Theory of IRE with (α,β,γ) norm”an engineering model for higher education management (HEM) policy administration in india

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Chapter 13

“Theory of IRE with
(α,β,γ) Norm”:

An Engineering Model for Higher
Education Management (HEM) &
Policy Administration in India
Ranjit Biswas
Jamia Hamdard University, India

ABSTRACT
This chapter introduces a new theory called by “Theory of IRE with (α,β,γ) Norm” which provides an
almost complete solution for Higher Education Management (HEM) & Policy Administration in any
vast country like India, China, France, Germany, Australia, Brazil, Indonesia, Pakistan, Malaysia,
USA, UK, Canada, Gulf countries and others in the world. The “Theory of IRE with (α,β,γ) Norm” is
an engineering model for solving HEM problems, basically seven major problems which are about:
(i) How To Continuously Monitor The Real Time Progress of Research Work of the Ph.D. Scholars in
the Universities/Institutions in any country by a Common Rule of the ‘Ministry of HRD’ (ii) A New
Improved Method for Recruitment of Teachers in Universities (iii) A New Method for Promotion Policy
of Teachers In Universities (iv) How to select the ‘Most Suitable Candidate’ for the various prestigious
awards/honors in a country (v) How to restrict the publications of bad quality research papers in fake/
bad journals? (vi) How to select the true experts for every visiting team of NAAC of UGC? and (vii) How
to select the ‘Most Suitable Candidates’ to fill-up the reserved quota. It is claimed that if this new theory
be implemented by the ‘Ministry of HRD (MHRD)’ in all its universities/institutions, then a huge amount
of quality-assurance can be achieved in pursuance of Excellence in Higher Education Management &
Policy Administration in that Country.

INTRODUCTION

This chapter introduces a new theory called by “Theory of IRE with (α,β,γ) Norm” which is an engineering model for Higher Education Management (HEM) & Policy Administration in vast countries like
DOI: 10.4018/978-1-5225-0672-0.ch013

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“Theory of IRE with (α,β,γ) Norm”

India, China, France, Germany, Australia, Brazil, Indonesia, Pakistan, Malaysia, USA, UK, Canada, Gulf
countries and others in the world. India and China are the two giant countries having a large number of
in-built talents in every subject area. Our model is called an engineering model because of the fact that
the model works dynamically on engineering & technology based elements: internet search engines,
several databases of heterogeneous big data, intelligent software, computer hardware and distributed
systems, mechatronics hardware, Information Technology, Electronics & Communication Engineering,
Mechatronics, Fuzzy Logic (Zadeh, 1965), Soft Computing, Big Data (Biswas, 2015a, 2015b), and of
course on Mathematics & Statistics of both R-Statistics and NR-Statistics (Biswas, 2016), up to the extent
of Big Data Statistics (Biswas, 2016). Retaining the idea, core logic and philosophy behind its innovation,
this model can be easily improved (extended) in future by the growth of various technologies, mainly
of the subject’s computer engineering, information technology and electronics engineering. In the giant
countries like India, China and other vast countries, every year a very large number of scholars take
admissions for higher education, a very large number of students become graduates and post-graduates,
a large number of students enroll for Ph.D. study, a large number of teachers retire in universities and
institutions, a large number of fresh teachers are recruited in universities and institutions, a large number
of teachers are promoted in universities and institutions, a large number of talents are awarded various
prestigious awards/honors, etc. and many other academic/research oriented activities which are controlled
by Higher Education Management (HEM) & Policy Administration. Consequently, the topic of Higher
Education Management (HEM) & Policy Administration in such giant countries is itself a big subject
and a major subject for their governments which cater to the overall academic/economic growth of the
countries. For a hypothetical example, in India (or China) there could be more than 10,000 eligible

candidates applying against only ten vacant post of Lecturers in Mathematics advertised in a newspaper.
There are many other similar HEM functionalities and activities on every day and are of concern to the
Government authorities on how to conclude daily work with correct, fair, transparent and successful
solutions. This is quite naturally not always the situation in small but academically advanced countries
like Japan, Finland, Ireland, Poland, Bulgaria, Singapore, etc. For the sake of smooth presentation of
our new theory entitled “Theory of IRE with (α,β,γ) Norm”, we have identified the country ‘India’ and
we have developed this theory in the context of ‘India’. But the theory can be well extended and applicable to other vast countries like China, Brazil, Indonesia, Pakistan, Malaysia, USA, UK, Canada, Gulf
countries and in fact to any country in this world be it a small or big, without making any changes in the
core philosophy/logic of the theory but incorporating slight customized adjustments in the equivalent
nomenclatures of the respective country. One basic assumption in the Theory of IRE is that there is
no rounding-off of any numerical results. Results of all numerical computations are to be made upto 3
decimal places only. Bracket expressions are to be computed with priority, in any complex mathematical
or logical expression in this theory.

THE MAJOR PROBLEMS OF MHRD IN INDIA IN HEM
There exists a body of the MHRD which is known as University Grants Commission (UGC) in India,
but may be with different nomenclatures in other countries. For instance, in Bangladesh, Pakistan, Sri
Lanka, Nepal, the body name is UGC whose expanded phrase is also University Grants Commission,
in UK and HK it is also UGC but it stands for the phrase University Grants Committee, etc. The main
role of UGC is to look after the Higher Education Management (HEM) & Policy Administration in the

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country. With no loss of generality, we shall use the nomenclature UGC all through in this article, but
the literature can be well customized and made compatible for any country incorporating in it the local
nomenclatures and terminologies of that country suitably.

In the last three decades in particular, India took a very bold step by allowing for privately run universities in the style of USA, by opening many new IITs, by opening many new NITs offering them the status
of university, by converting many colleges/RECs into universities/NITs. This is a major step taken by
India for the benefit of the people aspiring for higher studies in UG/PG programmes like B.Sc., B.Tech.,
M.Sc., LLB, LLM, MBA, M.Pharm, MBBS, BDS, M.Phil., M.Tech., and other Master Programmes
and Ph.D. etc. The today’s concern is not about the top-graded universities/institutions of India which
are few only. Today’s extreme concern is about most of the other universities in India, in particular the
private universities, newly born/converted universities, poorly graded Govt. universities, newly born
NITs, etc. To ensure at least a minimum amount of quality of education at Bachelor Programmes, Master
Programmes and Ph.D. programmes, the “Ministry of HRD (MHRD)” or UGC may have prescribed
across the country yardsticks to such universities (including private Universities and private colleges/
institutions) on various quality monitoring parameters viz. Teacher-student ratio, faculty qualifications,
faculty strength, maximum allowable students strength in a Theory class, in a Lab/Tutorial class, lab
requirements, space requirements, etc. Consequently, any university/college deviating from the prescribed
minimum requirements has to answer to the investigation team of the “Ministry of HRD (MHRD)” of
the country. Nevertheless, the real ground level scenario in such newly born poor government/private
universities/NITs is pathetic. The alarming consequences to India (or the concerned country) will be
resulted when in future the graduates of the poor institutes will take charge and responsibilities of some
office in Government or private organizations, will take decisions, will adopt self-constructed policies,
will implement those policies, etc; and the extremely alarming situation will happen when they will
become teachers to impart education, knowledge, ethics, morality, character elements, etc. because of
hidden propagation error of slow but continuous damages. However, there could be 0.1% or 0.2% or
more number of good graduates produced by them, whose cases are not of our concern.
Country’s growth, be it in economy or technology or science or literature or health/medical or politics or law & order or in any major/minor areas, depends always upon the new generation youths who
will take charge of the various kind of future responsibilities of the country as well as of the world. But
excellent quality of graduates/post-graduates cannot be produced until and unless the UG/PG academic
programmes be taught by excellent quality teachers.
An excellent quality of Syllabus/Schemes/Bye-laws for the UG/PG academic programmes cannot
be designed in universities and institutes until and unless there are excellent quality teachers/experts/
scientists available in the universities.
An excellent quality of Lectures, Practicals, Assignments, Continuous Evaluation, Question Papers

settings, Evaluation of Answer-scripts, Projects, Summer Training, Industrial Training, Internship, etc.
cannot be delivered/executed in a university/institutes until and unless there are excellent quality teachers/experts/scientists available in that university/institute.
An excellent quality of Professors, Scientists, Engineers, Doctors, lawyers, IAS/IFS/IPS and other
admin officers, Politicians, etc., cannot be produced in the country until and unless there are excellent
quality teachers available in the universities and institutes.
All these academic responsibilities are directly at the hands of the teachers, experts and scientists in
the universities, institutions and research centres or organizations. Teachers are the core architects of

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future developments of the country. The real backbone of a country’s development is thus managed by
the Higher Education Management (HEM) & Policy Administration of the country.
The content of this chapter is a proposal to the Ministry of HRD (MHRD) for a huge improvement in
the system of Higher Education Management (HEM), for the enhancement of academic quality in higher
education in universities/institutions controlled by UGC in India (Biswas, 2015f) corresponding to the
most important seven issues in HEM identified to be most prominent in the last three decades basically.
There are in reality many other problems and sub-problems, issues, etc. which can be well controlled if
these seven major problems be solved by developing a correct, precise and well documented new theories
and models which should work on the basis of actual data of universal coverage.

THE SEVEN IMPORTANT PROBLEMS OF MHRD (UGC) IN HEM
Problem 1
A new unique Method on: How to Continuously Monitor the Real Time Progress of Research Work of
the Ph.D. Scholars in the Universities/Institutions in India by a Common Rule of UGC across all the
Universities in India.

Problem 2
Proposing a new method to UGC (and the same to UNESCO) on: “How to restrict the publications of bad
quality research papers in fake/bad journals? How to control these activities in higher education system?”

Problem 3
Proposing a Common Rule for UGC on: “A New Improved Method for Recruitment of Teachers in
Universities in India.”

Problem 4
Proposing a new improved method to Govt. of India on: “How to select the ‘Most Suitable Candidate(s)’
to fill-up the reserved quota in academics?”

Problem 5
Proposing a Common Rule for UGC on: “A New Improved Method for Promotion Policy of Teachers
in Universities in India.”

Problem 6
Accreditation of universities/institutes in India: How to select the true experts for every visiting team
of NAAC?

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Problem 7
Proposing a new improved method to MHRD, Govt. of India on: “How to select the ‘Most Suitable
Candidate(s)’ for the various highly prestigious top awards/honors in India?” (viz. India Science Award,
Shanti Swarup Bhatnagar Prize, INSA Young Scientists Award, FNA, etc.)

With no loss of generality, we introduce in this chapter the “Theory of IRE with (α,β,γ) Norm” making
it compatible with the vast country ‘India’, but as already mentioned earlier that the theory can be well
extended and applicable to other countries too, incorporating the local adjustments. Before providing
excellent solutions to these seven problems one by one, we introduce a number of new terminologies
and new measures in the subject of ‘Higher Education Management’ (HEM). These measures play key
roles in our proposed “Theory of IRE with (α,β,γ) Norm”: a new model for almost a complete solution in
Higher Education Management & Policy Administration in vast countries like India, China, Brazil, Indonesia, Malaysia, USA, UK, France, Germany, Australia, Canada, Gulf countries and others in the world.
The chapter here is organized with the following 23 Sections (each section having its own subsections):
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278

INTRODUCTION
THE MAJOR PROBLEMS OF MHRD IN INDIA IN HEM
JOURNAL IMPACT FACTOR (IF)
H-INDEX, G-INDEX, in-INDEX (i10-INDEX) AND OTHER BIBLIOMETRIC INDICATORS
INTRODUCING THREE NEW BIBLIOMETRICS, AS CORRECTIONS OF THE EXISTING
NOTION OF POPULAR BIBLIOMETRICS: H-INDEX, G-INDEX AND iN-INDEX
(i10-INDEX)
INTRODUCING A POWERFUL BIBLIOMETRIC ‘BIBLIOMETRIC INDEX’ (BI) OF A
RESEARCHER
“HEM ENGINEERING CENTRE”: A HIGH COMPUTING CENTRE IN UGC
INTRODUCING NEW IMPORTANT MEASURES FOR HEM
JOURNAL PUBLICATIONS INDEX (JPI)
AN IMPORTANT ISSUE WITH THE IF: SOLUTION BY NORMALIZATION
‘SIMPSON AREA’ (SA) OF A RESEARCHER (FOR WHOM LRY ≥5)
TWIN SUMMARY TABLES FOR EVERY RESEARCHER
ON PROBLEM STATEMENT 1: HOW TO MONITOR REAL-TIME PROGRESS OF PH.D.
WORK OF A REGULAR PH.D. SCHOLAR IN A UNIVERSITY.
INTRODUCING “FIVE CONDITIONS PH.D. RULE OF UGC”
“THEORY OF IRE WITH (α,β,γ) NORM”
ON PROBLEM STATEMENT 2: HOW TO RESTRICT POOR RESEARCH PUBLICATIONS
IN BAD/FAKE JOURNALS: A PROPOSAL TO UGC (and to UNESCO)
ON PROBLEM STATEMENT 3: UGC MODELS FOR ‘RECRUITMENT OF TEACHERS’ IN
UNIVERSITIES
ON PROBLEM STATEMENT 4: THEORY OF IRE WITH “CODED RESERVATION
FORMULA” (CRF)
ON PROBLEM STATEMENT 5: INTERNAL PROMOTION SCHEME FOR TEACHERS IN
UNIVERSITIES
ON PROBLEM STATEMENT 6: ACCREDITATION OF UNIVERSITIES/INSTITUTES IN
INDIA: HOW TO SELECT TRUE EXPERTS FOR EVERY VISITING TEAM OF NAAC?


“Theory of IRE with (α,β,γ) Norm”

•
•
•
•

ON PROBLEM STATEMENT 7: HOW TO SELECT THE “MOST SUITABLE CANDIDATE(S)”
FOR THE HIGHLY PRESTIGIOUS AWARDS/HONORS IN INDIA?
CONCLUSION
REFERENCES
KEY TERMS AND DEFINITIONS

The “Theory of IRE with (α,β,γ) Norm” is not and cannot be an absolutely frozen theory, except its
basic philosophy and architectural logic. The implementation of the theory is based upon internet search
data, upon the capability of searching with well coverage big data in internet, upon new and new type of
updated/improved bibliometrics being developed by the scientists every decade, etc. This theory may be
regarded as a new area in the subject of “Big Data Statistics” introduced in (Biswas, 2016). The Hadoop
and r-Atrain in ADS (Atrain Distributed System) are the most useful models developed in last decades to
deal with big data of any 4Vs (Biswas, 2015a; 2015b). The future improvement of the “Theory of IRE
with (α,β,γ) Norm” will certainly depends upon: How does the new subject “Big Data Statistics” grow
with time, What kind of new soft-computing statistical measures in R-Statistics or NR-Statistics (Biswas,
2016) be developed in future to model excellent kind of new bibliometrics of dynamic nature for the
researchers in the world, etc. However, the new bibliometrics ‘Hm-index’, ‘Gm-index’ and ‘im10-index’
introduced in this chapter can surely dominate the existing corresponding most popular bibliometrics
H-index, G-index and iN-index (i10-index).
We propose that our “Theory of IRE with (α,β,γ) Norm” be considered by the “Ministry of HRD

(MHRD)” of the concerned country, for implementation in all the universities or higher level institutions across the country. The complete theory can be easily implemented by a software-based HEM
System of the MHRD (a good HEM software package for the “Theory of IRE with (α,β,γ) Norm” can
be well developed by any good team of programmers, and hence the issue of software development is
not discussed in this chapter). JOURNAL IMPACT FACTOR (IF)
We begin with a brief note on the existing notion of Impact Factor (IF) of a journal, the notion which
is uniquely recognized by all the academic universities/institutes across the world.
The notion of “Impact Factor (IF)” of a Journal was devised in 1955 by Eugene Garfield, the founder
of the Institute for Scientific Information (ISI) in 1960, now part of Thomson Reuters. Impact Factors
(IF) are calculated on ‘yearly basis’ for those journals that are indexed in Thomson Reuter’s annual
Journal Citation Reports (JCR). Other related journal-level metrics include: Source normalized impact
per paper (SNIP) which is a factor released in 2012 by Elsevier based on Scopus to estimate impact.
The PageRank algorithm is a kind of recursive impact factor that gives citations from journals with high
impact greater weight than citations from low-impact journals. Such a recursive impact factor resembles
Google’s PageRank algorithm. Before recollecting a brief about IF, we present first of all the meaning
of the simple phrase ‘Core Subject’ which will be used throughout in this chapter.

Core Subject
The subjects like Mathematics, Statistics, Botany, Zoology, Sociology, Computer Science (Computer
Engineering), Electronics Engineering, Mechanical Engineering, Law, etc. are the core subjects in which
usually bachelor degrees are awarded by universities. Usually, the department names in a university exist in the name of core subjects. For example, while ‘Computer Science’, ‘Mathematics’, ‘Philosophy’,
‘Zoology’ are core subjects but an area like ‘Computer Network’ or ‘Algorithm’ or ‘Geometry’ will not

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be regarded as a core subject in our discussion here. They rather example of areas belonging to one or
more of the respective core subjects. Throughout our discussion in this article, we use the words ‘core

subject’ (or ‘subject’, in short) and ‘department name’ as synonyms.

About JCR
Journal Citation Report or JCR is issued by Thomson Reuter. Journal Citation Reports (JCR) offers a
systematic and objective means to critically evaluate the world’s leading journals, with quantifiable,
statistical information based on citation data. By compiling articles’ cited references, JCR Web helps to
measure research influence and impact at the journal and category levels, and then shows the relationship
between citing and cited journals. The JCR is an excellent design of the database of indexed journals. It
offers the following important information to the researchers of the world:
1. Sort journal data by clearly defined fields: Impact Factor, Immediacy Index, Total Cites, Total
Articles, Cited Half-Life, or Journal Title.
2. Sort subject category data by clearly defined fields: Total Cites, Median Impact Factor, Aggregate
Impact Factor, Aggregate Immediacy Index, Aggregated Cited Half-Life, Number of Journals in
Category, Number of Articles in Category.
3. View a journal’s impact with a five-year Impact Factor trend graph.
4. Understand a journal’s citation influence and prestige with Eigenfactor Metrics — five-year metrics
that consider scholarly literature as a network of journal-to-journal relationships.
5. Visualize impact factor by journal category with impact factor boxplots.
6. Rank journals in multiple categories.
7. See how journal self-citations affect impact factor.
8. Full integration with ISI Web of Knowledge lets you link from Web of Science to JCR Web; from
JCR journal records to ulrichsweb.com and recent Current Contents Connect tables of contents;
and to and from your library’s OPAC.

Indexed Journal
In our work here, a journal is termed as an ‘indexed journal’ if it is indexed in Thomson Reuter’s annual
Journal Citation Reports (JCR), indexed by SCI/SCIE (Science Citation Index Expanded).
By the term ‘indexed journal’ henceforth in this work, we shall always mean those journals by the
above definition only, i.e. which are indexed by SCI/SCIE (Science Citation Index Expanded).

Impact Factor (IF)
Impact Factor of an indexed journal in a given year is a finite non-negative real number. It is calculated
every year for every indexed journal. For a journal its IF varies from year to year; in some year it may
rise up, for another year it may fall down. But it cannot be a negative number, and is always a finite
number. A good journal can retain good IF every year by retaining its quality.
“Impact Factor” is defined as below:

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The “Impact Factor (IF)” of an indexed journal in a given year = the average number of citations
(in this journal or in any other indexed journal) received per paper which are published in that journal
during the n number of preceding years (where n ≥ 2, but a good value of n is 5 or more).
Thus, IF of a journal for the year Y can be calculated in the year (Y+1) or afterwards, not in the year
Y or before the year Y.
For example, if we choose n = 2 and if an indexed Journal has an Impact Factor (IF) of 1.3 in the
year 2014, it means that its all the papers published in 2012 and 2013 has received 1.3 citations each on
average in 2014 in indexed journals including itself.
How to calculate IF of an ‘Indexed Journal’ in a given year?
If the journal is not an indexed journal, there is no question of computing its IF. So we consider
here only the indexed journals, not the other journals (i.e. neither sub-indexed journals or non-indexed
journals, the new terminologies which are introduced later in this work).
We explain below the method of computing IF of an indexed journal by an example (with hypothetical data, for the sake of understanding only).
Consider a journal “JOURNAL OF XYZ”. The ‘2014 Impact Factor (IF)’ of this journal “JOURNAL
OF XYZ” with n = 2 would be calculated as follows:
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•

Let A = the number of times “the articles which were published in the JOURNAL OF XYZ during
2012 and 2013” were cited by all indexed journals during 2014.
Let B = the total number of “citable items” published by that journal JOURNAL OF XYZ in 2012
and 2013. Those which are not cited will not be counted. (“Citable items” means research papers
or articles, or notes; but not editorials publications or Letters-to-the-Editor, etc. There is no guarantee that a ‘citable item’ will be or have been cited in subsequent years).

Then, the ‘2014 IF’ of the journal ‘JOURNAL OF XYZ’ with two years (n = 2) consideration is
equal to = A/B. Clearly, IF of any journal in any year is a non-negative real number.
It may be noted that “2014 Impact Factor” of a Journal ‘JOURNAL OF XYZ’ are to be calculated
in the year 2015, NOT in the year 2014; because it cannot be calculated until all of the 2014 publications of JOURNAL OF XYZ and of other indexed journals have been investigated and then processed
by the indexing agency JCR. Thus impact factor for the nth year can be calculated on (n+1)th year only
or later, not earlier.

H-INDEX, G-INDEX, iN-INDEX AND OTHER BIBLIOMETRIC INDICATORS
The H-index is a bibliometric proposed by Jorge Hirsch in 2005 (Hirsch, 2005; Egghe, 2006a, 2006b,
2006c; Jin, 2005, 2006, 2007). A researcher has H-index equal to h if h of his N number of published
papers have at least h number of citations each, and the other (N−h) papers have no more than (h-1)
number of citations each. Thus the H-index is always a non-negative integer. The H-index reflects both
the number of publications and the number of citations per publication. The index is designed to improve
upon simple measures such as the total number of citations or publications. The index works properly
only for comparing researchers working in the same field; citation conventions differ widely among different core subjects. The h-index “gives an estimate of the importance, significance, and broad impact
of a scientist’s cumulative research contributions”. But the H-index has a lot of demerits too.

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The G-index was suggested by Leo Egghe in 2006. Given a set of publications of a researcher ranked
in decreasing order of the number of citations that they received, the G-index is the largest number such
that the top g publications have received together at least g2 citations i.e. most cited g papers have been
cited g or more times on the average. It is doubtful to the world academicians whether G-index is a better metric than H-index or whether H-index is a better metric than G-index. But it is fact that both are
good and have their independent in-built significance.
The iN-index is the number of articles with N or more citations, where N is a natural number. For
N = 10, the i10-index is simply the number of articles with 10 or more citations, the idea being that ten
citations means it got looked at. Similarly, the i100-index is the number of articles with 100 or more citations, the i500-index is the number of articles with 500 or more citations, etc. for different values of N.
There are several other bibliometrics which are m-index, c-index, s-index, e-index, RG score, etc.
defined on the basis of citations, but they are of very particular nature and of limited significance. Research is going on to find out a kind of absolutely best index metric applicable to all the researchers of
all the subjects.

How to Calculate H-Index of a Researcher Mr.X?
Let f is the function that corresponds to the number of citations for each publication. Consider a researcher
Mr. X. We compute the H-index of the researcher X as follow:
First we order the values of f in descending order. Then, we look for the last position in which f value
is greater than or equal to the position. This position h is accepted as the H-index of Mr.X.
For example, suppose that the researcher X has 6 publications P1, P2, P3, P4, P5 and P6 with 21,
17, 8, 5, 5 and 2 citations respectively. Then, f(P1) = 21, f(P2) = 17, f(P3) = 8, f(P4) = 5, f(P5) = 5 and
f(P6) = 2. Clearly the H-index of Mr.X is equal to 5.
One major demerit of H-index can now be explained by an example. Suppose that another researcher
Y has also 6 publications P1, P2, P3, P4, P5 and P6 with 3100, 2700, 1800, 1500, 5 and 2 citations
respectively. The data shows an excellence of the researcher Y having huge impact out of his top four
publications, unlike the researcher X. But the H-index of Mr. Y is also equal to 5, the H-index of Mr.X!,
i.e. the H-index of both the researchers X and Y are appearing equal. Thus one cannot compare the
researchers X and Y by the values of their respective H-index only.

INTRODUCING THREE NEW BIBLIOMETRICS, AS CORRECTIONS
OF THE EXISTING NOTION OF POPULAR BIBLIOMETRICS:
H-INDEX, G-INDEX AND iN-INDEX (i10-INDEX)

The H-index is a good indicator, but it has a lot of weakness too. For an instance, consider the publication P1 of the researcher Mr. X and the publication P2 of the researcher Mr. Y. Suppose that P1 is a
single-authored paper and P2 is a multiple authored paper (five authors: Mr. Y and four co-authors).
Also suppose that P1 and P2 both are cited 1000 times so far by various researchers around the world.
Although both P1 and P2 has 1000 citations, but much more credit goes to Mr. X compared to Mr. Y.
This is a very important and significant issue to do justice to the method of estimation of index. This
logic is missing in the existing notion of H-index, G-index, i10-index and any other existing indices.

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We introduce below a new and modified version of H-index called by Hm-index, which removes the
inner and in-built weakness of the metric H-index caused due to number of co-authors. The notation Hm
here stands for ‘H modified’. The Hm-index is constructed considering the philosophy that one paper if
authored by a single researcher instead of multiple researchers should cater to full h-index to the author,
and if it is multiple authored then the h value is to be shared equally among all the authors. But one
further level of improvement of the newly introduced Hm-index can be made considering the amount or
weight of individual contribution of each author in a multi-authored publication, and proportionately
sharing the value of h accordingly. Truly speaking, as on today, it is an impossible task.

Introducing ‘Hm-Index’ of a Researcher
Suppose that at a certain day the researcher X has H-index equal to h. Consider his top h number of
publications (on the basis of number of citations) which are P1, P2, P3, …, Ph. Suppose that the publication Pi has ni number of authors (self and (ni – 1) number of co-authors) where ni ≥1 for each i = 1,
2, 3, …,h. Then the Hm-index of the researcher X is defined by
Hm-index = h2/n, where n =

h

∑n
i =1

i

.

As a particular case, if all the publications of a researcher are single-authored then n =

h

∑n
i =1

i

= h,

and in that case Hm-index reduces to H-index value h. The Hm-index is an improved version of H-index
as it gives due weightage to the single authored publications, or multiple authored publications according to the number of authors in the publications. In fact, Hm-index is a major correction of the existing
popular concept of H-index.

Introducing ‘Gm-Index’ of a Researcher
In a similar way, one can define Gm-index. Suppose that the researcher X has G-index equal to g. Consider his top g number of publications (on the basis of number of citations) which are P1, P2, P3, …,
Pg. Suppose that the publication Pi has ni number of authors (self and (ni – 1) number of co-authors),
where ni ≥1 for each i = 1, 2, 3, …, h. Then the Gm-index of the researcher X is defined by
Gm-index = g2/n, where n =

g

∑n
i =1

i

.

As a particular case, if all the publications of a researcher are single-authored then n =

g

∑n
i =1

i

= g,

and in that case Gm-index reduces to G-index value g. In fact Gm-index too is a major correction of the
existing popular concept of G-index.

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Introducing ‘im10-Index’ of a Researcher
In an analogous way, one can define imN-index and in particular the im10-index of a researcher incorporating the similar type of corrections in the existing concept of iN-index (i10-index). The ‘H-index’,
‘G-index’ and ‘i10-index’ (and even i5-index) may not be available for the beginners in research (say,

for a Ph.D. scholar in a university) even if he be an excellent researcher, because of short duration of
time. Consequently, the ‘Hm-index’, ‘Gm-index’ and ‘im10-index’ too may not exist for the beginners.
The notion of Hm-index, Gm-index, im-10 index can be further revised if the piece-wise information
about research contributions (weights) of each individual author in multi-authored publications can be
known. But as on today, probably it is not possible.
(Note: There are a number of several metrics for ranking of journals have emerged over the last
years in the literature in an effort to broaden the evaluation of scholarly journals (inger.
com/gp/authors-editors/journal-author/journal-author-helpdesk/impact-factor/18684). For example,
Eigenfactor, Google Scholar Metrics, SJR, SNIP, etc. The Eigenfactor is similar to the notion of Journal
Impact Factor, but weeds out journal self-citations. The citation frequency as well as the prestige of the
journals is taken into account. The type of publication and the citation patterns of different disciplines
are not considered in Eigenfactor. The Google Scholar Metrics summarize the recent citations to many
publications. One can browse the top 50 publications in several languages, ordered by their five-year
h-index and h-median metrics. The SJR-SCImago includes the journals and country specific indicators
developed from the information contained in the Scopus® database from 1996 onwards. This metric does
not consider all citations of equal weight; the prestige of the citing journal is taken into account. Besides
that, self-citations are not included in the calculation of SJR. The SNIP (Source-Normalized Impact per
Paper) measures a contextual citation impact by weighing citations based on the total number of citations in a core subject. It helps to make a direct comparison of sources in different core subjects. SNIP
especially considers the frequency at which authors cite other papers in their reference lists, the speed
at which citation impact matures. All these metrics have a lot of demerits too, besides their own merits).

INTRODUCING A POWERFUL BIBLIOMETRIC
“BIBLIOMETRIC INDEX” (BI) OF A RESEARCHER
The Hm-index, Gm-index and im10-index are corrected versions of the existing popular H-index, G-index
and i10-index respectively. These new indices are more useful indicators to quantify research talent of a
researcher because in these new indices the unfairness part of the existing popular H-index, G-index and
i10-index are removed by their ways of respective constructions. But none can be identified as absolutely
best, and at the same time none can be ignored too. Each of these indices independently has its own
merit and significance. For example, it is very common that two researchers may have equal Hm-index
but one may have much higher Gm-index than the other, and conversely. The cumulative amount of Hm,

Gm and im-10 indices rather can play a better role than any of the individuals among Hm, Gm and im-10
to measure the research performance of a researcher (who is not a beginner). Consequently, we define a
new powerful index called by Bibliometric Index (BI) of a researcher which is defined by:
BI = Hm-index + Gm- index + im10-index.

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Surely BI is a comprehensive index and better index than Hm, Gm and im-10 indices to compare the
research performance of n number of researchers in a given core subject S.

“HEM ENGINEERING CENTRE”: A HIGH COMPUTING CENTRE IN UGC
Although UGC like all other government offices is using computers/softwares for all its daily functioning, but there are need of high computing very rich and large labs in a centre in UGC called by “HEM
Engineering Centre” with one rich Big Data Computer Lab, with many other IT Labs, one Electronics
Lab and other labs, with sufficient number of computers and other engineering equipments and infrastructures. This is a mandatory requirement for successful implementation of the engineering model of
Higher Education Management (HEM) proposed by us in this chapter. The “HEM Engineering Centre”
will play a very important role in HEM in a country like India having a large number of universities,
institutions and colleges. Even as a mandatory requirement, the administration of this “HEM Engineering
Centre” is to be controlled by engineers only (preferably IT engineers or software engineers or electronics engineers) with the following hierarchy:
Director
Associate Director
Assistant Director
Sr. Technical Assistant
Technical Assistant, etc.
The Director is the overall in charge of the “HEM Engineering Centre,” who must be a very senior and
exceptionally talented M.Tech. & Ph.D. degree holder in Computer/IT/Electronics engineering. All data
processing job, website maintenance and updates, uploading of all HEM data of national importance, etc.

are done by the office of the Director. The Big Data Computer Lab of the “HEM Engineering Centre”
should preferably work in ‘Atrain Distributed System’ (ADS) using the data structures Atrain and Train
which are exclusively suitable for big data (Biswas, 2011, 2012, 2013, 2015a, 2015b). The importance
of the huge roles and responsibilities of the Director is one of the major keys of UGC for successful
implementation of the “Theory of IRE with (α,β,γ) Norm” in all the universities across the country.
For Higher Education Management (HEM) & Policy Administration in vast countries like India, China,
France, Germany, Australia, Brazil, Indonesia, Pakistan, Malaysia, USA, UK, Canada, Gulf countries
and others in the world, where there are large number of enrollments every year, large number of recruitments every year, large number of promotions every year in large number of universities, institutions
and colleges, no proper monitoring of quality can be done without a precise and rigid organizational
structure of the “HEM Engineering Centre ”. The justification behind the requirement of so many manpower (engineers) will be clearly understood while arriving at the end of “Theory of IRE” in this chapter.

INTRODUCING NEW IMPORTANT MEASURES FOR HEM
Making excellence in HEM is not an easy task. Both India and China have been following traditional
style in HEM. The government does not have any strong mathematical models in the policy administra-

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tion by which a continuous excellence can be achieved correctly, fairly and transparently in HEM with
guarantee. The existing methods followed are all obsolete methods. The proposed Theory of IRE in this
article provides a momentum in improving the HEM because of its powerful scientific and engineering construction and a comprehensive architecture. Before introducing new important measures for the
‘Theory of IRE’, we define few more terminologies which will be frequently used in our chapter. In our
proposal here henceforth, by IF (Impact Factor) we mean only the IF of Thomson Reuters, not of any
other organizations or agents.

‘List of AOIA’ of a Core Subject
Corresponding to every core subject, there are some indexing agents in the world which seem to be

growing well, doing well, seem to be promising, but presently not up to the excellence of SCI/SCIE.
The UGC has an excellent pool of “(α,β,γ) normed Type-1 experts” with respect to some pre-fixed high
value of (α,β,γ) corresponding to every subject (but different for different subjects) to give excellent
judgment on who are the other indexing agents in the world which seem to be growing well, doing well,
seem to be promising, and acceptable temporarily.
(Note: the new notion of “(α,β,γ) normed Type-1 experts” in the ‘Theory of IRE’ is explained later
in this article).
The abbreviation AOIA stands for “Acceptable Other Indexing Agents”. It is dependent upon the
concerned core subject of the area of research. This is a list of other indexing agents. By the word ‘other’, we mean here the agents other than the Thomson Reuter’s annual Journal Citation Reports (JCR)
indexed by SCI/SCIE. For every core subject, UGC will display a corresponding List of ‘Acceptable
Other Indexing Agents’ (AOIA) in its own website. List of AOIA is different for different core subjects.
UGC will never display the list of journals, but the list of ‘Acceptable Other Indexing Agents’ (AOIA)
in its website. UGC will update all these lists every year once in the month of January. All the research
scholars of all the universities in India may look at the updated list in UGC site in January every year.
For a hypothetical example, corresponding to the core subject “Computer Science”, the following
list may be displayed by UGC in its own website as its prescribed List of ‘Acceptable Other Indexing
Agents’ (List of AOIA) approved by an excellent pool of “(α,β,γ) normed Type-1 experts” in Computer
Science identified by UGC.
AOIA for “Computer Science”: Scopus, Academic Journals Database (Switzerland), Referativnij
Zhurnal (Russia), Zentralblatt fur Mathematik (Germany), MathSciNet (American Mathematical Society), Mathematical Reviews, Ulrich, Zeitschriften, IEEE Xplore.

Sub-Indexed Journal
There are some journals in the world in every core subject and seem to be doing well and growing well
but presently not ‘indexed journals’ as per our Definition presented earlier. If such a journal on a core
subject be indexed by any of the corresponding ‘List of AOIA’ prescribed by UGC, then it is called a
Sub-Indexed Journal in our Theory of IRE.

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Non-Indexed Journal
There are a number of journals (having ISSN) which are neither indexed journals nor sub-indexed journals. However, they may be indexed by some other agents not listed in the ‘List of AOIA’ of UGC or
may not be indexed at all. Such a journal is called a Non-Indexed Journal in our Theory of IRE.
Unfortunately, most of the journals in the world in any core subject nowadays are of this category,
unlike the situation of the preceding century.
The next definition is proposed by us with the objective for not blindly discouraging the researchers
to make publications in the sub-indexed journals too (if not in indexed journals). Decision is to be taken
by the researcher himself by doing self-assessment of the quality of the work done.

Provisional Impact Factor (PIF)
Only the sub-indexed journals can qualify to possesses PIF, neither indexed journals nor the non-indexed
journals. The PIF of a sub-indexed journal in a core subject in a given year is equal to the minimum value
of the IF values of all the indexed journals in that core subject in that year. The PIF of a sub-indexed
journal may vary every year.
To check the list of indexed journals and their IF, one could visit the sites:
.
/> /> />For example, consider any sub-indexed journal in the core subject ‘Computer Science’. Suppose that
the minimum value of all the IF values of all the indexed journals in Computer Science is 0.04 in the
year 2014. Then the PIF values of that sub-indexed journal for the year 2014 is 0.04. In fact, for a given
core subject the PIF of all its sub-indexed journals are equal in every year.

Which Journals Can Qualify to Possesses an IF?
If a Journal does not qualify to be indexed by Thomson Reuter’s annual Journal Citation Reports (JCR),
then question does not arise of having an ‘IF’ for this journal. Only indexed journals can qualify to
Thomson Reuter’s to possesses IF. There is no question arises like: “Whether an indexed journal can
have PIF?”. It is an invalid question, because it is not a sub-indexed journal and it already possess IF.
However, a journal (not an indexed journal, but either a sub-indexed journal or a non-indexed journal)

may carry a value of some kind of so-called IF which it prints on it and which is usually computed by
the concerned journal authority itself or by some private unauthorized organization/agent, but those type
of IF are not to be considered to be valid in our ‘Theory of IRE’ here (figure 1). There should not be
any confusion in it. To get more information about IF and fake IF, one could visit the link: http://www.
oajournals.info/impact-factor-2012-list/, and ).

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Figure 1. Three types of journals in a subject S

WHICH JOURNALS CAN QUALIFY TO POSSESSES AN PIF?
Only the sub-indexed journals can qualify to possesses PIF, neither indexed journals nor the non-indexed
journals. PIF varies from year to year for every sub-indexed journal.

“Impact Factor Score” (IFS) of a Researcher for Every Publication
For a beginner (say, a new researcher or a Ph.D. Scholar in a university), the number of citations of their
first or second publication may not come into birth during the short tenure of Ph.D. scholar which is the
beginning year(s) of him. Consequently, the Hm, Gm or im10 index are not applicable to his case to quantify his research performance, even if he be of an excellent research potential. But for such a beginner,
a publication in a “good journal of good IF” certainty guarantees the quality of his publication, at least
a minimum guaranteed amount can be always certified. Consequently, a beginner for whom Hm or Gm
or im10 is not available presently which he can use for self-assessment of his own research performance,
the IF of the journals is the only authenticated indicator which can guarantee him for his self-satisfaction
that his publications are good, because the journals with good IF do always follow a rigorous evaluation/
review system by a true implementation procedure involving top quality reviewers/experts in the area
concerned. With this philosophy in mind we introduce below the notion of “Impact Factor Score” (IFS)
of a Researcher (beginner or senior) corresponding to each publication of him.

Impact Factor Score (IFS) is a finite non-negative real number. It is a score earned by a researcher
(a Ph.D. scholar or a senior researcher or a teacher or a Scientist) corresponding to each publication of
research paper by him in an indexed or sub-indexed journal. Suppose that a research paper P, jointly
authored by x number of authors, has been published in an indexed or sub-indexed journal “Journal of
ABC” in the year Y. Then by virtue of this publication P, each of these x number of authors earns an
individual score called by ‘Impact Factor Score’ (IFS) which is equal to the non-negative real number
i/x, where i is the IF or PIF of the journal “Journal of ABC” in the year Y. It is obvious that an IFS can
not be a negative number, and is always a finite non-negative real number. IFS plays a very important
and a highly significant micro level role in our proposal on “Five Conditions Ph.D. Rule of UGC”, which
is proposed in subsequent section here.

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We explain IFS by a hypothetical example below (not real data):
Suppose that a research paper entitled “A Dynamic Fuzzy Routing Algorithm” has been published
by three authors in an indexed or sub-indexed journal “International Journal of Information Security
and Management” details of which is as mentioned below:
Ranjit Biswas, Supriyo De and Bashir Alam, A Dynamic Fuzzy Routing Algorithm, International
Journal of Information Security and Management, Vol.8(3) (2009) 214-226.
Suppose that the IF or PIF of this indexed or sub-indexed journal “International Journal of Information Security and Management” in the year 2009 is 1.41.
Then by virtue of this publication, the author Ranjit Biswas earns IFS = 1.41/3 = 0.47 in his credit.
Similarly, the author Supriyo De earns IFS = 0.47 in his credit, and the author Bashir Alam too earns
IFS = 0.47 in his credit.
However, instead of equal share of IF or PIF among the authors, we also propose for proportionate
distribution of the IF corresponding to each publication to define the term “Proportional IF Score (PIFS)”
for different authors according to individual contributions. We do not recommend that this metric PIFS

be applicable initially to the private universities or to the lower graded Govt. universities, in particular
while one author be a Ph.D. scholar. Nevertheless, we present below the definition of PIFS for our future
direction of research work only.

“Proportional Impact Factor Score” (PIFS) of a
Researcher for Every Publication
Proportional Impact Factor Score or PIFS is a finite non-negative real number. It is a score earned by
researchers (Ph.D. scholars or Professors or Scientists or teachers, etc) corresponding to each publication
of research paper in indexed or sub-indexed journals on the basis of the amount of actual individual
contribution of all the authors of the paper. Suppose that a research paper P, jointly authored by x number of authors A1, A2, A3, …, Ax has been published in an indexed journal “ABC” in the year Y. Suppose
that, in this work, the contribution of the author Ai (i = 1, 2, 3, …, x) is wi%. Then, by virtue of this
publication P, each of these x number of authors Ai earns an individual score called by ‘Proportional
Impact Factor Score’ (PIFS) according to his amount of contribution which is equal to the non-negative
real number α.wi/100, where α is the IF or PIF of the indexed or sub-indexed journal “ABC” in the year
Y and

x

∑w
i =1

i

= 100.

It is obvious that a PIFS cannot be a negative number, and is always a finite number. Also, in case
the contribution of all the authors are equal then the notion of PIFS reduces to the notion of IFS. And
hence, for a single authored paper, PIFS and IFS of the author are trivially same.
We explain PIFS by a hypothetical example below (not real data):
Suppose that a research paper entitled “A Dynamic Fuzzy Routing Algorithm” has been published

by three authors in an indexed or sub-indexed journal “International Journal of Information Security
and Management” details of which is as mentioned below:
Ranjit Biswas, Supriyo De and Bashir Alam, A Dynamic Fuzzy Routing Algorithm, International
Journal of Information Security and Management, Vol.8(3) (2009) 214-226.
Suppose that the IF or PIF of the indexed or sub-indexed journal “International Journal of Information
Security and Management” in the year 2009 is 1.41. Also suppose that the contribution of the author

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Ranjit Biswas in this work is about 50%, the contribution of the author Supriyo De in this work is about
20%, the contribution of the author Bashir Alam in this work is about 30%.
Then by virtue of this publication, the author Ranjit Biswas earns PIFS = 1.41 × 50/100 = 0.705 in
his credit. Similarly, the author Supriyo De earns PIFS = 1.41 × 20/100 = 0.282 in his credit, and the
author Bashir Alam too earns PIFS = 1.41 × 30/100 = 0.423 in his credit.

How to Earn IF/PIF from International Conferences?
Many of the International Conferences being of high standard (say, IEEE Conferences) publish the selected
excellent papers in indexed or sub-indexed journals too, besides publishing all the accepted papers in their
own Proceedings. Consequently, by contributing papers in such type of good conferences, a researcher
may also earn IF or PIF, if his paper does also come in their list of selected papers for publication in their
indexed or sub-indexed journals. The ‘Call for Paper’ (CFP) for a good conference always announces the
names of the journals where the conference organizer will publish selected papers, besides publishing
all the accepted papers in the Conference Proceedings.

LRY of a Researcher at a Real Instant of Time D
It is fact in almost 100% cases that for a teacher or a scientist or a statistical officer or a computer engineer

or an economist or holding any post related to academic/research, the research work for him commences
after his acquiring of Master degree. Exceptional cases are always exceptional, one extraordinary boy
may produce a new theory even while studying at his school/bachelor, or in contrast one person may
start research and produce a revolutionary theory at the age of 65 without producing any result earlier.
But in general, ignoring those exceptional cases, for any researcher his research work is expected to start
after his Master degree. The “Length of Research Years” (LRY) of a researcher is a dynamic value which
is to be computed by a simple straightforward arithmetic. It is basically the age of his Master degree.
Consider together the month and year of final semester/year marksheet(pass) of the Master degree of
the researcher denoted by M = (m,y). This paired value M is to be considered as a single entity data and
for a given researcher it is obvious that the value M is fixed for him for lifetime.
Now consider any date D after the date M. In the Theory of IRE, the “Length of Research Years”
(LRY) of a researcher at a real instant of time D is the real number N/12 where N is the total number
of months (including the extreme months: the month of M and the month of D) counting from M to D.
It is to be noted that the value of LRY of a researcher does not get effected whether he does research or
does not do research after his Master degree.

JOURNAL PUBLICATIONS INDEX (JPI)
This is true that the quality of research work of a researcher cannot be judged by the IF of the journals
only, except that a guarantee about some amount of quality of his publication can be blindly certified.
Each of the Hm-index, Gm-index, im10-index and surely the BI is rather a good indicator to be considered
for adjudging the research performance of the researcher. But for a researcher who is the beginner in
doing research, in particular for a Ph.D. scholar who has just started publishing papers for his Ph.D.
degree, the Hm-index or Gm-index or im10-index or the BI (or any such index which are based on the
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“Theory of IRE with (α,β,γ) Norm”

number of citations) cannot be used to estimate the progress of his research work in quality or quantity.

Nevertheless, a journal of good IF guarantees that any publication in it will be of good quality, at least
maintaining a quality of minimum acceptable threshold value. For example, a publication in any of the
IEEE Transactions, ACM transactions, in NATURE, in SCIENCE, etc. will be surely of good quality by
default. Therefore, for a Ph.D. scholar or for a beginner (or even for any senior researcher), publications
in journals of good IF surely ensures the quality of publications, but may not estimate exactly how much
is the quality. We here make use of the IF/PIF metric to ensure the progress of a Ph.D. research scholar
in our Theory of IRE. But we do not even ignore it for the senior or experienced researchers too. For
senior or experienced researchers, we use it as one input data only, out of the several other input data,
to judge their research potential and talent.
Consequently, in this section we define a new measure Journal Publications Index (JPI) for every
researcher (beginner or senior). There are three types of JPI for every researcher as below (see figure 2):
1. YJPI, used for evaluating his yearly performance
2. CJPI, used for evaluating his cumulative performance, and
3. AJPI, used for evaluating his average performance.

“Yearly Journal Publication Index” (YJPI) of a Researcher at the Year Y
Yearly Journal Publication Index or YJPI of a researcher at the year Y is denoted by the notation (YJPI)Y
and is defined by the yearly earned sum total of all the IFS of him at the year (Y-1). By a year, we mean
the English calendar year from January to December.
Thus, by default the YJPI = 0 in the first year of any researcher in his research career.

“Cumulative Journal Publication Index” (CJPI) of a Researcher
Cumulative Journal Publication Index or CJPI is a finite non-negative real number possessed by the researchers (Professors, Scientists, teachers, research scholars, etc) at a given point of time, and is defined by:
Figure 2. Three types of JPI for every researcher

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“Theory of IRE with (α,β,γ) Norm”

CJPI of a researcher at a point of time = Sum of his all IFS earned so far in his research career, at
that point of time.
CJPI is a kind of cumulative score earned by researchers by earning IFS, and hence CJPI of a researcher varies with time. It is obvious that CJPI of a researcher is a non-decreasing index because it is
a kind of cumulative statistic. For any researcher, his CJPI begins with the value 0, and then it increases
with good publications of him in indexed or sub-indexed journals with time. The CJPI does not increase
by way of publications in non-indexed journals or in poor journals or by contributing in such type of
Seminars/Conferences which cannot add any PIF to the researcher.
Thus, for any researcher if we draw his “CJPI - t” graph which is a graph of “CJPI” against the independent variable ‘time t” where t runs from the value 0 i.e. from the initial day of his research, then we
can see that it is a continuous non-decreasing step-up graph with
d
(CJPI) ≥ 0 at every point of time.
dt
For a good researcher, the number of steps will be more in the “CJPI – t” graph. For an excellent
researcher, there will be one more observation that most of the step-heights will be larger in the graph.

A Hypothetical Example
Recollect the previous hypothetical example of publication jointly authored by the three researchers:
Ranjit Biswas, Supriyo De and Bashir Alam. Suppose that prior to this publication, CJPI of the researcher
Ranjit Biswas was 19.21, CJPI of the researcher Supriyo De was 13.89 and the CJPI of the researcher
Bashir Alam was 17.63 in their respective credits.
Then, by the performance of this publication, the updated CJPI of the researcher Ranjit Biswas is
now 19.21 + 0.47 = 19.68, the updated CJPI of the researcher Supriyo De is now 13.89 + 0.47 = 14.36,
and the updated CJPI of the researcher Bashir Alam is now 17.63 + 0.47 = 18.10.
It is quite obvious that for every researcher,
CJPI (at a year Y) ≥ YJPI (of the year Y or of any preceding year).
If YJPI of a researcher is zero in some year, it means that the researcher could not publish any research
paper during the previous year. Thus at the end of first n years of research by a researcher (the consecutive
years being denoted by Y1, Y2, Y3, …., Y(n-1) and Yn, where Y(i+1) = Yi + 1) the following equality holds:
CJPI =

Y (n +1)

∑

Y =Y 1

(YJPI)Y

where (YJPI)Y is the YJPI of the researcher at the year (Y+1). It is obvious that (YJPI)Y1 = 0.
Average JPI (AJPI) of a researcher at the year Y
CJPI
, where LRY is the ‘Length
The ‘Average JPI’ (AJPI) of a researcher at the year Y is equal to
LRY
of Research Years’ of the researcher in the year Y.

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AN IMPORTANT ISSUE WITH THE IF: SOLUTION BY NORMALIZATION
There are few core subjects in which number of indexed or sub-indexed journals (even, non-indexed
journals) in the world are too less (high) compared to the number of good research papers or the amount
of good research work being carried out in those core subjects by the world researchers. In some core
areas the indexed or sub-indexed journals usually have high IF (PIF), whereas in some core areas the
indexed or sub-indexed journals usually does not have high IF (PIF) but have appropriate and reasonable
IF (PIF). Consequently, the researcher of some core areas earn IFS at higher amounts automatically by

every publication i.e. CJPI of them increases at higher rate of growth; whereas the researcher of other
core areas earns IFS at lower amounts by every publication i.e. CJPI of them increases not at higher
rate of growth but at appropriate rate only. This is an unsolved anomaly being faced by the researchers
in the world. We propose a new method below to solve this problem by the method of Normalization.
The Normalization process brings all the subjects in a common scale. On imposing normalization, the
heterogeneity arising out of nature of various subjects is removed, and all subject areas apparently seem
to be treated by a common thermometer. For this first of all we define the term AIF.

“Average Impact Factor” (AIF) for a Core Subject S
The list of SCI/SCIE indexed journals (not sub-indexed journals or non-indexed journals) is readymade
available in the Thomson Reuters website thomsonreuters.com. The total number of SCIE covered
journals in 2015 is less than 9000, and SCI covered journals in 2015 is less than 4000.
Consider now any particular core subject S in a given year Y. Suppose that the number of SCIE
indexed journals in the world in this core subject S is n. Surely n is not a large number whatever be the
core subject S. It will be either a two-digit integer or at most a three-digit integer, depending upon the
nature of the core subject. Since we are considering only SCIE indexed journals here on the subject S
of the year Y, each of them has a unique IF (the IF is available for indexed journals subject-wise in the
Thomson Reuters website thomsonreuters.com). Thus, corresponding to these n number of SCI/SCIE
indexed journals in the subject S, there are n number of Ifs which are n number of positive real numbers,
need not be all distinct always. The arithmetic mean of these n data is called the Average Impact Factor
(AIF) of the core subject S in the year Y, and is denoted by aY(S) or simply by a(S). The value of a(S)
for each subject S will be published by UGC every year (figure 3).

Normalized YJPI of a Researcher
Normalized Yearly Journal Publication Index (or Normalized YJPI) of a researcher at the year Y is
defined as below:
Normalized YJPI of the researcher X in the year Y =

YJPI
,

a(s )

where YJPI of the researcher at the year Y is the yearly earned sum total of all the IFS of him at the
year (Y-1).

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Figure 3. Normalization of all the three types of JPI (for every researcher)

Normalized CJPI and Normalized AJPI of a researcher at the year Y
Consider a researcher Mr.X in the core subject S. Consider a year Y. Then the following measures
can be regarded as normalized measures in the year Y:
Normalized CJPI of the researcher X in the year Y =

CJPI
.
a(s )

Normalized AJPI of the researcher X in the year Y =

AJPI
.
a(s )

An Example Showing the beautiful role of Normalization to compare the Researchers of different
core subjects in a unique common scale

We present an example here showing the philosophy of normalization which can eliminate the variation due to the various nature of the core subjects, while comparing talents of different core subjects.
Consider two researchers Mr. X and Mr. Z in the core subjects ‘Mathematics’ and ‘Nanoscience’
respectively.
It is fact that in some core subjects the IF values of almost all the indexed journals are usually low,
and in some core subjects the IF values are usually high.
Let us suppose that in the year Y we have
CJPI(X) = 5, CJPI (Z) = 6.
LRY(X) = 6.2, LRY (Z) = 5.4
Suppose that, in the year Y we have from the UGC data

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aY(Mathematics) = 0.4 and aY(Nanoscience) = 0.8.
It is quite obvious that whatever be the individual core subjects, both X and Z may not be of equal
or even almost equal talent as a researcher.
But there must exist some method for measuring research-talents, for comparing the talents and for
ranking of them. The beauty of the normalization process is that; it can provide solution to this problem
up to a good extent.
It can be easily calculated that,
Normalized CJPI(X) = 5/.4 = 12.5
Normalized CJPI (Z) = 6/.8 = 7.5
AJPI (X) = 12.5/6.2 = 2.016
AJPI (Z) =7.5/5.4 = 1.388
Normalized AJPI (X) = 2.016/.4 = 5.04
Normalized AJPI (Z) = 1.388/.8 = 1.735
Therefore, in the year Y considered here, we are in a position to compare the two researchers X and

Z, although they are of different core subjects. The researcher X seems to be better researcher than Z.

‘SIMPSON AREA’ (SA) OF A RESEARCHER (FOR WHOM LRY ≥5)
The Simpson Area (SA) is a good measure to evaluate the research-talent of a researcher, and applicable
to those only for whom LRY ≥ 5, i.e. who have at least 5 completed years of research experience, even
if no research work done during any year after obtaining Master degree. It is mentioned earlier that the
value of LRY of a researcher does not get effected whether he does research or does not do research
after his Master degree.
Consider a researcher having n completed year of research experience, where n is an integer (≥5).
Construct the following table (table 1) for the researcher:

Table 1.­
LRY No.
YJPI of the researcher in this year

1
y1

2
y2

3
y3

………

(n-1)
y(n-1)

n

yn

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Here the value of n may be odd or even. We define Simpson Area of a researcher for odd and even
n separately below.
If n = ODD:
Then the Simpson Area of the researcher for his last n number of completed years is denoted by (SA)
and
is defined by
n
n

(SA)n =

∫ (YJPI ) dt + Residue.
t

1

=

1
. [ (y1+yn) + 4 (y2 + y4 + … + y(n-1)) + 2 (y3 + y5 + … + y(n-2))] + Residue.
3

Clearly we have for n = 5, 7, 9, ……….
5

(SA)5 =

∫ (YJPI ) dt + Residue.
t

1

=

1
. [ (y1+y5) + 4 (y2 + y4) + 2 y3] + Residue.
3
7

(SA)7 =

∫ (YJPI ) dt + Residue.
t

1

=

1
. [ (y1+y7) + 4 (y2 + y4 + y6) + 2 (y3 + y5)] + Residue.
3
9

(SA)9 =

∫ (YJPI ) dt + Residue.
t

1

=

1
. [ (y1+y9) + 4 (y2 + y4 + y6 + y8) + 2 (y3 + y5 + y7)] + Residue.
3

and so on.

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Here, Residue = sum total of the IFS earned by him during this ongoing incomplete year only (because
the researcher has made n completed research years so far, and he is currently at some interim point of
his (n+1)th year of his research tenure).
If n = EVEN:
Suppose that m = n-1.
Then the Simpson Area of the researcher for his last n number of completed years is denoted by (SA)
and
is defined by

n
m

(SA)n =

∫ (YJPI ) dt + (YJPI) + Residue
t

n

1

=

1
. [ (y1+ym) + 4 (y2 + y4 + … + y(m-1)) + 2 (y3 + y5 + … + y(m-2))] + (YJPI)n+ Residue
3

Both CJPI and SA are the sum-total of YJPI, but the metric SA carries more properties about the
researcher as this sum is according to the trend of the curve of YJPI of the researcher. SA takes care of
down or fall of the curve of YJPI and calculates the sum accordingly.

TWIN SUMMARY TABLES FOR EVERY RESEARCHER
Two summary tables are the important key twin tables for a researcher showing all details information
about the research performance of him. These two dynamic twin tables are:
1. BI Computing Table
2. JPI Computing Table
These twin tables are called Summary Tables of a researcher, which can be updated by the concerned
researcher at any time he desires, as many time he needs to do. They are called ‘twin tables’ in the sense
that whenever these two tables are to be submitted by the researcher to any authority, both must be

computed on the same date. The date of Search for both the tables must be same (it is strongly recommended that whenever a need for submission arises (say, for a job, for an interview, for a fellowship, etc.)
a researcher fill-up both of the twin tables on the same day; the necessary searches will not take much
time except few minutes only). However, in case two consecutive days or even three consecutive days are
used to fill-up these two tables, the researcher will record the most senior date in both the tables. Twin
summary tables are not suitable for the beginners (say, for a Ph.D. scholar in a university), but they are
strongly encouraged to make these twin tables and update them time to time even if some of the items
in these tables cannot be filled-up or if some of the items in these tables are not applicable, and even

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if these twin tables are not useful presently for any purpose for them. The role of these twin summary
tables is highly significant in the ‘Theory of IRE’.

BI Computing Table
The “BI Computing Table” of a researcher contains the information which are required by him to compute his BI. This table is to be filled up by the researcher on the concerned date of his interest (say, for
applying for a job or for a fellowship or for a promotion or for an award/honor, etc.).
Although the h-index can be manually calculated using citation databases or using automatic tools,
but there are free or subscription-based databases such as Scopus, Web of Knowledge, etc. which provide
automated calculators. In July 2011 Google offered a simple tool which allows researchers to keep track
of their own citations and also produces an h-index and an i10-index. However, there are few specific
databases applicable subject-wise, viz. INSPIRE-HEP database which can automatically calculate the
h-index for researchers working in high energy physics. But each database is likely to produce a different h for the same scholar, because of different coverage. For the sake of homogeneity, in the Theory of
IRE here we presently use ‘Google Scholar’ only as a common tool for everybody, for all researchers,
ignoring any sense of biasness or unbiased with any tool. Therefore, the BI of a researcher is presently
proposed to be calculated using ‘Google Scholar’ as a common tool across the subjects, across the universities, across the country. However, with the discovery of better tools, the choice of database search
engine may be updated in future (table 2).

Table 2. BI Computing Table
Rank

Title of the Paper

(i) Journal Name:
(ii) Year of Publication:
(iii)Vol., Page No.:
(iv) Publisher:

No. of Authors
(including self)

No. of Citations
(in descending
order)

1
2
3
.
.
.
NORMS:
1. Journal Publications in BI Computing Table are to be furnished in descending order of the number of citations. The publication with
maximum number of citations will correspond to Rank 1. All the data are to be correct on the date of search.
2. The common search engine to be used is: Google Scholar
3. The citations of all the papers is to be searched in one day or in two consecutive days.
4. Date of Search (on which data are filled-up by the researcher):

5. LRY on this date of search =
6. All the data in this BI Table are to be filled-up correctly by the researcher on the date of search.
7. Index values (to be calculated from the BI table): Hm-index = xxx, Gm-index = xxx, im10-index = xxx.

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