(-1-1Phase 5 physicalactivity)wasremovedfrom , ( ⁄) * +,weobtain ( ) ( ) { ,* }}= ( ) is thebasisfor ( ) ( ),then ( ) ( ) ( ) ( ()()⁄) { , * ++ * *+ + * + { * }* *+ + * + * * *++*+ + * + { ,* *++ +{ + * + { ,* *++*+ + * +
:Theattributewhen(Childnotengagingin21Phase 5 physicalactivity)isremovedfrom , ( ⁄) { },weobtain ( ) ( ) { ,* ++= ( ) isthebasis for ( ) ( ),then ( ) ( ) ( ) Note :thevariablesareindependentoneachother Decision 5 2:childrenwhoareoverweight withrespect to Then, ( ) * * + * ++,so ( ) ={ }isbasisfor ( ). physicalChildengagingin: Theattributewhen(-2-1Phase 5 activity)isremovedfrom , ( ⁄) * +,weobtain ( ) ( ) { ,* ++ ( ) isthebasis for ( ) ( ),then ( ) ( ) ( ). :Theattributewhen(Child notengagingin22Phase 5 physicalactivity)isremovedfrom , ( ⁄) * },weobtain ( ) ( ) { ,* }}= ( ) isthebasisfor ( ) ( ),then ( ) ( ) ( ) Note :thevariablesareindependentoneachother. 3. Compare and analyze Example 3.1 Wearegoingtodiscussthedifferenceproblemandthe relationshipbaseddependingontheapproximationsand findingtheNanoPentadegreeinallcases, fromtheideal combinationofthefive<badhealthhabit,socialfactors,the economicfactor,familyhistory,physicalactivity>torid a childofobesity. Table2showedanintegratedinformationsystemandis givenby( ),where * , , , , , , , , , }setofchildrenand ={bad healthhabit,socialfactors,theeconomicfactor,familyhistory andphysicalactivity},setofvariablesfromtable2. ** + * + * + * + * + * ⁄++ ⁄ ** +,* }} ⁄ {* +,* + * },* ++ ⁄ {* + * +,* + * },{ }} ⁄ {* },* ++ Decision 1:Let * +,thesetofObeseChildren. Table 3:Tableofinformationonobesitychildren ,5=1,2,3,4 ( ) { } * + * + ( ) * + * + ( ) * + * + * + Hence ∑ ( ) { + ∑ ( ) * +,togettheresults ∑ ( ) * * + * + * ++ So ∑ ( )={ * + * ++isthebasis for ∑ ( ) Decision 2:Let * +,thesetofChildrenarenot obese Table-4:Informationtableforoverweightchildren 3,4,5=1,2, ( ) { } { } ( ) * + * + * + ( ) * + * + * + Wegottheresultsas following ∑ ( ) * +, ∑ ( ) * +, ∑ ( ) * * + * + * ++ So ∑ ( )={ * + * ++isthebasis for ∑ ( ) Wehave * +, * +, * +, where ⁄ ** + * ++. TogettheNanoPentadegreefromtable(2,3,4),we 1.calculate ( ) and ( ) , , - | |[| ( )| | ( )|] 2. ( ) * + and ( ) , , - | |[| ( )| | ( )|] 3. ( ) and ( ) , , - | |[| ( )| | ( )|] 4. ( ) * + and ( ) , , - | |[| ( )| | ( )|] 5. ( ) and ( ) , , - | |[| ( )| | ( )|] and thenobtain ∑ ( ) * + and ∑ ( ) * + Weget ,∑ - | |[| ∑ ( )| | ∑ ( )|] Nowfromtheaboveitispossibletoreviewthefollowing result. , - ,∑ -, , - ,∑ -,
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4.CONCLUSION
Observation 3.2: By using the measure named as Nano Penta degree of dependence on X , for all the cases we infer that the Multi Granular Nano Penta topology became more accuratethantheNanoPentatopology.
[ 2] E. Salh and T. Jasim , “On Certain Types of Set in Micro TopologicalSpaceswithanApplicationinThalassemiaSick,” TikritJournalofPureScience,26(2),2021,pp.103-107. [3] J.F. AL arjan ,“The Prevalence of Obesity, Overweigh and UnderweightAmongStudentsofAl-BalqaAppliedUniversity in Jordan,” Educational Sciences Studies, 38(6), 2011, pp .2019 2036. [4] L.ThivagarandC.Richard,“OnNanoFormsOf WeaklyOpenSets,”IternationalJournalMath.Stat. [7]MD.SeemaandS.Aaron,“ReviewofChildhoodObesity: FromEpidemiology,Etiology,andComorbiditiestoClinical AssessmentandTreatment,”MayoClin,92(2),2017,pp.251[8] R.B.Yaseen, A. Shihab and M. Alobaidi , “On Nano PentaTopologicalSpaces”AIPPublishing(ICCEPS-2021) [9] R.B.Yaseen,A.ShihabandM.Alobaidi“Characteristics of Penta- open sets in Penta topological spaces ” Int. J. Nonlinear Anal. Appl.,12,(2), 2021, pp. 2463 2475, http://dx.doi.org/10.22075/ijnaa.2021.5388.
[5] L. Thivagar and C. Richard, “Computing technique for recruitement process viananotopology,”Sohag J. Math. 3(1), 2016,pp.37 45.
International Research Journal of Engineering and Technology (IRJET) e ISSN: 2395 0056 Volume: 09 Issue: 02 | Feb 2022 www.irjet.net p ISSN: 2395 0072 © 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 969 , - ,∑, - ,∑, - ,∑ -
[6]M.KhanandG.Khan,“p-Continuityandp-Homeomorphism inPenta Topological Spaces,”EuropeanInternational Journal ofScienceandTechnology,7,(5),2018,pp.1-8.
Inven.,1(1),2013,pp.31 37. [1]A.S.Qadouri,N.J.MohammedandZ.T.AbdelQader,“Use Factor Analysis in Determining Most Important Factors Affecting Childhood Obesity,” Turkish Journal of Computer andMathematicsEducation,12(12)2021,pp 4621-4630.
As a result of the intervention of many biological and social factors, children could get overweight or obese, we noticed that the family history , the Economic Factor and physical activity an ideal combination for children to reach an ideal weight. Proper care and behavioral change can prevent the risk of childhood obesity. It was concluded that the Multi Granular Nano Penta topology more accurate than the Nano Pentatopology REFERENCES 265. accepted.