A Study of Personality Influence in Building Work Life Balance Using Fuzzy Relation Mapping (FRM)

Integrated Intelligent Research (IIR) International Journal of Data Mining Techniques and Applications
Volume: 02 Issue: 02 June 2013 Page No.33-37
ISSN: 2278-2419
33
A Study of Personality Influence in Building Work
Life Balance Using Fuzzy Relation Mapping
(FRM)
A.Victor Devadoss1
, J. Befija Minnie2
PG & Research Department of Mathematics, Loyola College, Chennai, India
Email: 1
hanivictor@ymail.com , 2
befija@yahoo.co.in
Abstract -Personality plays an important role in work life
balance irrespective of the organizational setups and other
factors. It has become a subject of concern in terms of
technological, market and organizational changes associated
with an individual’s personality. Here in this study an attempt is
made to study about the holistic picture of personality influence
in work-life balance on the basis of experts’ opinion. The
influence of personality is studied from the big five factors of
personality traits. The data were analyzed using Fuzzy
Relational mapping (FRM) model and conclusions arrived for
which personality has more influence in building work life
balance and which one is more vulnerable for work life
imbalance.
Keywords - Personality, Work Life balance, Fuzzy Relational
mapping.
I. INTRODUCTION
A. Personality
Personality is made up the characteristic patterns of thoughts,
feelings, and behaviors that make a person unique. In different
situations personality and our responses are generally stable.
Personality is psychological, but is influenced by biological
needs and processes. Personality of an individual is a set of
qualities that make the person distinct from another and assume
a role or manner of behavior. Within ones personality the
complex of all the attributes such as behavioral, temperamental,
emotional and mental are considered. Guest (2002) defined the
personality as the extent to which family or work is a central
life interest influences the perceptions of balance of every
individual. “Personality is the entire mental organization of a
human being at any stage of his development. It embraces
every phase of human character: intellect, temperament, skill,
morality and every attitude that has been built up in the course
of one's life”, (Warren & Carmichael 1930, Elements of human
psychology). “Personality is the essence of a human being”,
(Gordon Allport 1957, Hall & Lindzey, 1957, p. 9,
characterizing statements by Gordon Allport). “Personality is a
result of interaction between the individual and the
environment”. (B. F. Skinner (1953) Science and Human
Behavior). “The poor ego has a still harder time of it; it has to
serve three harsh masters and it has to do its best to reconcile
the claims and demands of all three...The three tyrants are the
external world, the superego, and the id”, (Sigmund Freud,
1923, The Ego and the Id). “An individual's pattern of
psychological processes arises from motives, feelings, thoughts
and other major areas of psychological function. Personality is
expressed through its influences on the body, in conscious
mental life and through the individual's social behavior”,
(Mayer, 2005, Comprehensive handbook of personality and
psychopathology CHOPP Vol. 1: Personality and everyday
functioning).
B. What Are the Big Five Dimensions of Personality?
Today, most of the researchers believe that there are five core
personality traits. Support to this theory has been increasing for
the past 50 years, beginning with the research of D. W. Fiske
(1949) and later expanded upon by other researchers including
Norman (1967), Smith (1967), Goldberg (1981) and McCrae &
Costa (1987). The "big five" are broad categories of personality
traits. While there is a significant body of literature supporting
this five-factor model of personality, some of the researchers
don't always agree on the exact labels for each dimension.
However, these five categories are usually described as follows:
 Extraversion: This trait includes characteristics such as
excitability, sociability, talkativeness, assertiveness and
high amounts of emotional expressiveness.
 Agreeableness: This personality dimension includes
attributes such as trust, altruism, kindness, affection, and
other pro-social behaviors.
 Conscientiousness: Common features of this dimension
include high levels of thoughtfulness, with good impulse
control and goal-directed behaviors. Those high in
conscientiousness tend to be organized and mindful of
details.
 Neuroticism: Individuals high in this trait tend to
experience emotional instability, anxiety, moodiness,
irritability and sadness.
 Openness: This trait features characteristics such as
imagination, inventive and insight and those high in this
trait also tend to have a broad range of interests.It is
important to note that each of the five personality factors
represents a range between two extremes. For example,
extraversion represents a continuum between extreme
extraversion and extreme introversion. In the real world,
most people lie somewhere in between the two polar ends
of each dimension.
C. Work Life Balance
Work life balance is about people having measure of their
control over when, where and how they work. Most of the
people view this as work life balance is what the organization
allows for an individual to experience.
However, work-life balance is a bi dimensional approach. The
other dimension of work-life balance, which many individuals

ISSN: 2278-2419
34
overlook, relates to what individuals do for themselves. The
success of work life balance is always sustain with achievement
along with enjoyment.
Achievement and enjoyment at work is a critical part of work-
life balance. Moreover, achievement and enjoyment in the other
three quadrants of one's life (e.g. family, friends and self) is
critical as well. New modern life work culture is forcing the
individuals for inflexibility to flexibility. The importance of the
balance between personal life and work life is ignored
today. There is a life at work and at home and also a life having
space for leisure. Due to the modernization practices and
globalization the work life imbalance became hot topic for
discussion. Work-life 'imbalance' is a big concern in this
century because of increasing problems related to employee
health, monotony at work place, declining levels of productivity
and efficiency at the employee level. The imbalance also has a
negative impact in the personal life of working people, some of
which have even become social hazards- increasing number of
divorces, infertility due high stress levels, advent of nuclear
families etc.
D. Personality influence on work life balance
An individual should be able to strike a proper balance between
work and life, there are many factors which are influencing the
work life balance, however and individual’s personality also
plays a vital role in balancing the work life. The approach of
psychology of individual differences may be also fruitful for
research of Work Life Balance due to the fact that studying
aspects of different personality types can enhance our
understanding of perceptions of work life balance. It is easy to
be realized that the Personality of an individual can have effects
on his/her own balance between work and life. Consequently,
purpose of this study is to identify the impact of personality on
Work Life Balance and the vulnerability of a particular
personality to work life imbalance.
II. DEFINITION AND ILLUSTRATION OF FUZZY
RELATIONAL MAPS (FRMS)
Fuzzy relational mappings are constructed analogous to FCMs.
In FCMs correlations between causal associations among
concurrently active units are promoted. But in FRMs the very
causal associations are divided into two disjoint units. Thus a
domain space and a range space which are disjoint in the sense
of concepts are needed to define an FRM.The elements of the
domain space are taken from the real vector space of dimension
n and that of the range space are real vectors from the vector
space of dimension m (m in general need not be equal to n). D
denotes the nodes D1, D2, …, Dn of the domain space where D
= {(x1,…, xn) / xj = 0 or 1} for i = 1, 2,…, n. If xi = 1 it means
that the node Di is in the on state and if xi = 0 it means that the
node Di is in the off state. We denote by R the set of nodes
R1,…, Rm of the range space, where R = {(x1,…, xm) / xj = 0 or
1 } for j = 1, 2, …, m. If xi = 1, it means that the node Ri is in
the on state and if xi = 0 it means that the node Ri is in the off
state.
A. Definitions
a) Definition
A FRM is a directed graph or a map from domain space D to
range space R with concepts like policies or events etc, as
nodes and causalities as edges. It represents causal relations
between spaces D and R. Let Di and Rj denote that the two
nodes of an FRM. The directed edge from Di to Rj denotes the
causality of Di on Rj called relations. Every edge in the FRM is
weighted with a number in the set {0, ±1}. Let eij be the weight
of the edge DiRj, eij ∈ {0, ±1}. The weight of the edge Di Rj is
positive if increase in Di implies increase in Rj or decrease in Di
implies decrease in Rj i.e., causality of Di on Rj is 1. If eij = 0,
then Di does not have any effect on Rj . We do not discuss the
cases when increase in Di implies decrease in Rj or decrease in
Di implies increase in Rj .
b) Definition
When the nodes of the FRM are fuzzy sets then they are called
fuzzy nodes. FRMs with edge weights {0, ±1} are called simple
FRMs.
c) Definition
Let D1, …, Dn be the nodes of the domain space D of an FRM
and R1, …, Rm be the nodes of the range space R of an FRM.
Let the matrix E be defined as E = (eij) where eij is the weight of
the directed edge DiRj (or RjDi), E is called the relational matrix
of the FRM.
d) Definition
Let D1, ..., Dn and R1,…, Rm denote the nodes of the FRM. Let
A = (a1,…,an), ai ∈ {0, 1}. A is called the instantaneous state
vector of the domain space and it denotes the on-off position of
the nodes at any instant. Similarly let B = (b1,…, bm), bi ∈ {0,
1}. B is called instantaneous state vector of the range space and
it denotes the on-off position of the nodes at any instant ai = 0 if
ai is off and ai = 1 if ai is on for i= 1, 2,…, n Similarly, bi = 0 if
bi is off and bi = 1 if bi is on, for i= 1, 2,…, m.
e) Definition
Let D1, …, Dn and R1,…, Rm be the nodes of an FRM. Let DiRj
(or Rj Di) be the edges of an FRM, j = 1, 2,…, m and i= 1, 2,…,
n. Let the edges form a directed cycle. An
FRM is said to be a cycle if it possess a directed cycle. An
FRM is said to be acyclic if it does not possess any directed
cycle.
f) Definition
An FRM with cycles is said to be an FRM with feedback.
g) Definition
If the FRM settles down with a state vector repeating in the
form A1 → A2 → A3 → … → Ai → A1 (or B1 → B2 → ….→
Bi → B1) then this equilibrium is called a limit cycle.
B. Method of determining the Hidden pattern
Let R1, R2, …, Rm and D1, D2, …, Dn be the nodes of a FRM
with feedback. Let E be the relational matrix. Let us find a
hidden pattern when D1 is switched on i.e. when an input is
given as vector A1 = (1, 0, …, 0) in D1, the data should pass
through the relational matrix E. This is done by multiplying A1
with the relational matrix E. Let A1E = (r1, r2, …, rm), after
thresholding and updating the resultant vector we get A1 E ∈ R.
Now let B = A1 E we pass on B into ET
and obtain BET
. We

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update and threshold the vector BET
, so that BET
∈ D. This
procedure is repeated till we get a limit cycle or a fixed point.
III. DESCRIPTION OF THE STUDY
The expert’s opinion on the personality types are not statistical
model in nature. That makes the study more complex and
difficult to make use of other mathematical model like data
interpretation and operational research, etc.
The subject is linguistic in nature and does not have the
mathematical or statistical data associated with it. In this study,
the influence of personality in building work life balance is
analyzed using Fuzzy Relational Maps.The experts’ opinions
are taken to study the impact of personalities on work life
balance issues using FRM. The following attributes are taken as
the nodes of the domain space of FRM. D = {D1, D2, D3, D4,
D5} where D1, D2, D3, D4, D5 are described as
D1 – Openness
D2 – Neuroticism
D3 – Extraversion
D4 – Conscientiousness
D5 – Agreeableness
The attributes taken for the range space are {R1, R2, R3, R4, R5,
R6, R7, R8, R9, R10} where R1, R2, R3, R4, R5, R6, R7, R8, R9, R10
are listed below.
R1 – Good in coping skills
R2 – Compassionate towards spouse
R3 – Spending time with family
R4 – Time management
R5 – Social involvement
R6 – Physically and mentally well being
R7 – Child care
R8 – Spend time for hobbies
R9 – Having fun in leisure time
R10 – Emotionally balanced
The related graph based on the experts’ opinion is given in Figure 3.1
.
Figure 3.1 Illustrates the related graph given by experts
A. Determining the hidden pattern of the model
The related matrix E of the directed graph given in Figure 2 is
as follows

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1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
R R R R R R R R R R
D 1 0 0 0 0 1 0 1 0 0
D 0 0 0 0 0 0 0 0 0 0
D 0 0 0
D
D
0 1 1 0 0 1 1
1 0 0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0







 
 
 
 
The attributes associated with personality are taken as the rows
of the matrix E and attributes associated with work life balance
characteristics are taken as the columns of the matrix. Thus we
obtain a 5 × 10 related matrix of the directed graph. In order to
study the effect of each attribute on the dynamical system E, the
hidden pattern of the dynamical system E (related matrix) for
each state vector is to be found.Suppose node D1 is in the on
state i.e., the personality Openness is in the on state and all
other nodes are in off state, the effect of the state vector X = (1
0 0 0 0) on the dynamical system E is given as follows:
X = (1 0 0 0 0)
XE ↪ (1 0 0 0 0 1 0 1 0 0 ) = Y say
YET
↪ (1 0 1 1 0) = X1 say
X1E ↪ (1 0 0 1 1 1 0 1 1 1 ) = Y1 say
Y1 ET
↪ (1 0 1 1 1) = X2 say
X2E ↪ (1 1 1 1 1 1 1 1 1 1 ) = Y2 say
Y2 ET
↪ (1 0 1 1 1) = X3 say = X2
The resultant vector is a fixed point given by the binary pair {(1
0 1 1 1), (1 1 1 1 1 1 1 1 1 1 ) }. This resultant vector
shows that all nodes in the domain space except the node D2
and all the nodes in the range space are in the on state.
Now consider the node D2 is in the on state i.e., the personality
Neuroticism is in the on state and all other attributes are in off
state. Let the state vector of this node is C = (0 1 0 0 0).
The effect of C on E is as follows
C = (0 1 0 0 0)
CE ↪ (0 0 0 0 0 0 0 0 0 0 ) = K say
KET
↪ (0 0 0 0 0) = C1 sayThe resultant vector is the fixed
vector given by the binary pair {(0 0 0 0 0), (0 0 0 0 0 0 0
0 0 0 ) }. This shows all the nodes in the domain and the range
space are in the off state.Suppose to find the effect of the node
D3 on the dynamical system E, let the state vector be A = (0 0
1 0 0). i.e, the personality Extraversion is in the on state and
all other nodes are in off state. The effect of A on E is given by
A ↪ (0 0 1 0 0)
AE ↪ (0 0 0 0 1 1 0 0 1 1) = B say
BET
↪ (1 0 1 0 0) = A1 say
A1E ↪ (1 0 0 0 1 1 0 1 1 1) = B1 say
B1ET
↪ (1 0 1 1 0) = A2 say
A2E ↪ (1 0 0 1 1 1 0 1 1 1) = B2 say
B2ET
↪ (1 0 1 1 0) = A3 say = A2
Thus the fixed point is a binary pair given by {(1 0 1 1 0), (1
0 0 1 1 1 0 1 1 1) }. The on state of D3 makes R1, R4, R5,
R6, R8, R9, R10, D1 and D4 on state.Now to study the effect of
the state vector G = (0 0 0 1 0) i.e., only the node D4 is in the
on state and all other nodes in the off state. The effect of the
personality Conscientiousness on the dynamical system E is
given by
G ↪ (0 0 0 1 0)
GE ↪ (1 0 0 1 0 0 0 0 0 0) = H say
HET
↪ (1 0 0 1 0) = G1 say
G1E ↪ (1 0 0 1 0 1 0 1 0 0) = H1 say
H1ET
↪ (1 0 1 1 0) = G2 say
G2E ↪ (1 0 0 1 1 1 0 1 1 1) = H2 say
H2ET
↪ (1 0 1 1 0) = G3 say = G2
Thus the hidden pattern is a fixed point of the dynamical
system given by the binary pair {(1 0 1 1 0), (1 0 0 1 1 1
0 1 1 1)}. Now consider the node D5 is in the on state i.e., the
personality Agreeableness is in the on state and all other
attributes are in off state. Let the state vector of this node is R =
(0 0 0 0 1).
R ↪ (0 0 0 1 0)
RE ↪ (1 0 0 1 0 0 0 0 0 0) = S say
SET
↪ (1 0 0 1 0) = R1 say = R
The hidden pattern of the dynamical system is a fixed point
given by the pair {(1 0 0 1 0), (1 0 0 1 0 0 0 0 0 0)}.
IV. RESULTS AND DISCUSSIONS
The result of the study indicates that the on state of the
personality openness in the domain space leads to the on state
of all the work life balance characteristics in the range space.
Next to openness the personality conscientiousness and
extraversion each makes seven of the attributes in the range
space to on state. The on state of the personality agreeableness
leads to the on state of just two attributes in the range space.
Finally the on state of the personality neuroticism has no role to
play in building work life balance since it leads to the off state
of all the attributes in the range space.
V. CONCLUSION
The result provides clear evidence that the personality type
‘openness’ is able to strike a proper balance between work and
life, this is due to the positive impact of the personality at work
and family. Also, neuroticism is in a bad shape of maintaining a
balance between work and life. Hence, it is concluded that the
personality type ‘neuroticism’ is more vulnerable to work life
imbalance.A broad area of personality type behavioral
difference at work and outside of work still left unstudied. It is
noticeable that each personality behavior is not unique at work
and outside of work. This is making the analysis of
psychometric tests to be more complex than it appears. This
area can be studied to find out which personality tends to show
more difference at professional and personal life and which
personality shows less difference.
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[4]Fiona Jones, Ronald Burke and Mina Westman, “Work-Life Balance: A
Psychological Perspective”. Psychology press (UK), (2006).
[5]Frank Bauer, Hermann Grob, Gwen Oliver, Georg Sieglen, Mark Smith
“Time use and work–life balance in Germany and the UK”.(July 2007)
[6]Jim Taylor,. Work life balance:
http://www.psychologytoday.com/blog/thepower-prime/2009/business-
worklife-balance-part-i ,(2009)

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37
[7] Jerry S. Wiggins, “The Five-Factor Model of Personality: Theoretical
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[11]Vasantha Kandasamy W.B, Florentin Smarandache and Ilanthenral,
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[14]Big five factor personality traits: http://www.psychometric-
success.com/personality
[15]Big five personality aspects:
http://www.themotivator.in/bigfive_Profile.pdf

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