In solving real life assignment problem, we often face the state of uncertainty as well as hesitation due to varies uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, computationally a simple method is proposed to find the optimal solution for an unbalanced assignment problem under intuitionistic fuzzy environment. In conventional assignment problem, cost is always certain. This paper develops an approach to solve the unbalanced assignment problem where the time/cost/profit is not in deterministic numbers but imprecise ones. In this assignment problem, the elements of the cost matrix are represented by the triangular intuitionistic fuzzy numbers. The existing Ranking procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the AP . Finally, the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.

2. The Journal of Fuzzy Mathematics Vol. 24, No. 2, 2016 289
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__________________________
Received February, 2015
1066-8950/16 $8.50
© 2016 International Fuzzy Mathematics Institute
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An Algorithm for Solving Unbalanced Intuitionistic Fuzzy
Assignment Problem Using Triangular
Intuitionistic Fuzzy Number
P. Senthil Kumar
Assistant Professor, PG and Research Department of Mathematics, Jamal Mohamed College,
Tiyuchirappalli-620020, Tamil Nadu, Corresponding author
Email: senthilsoft_5760@yahoo.com
R. Jahir Hussain
Associate Professor PG and Research Department of Mathematics,
Jamal Mohamed College, Tiruchirappalli-620020, India.
Email: hssn_jhr@yahoo.com
Abstract:
In solving real life assignment problem, we often face the state of uncertainty as well
as hesitation due to varies uncontrollable factors. To deal with uncertainty and hesitation
many authors have suggested the intuitionistic fuzzy representation for the data. In this
paper, computationally a simple method is proposed to find the optimal solution for an
unbalanced assignment problem under intuitionistic fuzzy environment. In conventional
assignment problem, cost is always certain. This paper develops an approach to solve the
unbalanced assignment problem where the time/cost/profit is not in deterministic
numbers but imprecise ones. In this assignment problem, the elements of the cost matrix
are represented by the triangular intuitionistic fuzzy numbers. The existing Ranking
procedure of Varghese and Kuriakose is used to transform the unbalanced intuitionistic
fuzzy assignment problem into a crisp one so that the conventional method may be
applied to solve the AP . Finally the method is illustrated by a numerical example
which is followed by graphical representation and discussion of the finding.
Keywords:
Intuitionistic Fuzzy Set, Triangular Intuitionistic Fuzzy Number, Unbalanced
Intuitionistic Fuzzy Assignment Problem, Optimum Schedule.
1. Introduction

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4. An Algorithm for Solving Unbalanced Intuitionistic Fuzzy Assignment 301
Problem Using Triangular Intuitionistic Fuzzy Number
The degree of acceptance of the production of toys for the DM increases if the
production of toys increases from 148 to 182; while it decreases if the production of toys
increases from 182 to 262. Beyond (182, 342), the level of acceptance or the level of
satisfaction for the DM is zero. The DM is totally satisfied or the production of toys
is totally acceptable if the production is 262. The degree of non-acceptance of the
production for the DM decreases if the production increases from 148 to 262 while it
increases if the production increases from 262 to 376. Beyoned (148, 376), the
production of toys is totally un-acceptable.
Assuming that ( )I
Z
pm is membership value (degree of acceptance) and ( )I
Z
pJ is non-
membership value (degree of non-acceptance) of production p . Then the degree of
acceptance of the production p is ( )100 %I
Z
pm for the DM and the degree of non
acceptance is ( )100 %Z
pn for the DM . DM is not sure by ( ) ( )( )100 1 %I I
Z Z
p pm J- -
that he/she should accept the production p or not. Values of ( )I
Z
pm and ( )I
Z
pJ at
different values of p can be determined using equations given below.
( )
0 for 182
182
for 182 262
80
1 for 262
342
for 262 342
80
0 for 342
Z
p
p
p
p p
p
p
p
m
<Ï
Ô -
Ô £ £
Ô
Ô
= =Ì
Ô -
Ô £ £
Ô
Ô >Ó
( )
1 for 148
262
for 148 262
114
0 for 262
262
for 262 376
114
1 for 376
Z
p
p
p
p p
p
p
p
J
<Ï
Ô -
Ô £ £
Ô
Ô
= =Ì
Ô -
Ô £ £
Ô
Ô >Ó
6. Conclusion
In this paper we have proposed a simple computational method for solving unbalanced
intuitionistic fuzzy assignment problem. This proposed method gives the opportunity to
find the optimum schedule and optimum objective value of UIFAP directly. On the
basis of the present study, it can be concluded that the UIFAP , BIFAP and MIFAP
which can be solved by the existing methods (Kumar and Hussain (2014)) can also be
solved by the proposed method. Hence the proposed method is computationally very
simple and easy to understand and it can be easily applied by decision maker to solve real
life UIFAP . This technique can also be used in solving other types of problems like,
project schedules, transportation problems and network flow problems.
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