Fuzzy bi-objective linear programming (FBOLP) model is bi-objective linear programming model in fuzzy number set where the coefficients of the equations are fuzzy number. This model is proposed to solve portfolio selection problem which generate an asset portfolio with the lowest risk and the highest expected return. FBOLP model with normal fuzzy numbers for risk and expected return of stocks is transformed into linear programming (LP) model using magnitude ranking function.
REFERENCES
1.
2.
R. T.
Rockafellar
and S.
Uryasev
, Optimization of conditional value at risk
, Journal of Risk
2
, 21
–41
(2000
).3.
H.
Konno
and H.
Yamazaki
, Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market
, Management Science
37
, 519
–531
(1991
).4.
W.
Cooper
, V.
Lelas
, and T.
Sueyoshi
, Goal programming models and their duality relations for use in evaluationg security portfolio and regression relations
, European Journal of Operational Research
98
, 431
–443
(1997
).5.
A.
Yoshimoto
, The mean-variance approach to portfolio optimization subject to transaction costs
, Journal of The Operational Research Society of Japan
39
, 99
–117
(1996
).6.
G. A.
Pogue
, An extension of the Markowitz portfolio selection model to include variable transaction costs, short sales, leverage policies and taxes
, Journal of Finance
25
, 1005
–1028
(1970
).7.
W.
Ogryczak
, Multiple criteria linear programming model for portfolio selection
, Annals of Operation Research
97
, 143
–162
(2000
).8.
H. J.
Zimmermann
, Fuzzy programming and linear programming with several objective functions
, Fuzzy Sets and Systems
1
, 45
–55
(1978
).9.
L.A.
Zadeh
, Fuzzy sets, Information and control
8
, 338
–353
(1965
).10.
R.E.
Bellman
, L.A.
Zadeh
, Decision making in a fuzzy environment
, Management Science
17
, 141
–164
(1970
).11.
H.
Tanaka
, P.
Guo
, and I. B.
Turksen
, Portfolio selection based on fuzzy probabilities and possibility distributions
, Fuzzy Sets and Systems
111
, 387
–397
(2000
).12.
M. A.
Parra
, A. B.
Terol
, and M. V. R.
Uria
, A fuzzy goal programming approach to portfolio selection
, European Journal of Operational Research
133
, 287
–297
(2001
).13.
T. A.
Billbao
, Perz
G.B.
, Arenas
P. M.
and U.M.V.
Rodriguez
, Fuzzy compromise programming for portfolio selection
, Applied Mathematics and Computation
173
, 251
–264
(2006
).14.
H. W.
Liu
, Linear programming for portfolio selection based on fuzzy decision-making theory
. Proceeding of The Tenth International Symposium on Operations Research and Its Applications
, Dunhuang, China
2011
, pp. 195
–202
.15.
M.
Detyniecki
and R.R.
Yager
, Ranking Fuzzy Numbers Using Weighted Valuations
. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
8
, 573
–592
(2001
)16.
G. J.
Klir
, U. S.
Clair
, B.
Yuan
, Fuzzy Set Theory: Foundation and Applications
. (Prentice-Hall
, Inc. USA
, 1997
)17.
H. R.
Maleki
, M.
Tata
, and M.
Manshinchi
, M., Linear Programming with Fuzzy Variable
, Fuzzy Sets and Systems
109
, 21
–33
(2000
)18.
A.
Kumar
, P.
Singh
, and J.
Kaur
, Generalized Simplex Algorithm to Solve Fuzzy Linear Programming Problems with Ranking of Generalized Fuzzy Numbers
, Turkish Journal of Fuzzy Systems
1
, 80
–103
(2010
).19.
A.
Kumar
and J.
Kaur
, A New Method for Solving Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers
. Journal of Fuzzy Set Valued Analysis
, 1
–12
, (2011
).20.
S.
Abbasbandy
, T.
Hajjari
, A new approach for ranking of trapezoidal fuzzy numbers
, Computers and Mathematics with Applications
57
, 413
–419
(2009
).21.
D.
Das
, S.
Mahanta
, R.
Chutia
, H. K.
Baruah
, Construction of normal fuzzy numbers: case studies with stock exchange data
, Annals of Fuzzy Mathematics and Informatics
5
, 505
–514
(2013
).
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