In solving real life transportation problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. So, in this paper, we consider a transportation problem having uncertainty and hesitation in supply, demand and costs. We formulate the problem and utilize triangular intuitionistic fuzzy numbers (TrIFNs) to deal with uncertainty and hesitation. We propose a new method called PSK method for finding the intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem in single stage. Also the new multiplication operation on TrIFN is proposed to find the optimal object value in terms of TrIFN. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.

1. 1 23
International Journal of System
Assurance Engineering and
Management
ISSN 0975-6809
Int J Syst Assur Eng Manag
DOI 10.1007/s13198-014-0334-2
Computationally simple approach for
solving fully intuitionistic fuzzy real life
transportation problems
P. Senthil Kumar & R. Jahir Hussain

2. 1 23
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3. ORIGINAL ARTICLE
Computationally simple approach for solving fully intuitionistic
fuzzy real life transportation problems
P. Senthil Kumar • R. Jahir Hussain
Received: 26 September 2014 / Revised: 18 December 2014
Ó The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and
Maintenance, Lulea University of Technology, Sweden 2015
Abstract In solving real life transportation problem we
often face the state of uncertainty as well as hesitation due
to various uncontrollable factors. To deal with uncertainty
and hesitation many authors have suggested the intuition-
istic fuzzy representation for the data. So, in this paper, we
consider a transportation problem having uncertainty and
hesitation in supply, demand and costs. We formulate the
problem and utilize triangular intuitionistic fuzzy numbers
(TrIFNs) to deal with uncertainty and hesitation. We pro-
pose a new method called PSK method for finding the
intuitionistic fuzzy optimal solution for fully intuitionistic
fuzzy transportation problem in single stage. Also the new
multiplication operation on TrIFN is proposed to find the
optimal object value in terms of TrIFN. The main advan-
tage of this method is computationally very simple, easy to
understand and also the optimum objective value obtained
by our method is physically meaningful. Finally the
effectiveness of the proposed method is illustrated by
means of a numerical example which is followed by
graphical representation of the finding.
Keywords Intuitionistic fuzzy set Á Triangular
intuitionistic fuzzy number Á Fully intuitionistic
fuzzy transportation problem Á PSK method Á Optimal
solution
1 Introduction
In several real life situations, there is a need for shipping
the product from different origins (Factories) to different
destinations (Warehouses). Here the aim of the decision
maker (DM) is to find how much quantity of the product
from which origin to which destination should be shipped
subject to all the supply points are fully used and all the
demand points are fully received in such a way that the
total transportation cost is minimum for a minimization
problem or total transportation profit is maximum for a
maximization problem.
In today’s real world problems such as in corporate or in
industry many of the distribution problems are imprecise in
nature due to variations in the parameters. To deal quan-
titatively with imprecise information in making decision,
Zadeh (1965) introduced the fuzzy set theory and has
applied it successfully in various fields. The use of fuzzy
set theory become very rapid in the field of optimization
after the pioneering work done by Bellman and Zadeh
(1970). The fuzzy set deals with the degree of membership
(belongingness) of an element in the set but it does not
consider the non-membership (non-belongingness) of an
element in the set. In a fuzzy set the membership value
(level of acceptance or level of satisfaction) lies between 0
and 1 where as in crisp set the element belongs to the set
represent 1 and the element not in the set represent 0.
In conventional transportation problem supply, demand
and costs are fixed crisp numbers. Therefore in this situation
the DM can predict transportation cost exactly. On the con-
trary in real world transportation problems, the availabilities
and demands are not known exactly. These are uncertain
quantities with hesitation due to various factors like lack of
good communications, error in data, understanding of
P. S. Kumar (&) Á R. J. Hussain
PG and Research Department of Mathematics, Jamal Mohamed
College (Autonomous), Tiruchirappalli, Tamilnadu, India
e-mail: senthilsoft_5760@yahoo.com
R. J. Hussain
e-mail: hssn_jhr@yahoo.com
123
Int J Syst Assur Eng Manag
DOI 10.1007/s13198-014-0334-2
Author's personal copy

4. Reference to this paper should be made as follows:
Kumar, P.S. & Hussain, R.J. Int J Syst Assur Eng Manag (2016) 7(Suppl 1): 90.
https://doi.org/10.1007/s13198-014-0334-2
MLA
Kumar, P. Senthil, and R. Jahir Hussain. "Computationally simple approach for
solving fully intuitionistic fuzzy real life transportation problems." International
journal of system assurance engineering and management 7.1 (2016): 90-101.
DOI: 10.1007/s13198-014-0334-2
APA
Kumar, P. S., & Hussain, R. J. (2016). Computationally simple approach for
solving fully intuitionistic fuzzy real life transportation problems. International
journal of system assurance engineering and management, 7(1), 90-101.
DOI: 10.1007/s13198-014-0334-2
Chicago
Kumar, P. Senthil, and R. Jahir Hussain. "Computationally simple approach for
solving fully intuitionistic fuzzy real life transportation problems." International
journal of system assurance engineering and management 7, no. 1 (2016): 90-
101. DOI: 10.1007/s13198-014-0334-2
Harvard
Kumar, P.S. and Hussain, R.J., 2016. Computationally simple approach for
solving fully intuitionistic fuzzy real life transportation problems. International
journal of system assurance engineering and management, 7(1), pp.90-101.
DOI: 10.1007/s13198-014-0334-2
Vancouver
Kumar PS, Hussain RJ. Computationally simple approach for solving fully
intuitionistic fuzzy real life transportation problems. International journal of
system assurance engineering and management. 2016;7(1):90-101.
DOI: 10.1007/s13198-014-0334-2

5. computationally very simple when compared to all the
existing methods. Further, it can be concluded that the
IFTP and MIFTP which can be solved by the existing
methods (Hussain and Kumar 2012c); (Nagoor Gani and
Abbas 2012); Antonyet al. (2014); Singh and Yadav
(2014)) can also be solved by the proposed method.
Acknowledgments The authors gratefully acknowledge the critical
comments given by the learned reviewers which helped us to improve
the manuscript. The first author would like to thank the people who
helped continuously support the way to publish this paper.
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