Bull. Pure Appl. Sci. Sect. E Math. Stat. 39E(2), 183–187 (2020) Bulletin of Pure and Applied Sciences e-ISSN:2320-3226, Print ISSN:0970-6577 DOI 10.5958/2320-3226.2020.00017.X Section - E - Mathematics & Statistics ©Dr. A.K. Sharma, BPAS PUBLICATIONS, 115-RPS-DDA Flat, Mansarover Park, Website : https : //www.bpasjournals.com/ Shahdara, Delhi-110032, India. 2020 Improved, extended, and total impact factor of a journal ∗ Florentin Smarandache1,† 1. Mathematics and Science Division, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA. 1. E-mail: [email protected] Abstract In this short paper we recall the (Garfield) Impact Factor of a journal, we improve and extend it, and eventually present the Total Impact Factor that reflects the most accurate impact factor. Key words Impact factor, Journal impact factor, Garfield impact factor, improved impact factor, extended impact factor, total impact factor. 2020 Mathematics Subject Classification 00A05, 00A06, 00A09, 00A64, 00A99. 1 Introduction TheImpactFactor(IF)orJournalImpactFactor(JIF),thatisusedtoday,wasproposedbyEugeneEli Garfield(1925–2017),anAmericanlinguistandbusinessman,thefounderoftheInstituteofScientific Information(ISI),ScienceCitationIndex(SCI),andespeciallyJournalCitationReports(JCR).Among otherstheImpactFactoriscomputedsince1975onlyforthejournalsregisteredinthedatabaseofthe Journal Citation Reports (see [1]). We call it the Garfield Impact Factor (GIF) to distinguish it from the three new types of impact factors that we propose now, in order to improve, extend, and totalize the impact factors’ formulas for a better accuracy of the citations of articles published in a specified journal. 2 Garfield impact factor Let us consider a journal J that started in the year Y . We want to compute its impact factor in the 1 year Y , where Y <Y , and the calculation is done in the year Y +1. 2 1 2 2 The Garfield IF of the journal J for the year Y is defined as follows: 2 C(Y , Y −1)+C(Y , Y −2) IFGarfield(J)= 2 2 2 2 , (2.1) Y2 P(Y −1)+P(Y −2) 2 2 whereC(Y , Y −1)meansthenumberofcitationsduringtheyearY ofthesaidjournal’spublished 2 2 2 articles during the previous year Y −1; C(Y , Y −2) is similarly the number of citations during the 2 2 2 yearY ofthejournal’spublishedarticlesduringthepasttwoyears,i.e.,Y −2andY −1. P(Y −1) 2 2 2 2 and P(Y −2) represent the number of the journal’s published articles during the years Y −1, and 2 2 Y −2 respectively. IFGarfield(J) is calculated for the next year Y +1. 2 Y2 2 ∗ Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief). Received October16, 2019 / Revised November06, 2020 / Accepted November28, 2020. Online First Published on December 26, 2020 at https://www.bpasjournals.com/. †Corresponding author Florentin Smarandache, E-mail: [email protected] 184 Florentin Smarandache 3 Flaws of the Garfield IF We list the following flaws of the Garfield impact factor: a) Thenumberofcitationsofthejournal’sarticlespublishedintheyearY andcitedinthesameyear 2 Y are missed. 2 b) Thejournal’spublishedarticlestakenintoconsiderationareonlyfortheprevioustwoyearsY −1 2 and Y −2, which is superficial. 2 4 The improved impact factor The case a) is always omitted by IFGarfield that never takes into consideration the citations in the same year in which the articles were published. An improved and more accurate IFGarfield is: C(Y , Y )+C(Y , Y −1)+C(Y , Y −2) IFImproved(J)= 2 2 2 2 2 2 , (4.1) Y2 P(Y2)+P(Y2−1)+P(Y2−2) byincludingthecitationsduringyearY ofthejournal’spaperspublishedduringtheyearY . Thisis, 2 2 of course, computed in the year Y +1. 2 5 The extended impact factor The case b) shows the incompleteness of the Garfield IF which we remove by defining the Extended Impact Factor as follows: ∑ Y2 C(Y , k) IFExtended(J)= ∑k=Y1 2 , (5.1) Y2 Y2 P(k) k=Y1 where C(Y ,k) is the number of citations during the year Y of the journal’s published articles during 2 2 the year k; and P(k) is the number of the journal’s published articles during the year k; of course, k∈{Y ,Y +1, Y +2,...,Y }. 1 1 1 2 5.1 Distinctions between the extended impact factor and the Garfield impact fac- tor The main distinctions with respect to the Garfield Impact Factor are the following: • IFExtended shows all the citations during the year Y of the journal’s all published articles since 2 thestartingoftheyearY ,while,IFGarfieldshowsthecitationsduringtheyearY ofonlyprevious 1 2 two years’ published articles, therefore IFGarfield is incomplete; • IFExtended alsoincludesthecitationsduringtheyearY ofthejournal’spublishedarticlesinthe 2 same year Y , while, IFGarfield misses it, so IFGarfield is less accurate. 2 6 The total impact factor Now we define the best and the most accurate and complete or exact impact factor, i.e, the Total Impact Factor, as defined below: ∑ Y2 C(k, [Y , k]) IFTotal(J)= k=∑Y1 1 , (6.1) Y2 Y2 P(k) k=Y1 whereC(k, [Y , k])isthenumberofcitationsduringtheyearkofthejournal’sallthepublishedarticles 1 during the years Y ,Y +1,...,k altogether, where Y ≤k≤Y , and [Y ,k]={Y ,Y +1,...,k}; and 1 1 1 2 1 1 1 P(k) is the number of the journal’s articles published during the year k. 7 Accuracy relationship of order Let us consider the relationship of order ”> ”, that means “better accuracy”. a Then we have: IFTotal > IFExtended > IFImproved > IFGarfield. a a a BulletinofPureandAppliedSciencesSectionE-Mathematics&Statistics,Vol. 39E,No. 2,July-December,2020 Improved, extended, and total impact factor of a journal 185 8 Numerical example We present an illustrative example in Table 1. We read this table on columns, for example: intheyear2015thejournal(J)haspublished20articles;thesearticlespublishedintheyear2015got: 6 citations in the year 2015; 15 citations in the year 2016; 4 citations in the year 2017; no citations in the year 2018; and 9 citations in the year 2019; then, the total number of citations of the articles published in the year 2015 in the journal J is 6+15+4+0+9=34; and so on; intheyear2019,thejournal(J)published40articles,andtheygot90citationsinthesameyear2019. Let’suseallfourimpactfactorformulastocomputethejournal’simpactfactorsforyear2019(thatis computing in the year 2020). 1. Garfield Impact Factor for year 2019: C(2019, 2018)+C(2019, 2017) 16+55 71 IFGarfield(J)= = = ≃0.747. 2019 P(2018)+P(2017) 45+50 95 2. Improved Impact Factor for year 2019: C(2019, 2019)+C(2019, 2018)+C(2019, 2017) IFImproved(J)= 2019 P(2019)+P(2018)+P(2017) 90+16+55 161 = = ≃1.193. 40+45+50 135 3. Extended Impact Factor for year 2019: C(2019, 2015)+C(2019, 2016)+C(2019, 2017)+C(2019, 2018)+C(2019, 2019) IFExtended(J)= 2019 P(2015)+P(2016)+P(2017)+P(2018)+P(2019) 9+11+55+16+90 181 = = ≃0.928. 20+40+50+45+40 195 4. Total Impact Factor for year 2019: 34+38+135+28+90 325 IFTotal(J)= = ≃1.667. 2019 20+40+50+45+40 195 Therefore, according to the accuracy relationship of order > we have: a 1.667> 0.928> 1.1928> 0.747. a a a Whence, the exact (correct, most accurate) impact factor of journal (J) is equal to 1.667. BulletinofPureandAppliedSciencesSectionE-Mathematics&Statistics,Vol. 39E,No. 2,July-December,2020 1 8 Table 1: Illustrative table to show the comparative study of the proposed impact factors. 6 Example Journal (J) B ulle Year of Publication 2015 2016 2017 2018 2019 tin Number of published 20 40 50 45 40 o f P articles u re Year of citations 2015 2016 2017 2018 2019 2016 2017 2018 2019 2017 2018 2019 2018 2019 2019 a n d Number of citations per 6 15 4 0 9 19 0 8 11 10 70 55 12 16 90 A p plied year S Total number of 34 38 135 28 90 c ie n citations ce s S ec tio n E - M a th e m a tic s & S tatistic Flor s, en V t ol. in 3 S 9 m E , a No. ran 2 d , a J c u h ly e -D ece m be r , 2 0 2 0 Improved, extended, and total impact factor of a journal 187 9 Conclusion We have defined for the first time three new types of impact factors of a journal and we designed an accuracy relationship of order. On a numerical example each type of impact factor was computed. Upon each impact factor’s formula we clearly have: The Total Impact Factor is more accurate than theExtendedImpactFactor,whichismoreaccuratethantheImprovedImpactFactor,which,inturn is more accurate than the Garfield Impact Factor. Acknowledgments TheauthorisgratefultotherefereesandtheEditor-in-Chieffortheircomments which have helped him in upgrading the quality of this paper. References [1] Editors, Find impact factor / check impact index of thousands of worldwide journals, https: //www.resurchify.com/impact-factor.php BulletinofPureandAppliedSciencesSectionE-Mathematics&Statistics,Vol. 39E,No. 2,July-December,2020