International Journal of Mathematics Research.
ISSN 0976-5840 Volume 4, Number 4 (2012), pp. 411-420
© International Research Publication House
http://www.irphouse.com
The Transportation Problem in an Intuitionistic
Fuzzy Environment
R. Jahir Hussain
1
and P. Senthil Kumar
2
1
Associate Professor and
2
Research Scholar
PG and Research Department of Mathematics, Jamal Mohamed College,
Tiruchirappalli: 620 020 India
E-mail: hssn_jhr@yahoo.com, senthilsoft_5760@yahoo.com
Abstract
In this paper, we investigate transportation problem in which supplies and
demands are intuitionistic fuzzy numbers. Intuitionistic Fuzzy Vogel’s
Approximation Method is proposed to find an initial basic feasible solution.
Intuitionistic Fuzzy Modified Distribution Method is proposed to find the
optimal solution in terms of triangular intuitionistic fuzzy numbers. The
solution procedure is illustrated with suitable numerical example.
Keywords: Triangular intuitionistic fuzzy numbers, intuitionistic fuzzy
transportation problem, intuitionistic fuzzy vogel’s approximation method,
intuitionistic fuzzy modified distribution method, initial basic feasible
solution, optimal solution.
Introduction
The theory of fuzzy set introduced by Zadeh[8] in 1965 has achieved successful
applications in various fields. The concept of Intuitionistic Fuzzy Sets (IFSs)
proposed by Atanassov[1] in 1986 is found to be highly useful to deal with vagueness.
The major advantage of IFS over fuzzy set is that IFSs separate the degree of
membership (belongingness) and the degree of non membership (non belongingness)
of an element in the set .The concept of fuzzy mathematical programming was
introduced by Tanaka et al in 1947 the frame work of fuzzy decision of Bellman and
Zadeh[2].
In [4], Nagoor Gani et al presented a two stage cost minimizing fuzzy
transportation problem in which supplies and demands are trapezoidal fuzzy number.
In [7], Stephen Dinager et al investigated fuzzy transportation problem with the aid of
trapezoidal fuzzy numbers. In[6], Pandian.P and Natarajan.G presented a new