The concept of ranking method is an efficient
approach to rank fuzzy numbers. The aim of the paper is to
find the pareto optimal solution of fuzzy multiobjective linear
fractional programming (FMOLFP) problem. To study
FMOLFP problem, the fuzzy coefficients and scalars in the
linear fractional objectives and the fuzzy coefficients are
characterised by triangular or trapezoidal fuzzy numbers. The
left hand side of the fuzzy constraints are characterised by
triangular or trapezoidal fuzzy numbers, while the right hand
sides are assumed to be crisp number. The fuzzy coefficients
and scalars in the linear fractional objectives and fuzzy
coefficients in the linear constraints are transformed to crisp
MOLFP problem using ranking method. The reduced problem
is solved by simplex method to find the pareto optimal solution
of MOLFP problem. To demonstrate the proposed approach,
one numerical example is solved.
Ms. Moumita Deb : completed her Masters degree in
Mathematics from Assam University, Silchar in the year 1998.
In 2000, she obtained B.Ed. degree from Assam University,
Silchar. Currently she is working as a Research scholar in
Department of Mathematics, NIT Silchar since 2011. Her
research interests includes linear fractional programming
problem and multiobjective linear fractional programming
problem.
Dr. Pijus Kanti De : obtained his M.Sc in Mathematics and
B.T teaching training degrees from Kalyani University . Also he
obtained his M.Phil and Ph.D in Applied Mathematics
degrees from Indian School of Mines Dhanbad. Presently he is
working as an Associate Professor in Mathematics in National
Institute of Technology Silchar since 2010. Previously Dr.De
was in Banasthali University (Raj), KIET Ghaziabad under
U.P.T.U, Delhi College of Engineering (D.T.U) and Centre for
Mathematical Modeling and Computer Simulation (C-MMACS),
National Aerospace Laboratories (NAL), Bangalore. His
research interest lies on Fuzzy Optimization and Decision
Making, Operations Research, Fuzzy Mathematics,
Mathematical Modeling , Uncertainty Modeling, Numerical
Optimization, Numerical Analysis, Elasto-Dynamics, Wave
Propagation and Applied Mathematics.
Fuzzy sets
Trapezoidal fuzzy number
Triangular fuzzy number
Multiobjective linear fractional
programming
Ranking
In this paper, fuzzy multiobjective linear fractional
programming (FMOLFP) problem is solved by using
ranking method. Here, we have applied ranking method
of triangular and trapezoidal fuzzy number in FMOLFP
problem. The fuzzy coefficients and scalars of both
objective functions and linear constraints are
transformed to crisp number by using metric distance
ranking (in triangular fuzzy number) and graded mean
integration representation method (in trapezoidal fuzzy
number). The reduced problem has been solved by using
standard LP package. After solving the problem, the
values of objective functions are obtained by using
different arithmetic operations of triangular or
trapezoidal fuzzy number.
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