Bull.PureAppl.Sci.Sect.EMath.Stat. 39E(2),183–187(2020) e-ISSN:2320-3226,PrintISSN:0970-6577 DOI10.5958/2320-3226.2020.00017.X ©Dr.A.K.Sharma,BPASPUBLICATIONS, 115-RPS-DDAFlat,MansaroverPark, Shahdara,Delhi-110032,India.2020
BulletinofPureandAppliedSciences Section-E-Mathematics&Statistics
Website:https: //www bpasjournals com/
Improved,extended,andtotalimpactfactorofajournal ∗
FlorentinSmarandache1,†
1.MathematicsandScienceDivision,UniversityofNewMexico, 705GurleyAve.,Gallup,NM87301,USA.
1.E-mail: smarand@unm.edu
Abstract Inthisshortpaperwerecallthe(Garfield)ImpactFactorofajournal,we improveandextendit,andeventuallypresenttheTotalImpactFactorthatreflectsthe mostaccurateimpactfactor.
Keywords Impactfactor,Journalimpactfactor,Garfieldimpactfactor,improved impactfactor,extendedimpactfactor,totalimpactfactor.
2020MathematicsSubjectClassification 00A05,00A06,00A09,00A64,00A99.
1Introduction
TheImpactFactor(IF)orJournalImpactFactor(JIF),thatisusedtoday,wasproposedbyEugeneEli Garfield(1925–2017),anAmericanlinguistandbusinessman,thefounderoftheInstituteofScientific Information(ISI),ScienceCitationIndex(SCI),andespeciallyJournalCitationReports(JCR).Among otherstheImpactFactoriscomputedsince1975onlyforthejournalsregisteredinthedatabaseofthe JournalCitationReports(see[1]).WecallittheGarfieldImpactFactor(GIF)todistinguishitfrom thethreenewtypesofimpactfactorsthatweproposenow,inordertoimprove,extend,andtotalize theimpactfactors’formulasforabetteraccuracyofthecitationsofarticlespublishedinaspecified journal.
2Garfieldimpactfactor
Letusconsiderajournal J thatstartedintheyear Y1.Wewanttocomputeitsimpactfactorinthe year Y2,where Y1 <Y2,andthecalculationisdoneintheyear Y2 +1 TheGarfieldIFofthejournal J fortheyear Y2 isdefinedasfollows: IF Garfield Y2 (J)= C (Y2,Y2 1)+ C (Y2,Y2 2) P (Y2 1)+ P (Y2 2) , (2.1) where C (Y2,Y2 1) meansthenumberofcitationsduringtheyear Y2 ofthesaidjournal’spublished articlesduringthepreviousyear Y2 1; C (Y2,Y2 2) issimilarlythenumberofcitationsduringthe year Y2 ofthejournal’spublishedarticlesduringthepasttwoyears,i.e., Y2 2 and Y2 1 P (Y2 1) and P (Y2 2) representthenumberofthejournal’spublishedarticlesduringtheyears Y2 1, and Y2 2 respectively. IF Garfield Y2 (J) iscalculatedforthenextyear Y2 +1 ∗
Communicated,editedandtypesetinLatexby LalitMohanUpadhyaya (Editor-in-Chief). ReceivedOctober16,2019/RevisedNovember06,2020/AcceptedNovember28,2020.OnlineFirst PublishedonDecember26,2020at https://www.bpasjournals.com/ †CorrespondingauthorFlorentinSmarandache,E-mail:smarand@unm.edu
3FlawsoftheGarfieldIF
WelistthefollowingflawsoftheGarfieldimpactfactor: a) Thenumberofcitationsofthejournal’sarticlespublishedintheyear Y2 andcitedinthesameyear Y2 aremissed. b) Thejournal’spublishedarticlestakenintoconsiderationareonlyfortheprevioustwoyears Y2 1 and Y2 2,whichissuperficial.
4Theimprovedimpactfactor
Thecase a) isalwaysomittedby IF Garfield thatnevertakesintoconsiderationthecitationsinthe sameyearinwhichthearticleswerepublished. Animprovedandmoreaccurate IF Garfield is:
IF Improved Y2 (J)= C (Y2,Y2)+ C (Y2,Y2 1)+ C (Y2,Y2 2) P (Y2)+ P (Y2 1)+ P (Y2 2) , (4.1)
byincludingthecitationsduringyear Y2 ofthejournal’spaperspublishedduringtheyear Y2.Thisis, ofcourse,computedintheyear Y2 +1
5Theextendedimpactfactor
Thecase b) showstheincompletenessoftheGarfieldIFwhichweremovebydefiningtheExtended ImpactFactorasfollows:
IF Extended Y2 (J)= ∑Y2 k=Y1 C(Y2,k) ∑Y2 k=Y1 P (k) , (5.1) where C(Y2,k) isthenumberofcitationsduringtheyear Y2 ofthejournal’spublishedarticlesduring theyear k;and P (k) isthenumberofthejournal’spublishedarticlesduringtheyear k;ofcourse, k ∈{Y1,Y1 +1,Y1 +2,...,Y2}
5.1DistinctionsbetweentheextendedimpactfactorandtheGarfieldimpactfactor
ThemaindistinctionswithrespecttotheGarfieldImpactFactorarethefollowing:
• IF Extended showsallthecitationsduringtheyear Y2 ofthejournal’sallpublishedarticlessince thestartingoftheyear Y1,while, IF Garfield showsthecitationsduringtheyear Y2 ofonlyprevious twoyears’publishedarticles,therefore IF Garfield isincomplete;
• IF Extended alsoincludesthecitationsduringtheyear Y2 ofthejournal’spublishedarticlesinthe sameyear Y2,while, IF Garfield missesit,so IF Garfield islessaccurate.
6Thetotalimpactfactor
(k, [Y1,k])
k
Nowwedefinethebestandthemostaccurateandcompleteorexactimpactfactor,i.e,the Total ImpactFactor,asdefinedbelow: IF Total Y2 (J)=
2 k=Y1 P (k) , (6.1) where C(k, [Y1,k]) isthenumberofcitationsduringtheyear k ofthejournal’sallthepublishedarticles duringtheyears Y1,Y1 +1,...,k altogether,where Y1 ≤ k ≤ Y2,and [Y1,k]= {Y1,Y1 +1,...,k};and P (k) isthenumberofthejournal’sarticlespublishedduringtheyear k
7Accuracyrelationshipoforder
Letusconsidertherelationshipoforder ” >a ”,thatmeans“betteraccuracy”. Thenwehave: IF Total >a IF Extended >a IF Improved >a IF Garfield BulletinofPureandAppliedSciencesSectionE-Mathematics&Statistics,Vol.39E,No.2,July-December,2020
Improved,extended,andtotalimpactfactorofajournal 185
8Numericalexample
WepresentanillustrativeexampleinTable 1 Wereadthistableoncolumns,forexample: intheyear2015thejournal(J)haspublished20articles;thesearticlespublishedintheyear2015got: 6citationsintheyear2015; 15citationsintheyear2016; 4citationsintheyear2017; nocitationsintheyear2018; and9citationsintheyear2019; then,thetotalnumberofcitationsofthearticlespublishedintheyear2015inthejournal J is 6+15+4+0+9=34; andsoon; intheyear2019,thejournal (J) published40articles,andtheygot90citationsinthesameyear2019. Let’suseallfourimpactfactorformulastocomputethejournal’simpactfactorsforyear2019(thatis computingintheyear2020).
1. GarfieldImpactFactorforyear2019:
IF Garfield 2019 (J)= C (2019, 2018)+ C(2019, 2017) P (2018)+ P (2017) = 16+55 45+50 = 71 95 ≃ 0 747
2. ImprovedImpactFactorforyear2019:
IF Improved 2019 (J)= C (2019, 2019)+ C (2019, 2018)+ C(2019, 2017) P (2019)+ P (2018)+ P (2017) = 90+16+55 40+45+50 = 161 135 ≃ 1 193
3. ExtendedImpactFactorforyear2019:
IF Extended 2019 (J)= C (2019, 2015)+ C (2019, 2016)+ C (2019, 2017)+ C (2019, 2018)+ C(2019, 2019) P (2015)+ P (2016)+ P (2017)+ P (2018)+ P (2019) = 9+11+55+16+90 20+40+50+45+40 = 181 195 ≃ 0 928
4. TotalImpactFactorforyear2019:
IF Total 2019 (J)= 34+38+135+28+90 20+40+50+45+40 = 325 195 ≃ 1 667
Therefore,accordingtotheaccuracyrelationshipoforder >a wehave: 1 667 >a 0 928 >a 1 1928 >a 0 747
Whence,theexact(correct,mostaccurate)impactfactorofjournal(J)isequalto1.667.
BulletinofPureandAppliedSciencesSectionE-Mathematics&Statistics,Vol.39E,No.2,July-December,2020
Table1: Illustrativetabletoshowthecomparativestudyoftheproposedimpactfactors.
Example Journal(J)
YearofPublication 2015 2016 2017 2018 2019
Numberofpublished articles 20 40 50 45 40
Yearofcitations 2015 2016 2017 2018 2019 2016 2017 2018 2019 2017 2018 2019 2018 2019 2019
Numberofcitationsper year 6 15 4 0 9 19 0 8 11 10 70 55 12 16 90
Totalnumberof citations 34 38 135 28 90
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9Conclusion
Wehavedefinedforthefirsttimethreenewtypesofimpactfactorsofajournalandwedesignedan accuracyrelationshipoforder.Onanumericalexampleeachtypeofimpactfactorwascomputed. Uponeachimpactfactor’sformulaweclearlyhave:TheTotalImpactFactorismoreaccuratethan theExtendedImpactFactor,whichismoreaccuratethantheImprovedImpactFactor,which,inturn ismoreaccuratethantheGarfieldImpactFactor.
Acknowledgments TheauthorisgratefultotherefereesandtheEditor-in-Chieffortheircomments whichhavehelpedhiminupgradingthequalityofthispaper.
References
[1] Editors, Findimpactfactor/checkimpactindexofthousandsofworldwidejournals, https: //www.resurchify.com/impact-factor.php
BulletinofPureandAppliedSciencesSectionE-Mathematics&Statistics,Vol.39E,No.2,July-December,2020