Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers
The fuzzy set theory has been applied in many fields,
such as operations research, control theory, and management
sciences, etc. In particular, an application of this theory in decision
making problems is linear programming problems with fuzzy
numbers. In this study, we present a new method for solving fuzzy
number linear programming problems, by use of linear ranking
function. In fact, our method is similar to simplex method that was
used for solving linear programming problems in crisp environment
before.
[1] M.S. Bazaraa, J.J. Jarvis and H.D. Sherali, Linear Programming and
Network Flows, John Wiley, New York, Second Edition, 1990.
[2] R.E. Bellman and L.A. Zadeh, "Decision making in a fuzzy environment",
Management Sci. 17 (1970) 141--164.
[3] M. Delgado, J.L. Verdegay, and M.A. Vila, "A general model for fuzzy
linear programming", Fuzzy Sets and Systems 29 (1989) 21--29.
[4] S.C. Fang and C.F. Hu, "Linear programming with fuzzy coefficients in
constraint", Comput. Math. Appl. 37 (1999) 63--76.
[5] N. Mahdavi-Amiri and S.H. Nasseri, "Duality in fuzzy variable linear
programming", 4th World Enformatika Conference, WEC'05, June 24-
26, 2005, Istanbul, Turkey.
[6] H.R. Maleki, "Ranking functions and their applications to fuzzy linear
programming", Far East J. Math. Sci. 4 (2002) 283--301.
[7] H.R. Maleki, M. Tata and M. Mashinchi, "Linear programming with
fuzzy variables", Fuzzy Sets and Systems 109 (2000) 21--33.
[8] H. Rommelfanger, R. Hanuscheck and J. Wolf, "Linear programming
with fuzzy objective", Fuzzy Sets and Systems 29 (1989) 31--48.
[9] J.L. Verdegay, "A dual approach to solve the fuzzy linear programming
problem", Fuzzy Sets and Systems 14 (1984) 131--141.
[10] H. J. Zimmermann, "Fuzzy programming and linear programming with
several objective functions", Fuzzy Sets and Systems 1 (1978) 45--55.
[1] M.S. Bazaraa, J.J. Jarvis and H.D. Sherali, Linear Programming and
Network Flows, John Wiley, New York, Second Edition, 1990.
[2] R.E. Bellman and L.A. Zadeh, "Decision making in a fuzzy environment",
Management Sci. 17 (1970) 141--164.
[3] M. Delgado, J.L. Verdegay, and M.A. Vila, "A general model for fuzzy
linear programming", Fuzzy Sets and Systems 29 (1989) 21--29.
[4] S.C. Fang and C.F. Hu, "Linear programming with fuzzy coefficients in
constraint", Comput. Math. Appl. 37 (1999) 63--76.
[5] N. Mahdavi-Amiri and S.H. Nasseri, "Duality in fuzzy variable linear
programming", 4th World Enformatika Conference, WEC'05, June 24-
26, 2005, Istanbul, Turkey.
[6] H.R. Maleki, "Ranking functions and their applications to fuzzy linear
programming", Far East J. Math. Sci. 4 (2002) 283--301.
[7] H.R. Maleki, M. Tata and M. Mashinchi, "Linear programming with
fuzzy variables", Fuzzy Sets and Systems 109 (2000) 21--33.
[8] H. Rommelfanger, R. Hanuscheck and J. Wolf, "Linear programming
with fuzzy objective", Fuzzy Sets and Systems 29 (1989) 31--48.
[9] J.L. Verdegay, "A dual approach to solve the fuzzy linear programming
problem", Fuzzy Sets and Systems 14 (1984) 131--141.
[10] H. J. Zimmermann, "Fuzzy programming and linear programming with
several objective functions", Fuzzy Sets and Systems 1 (1978) 45--55.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52061", author = "S. H. Nasseri and E. Ardil and A. Yazdani and R. Zaefarian", title = "Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers", abstract = "The fuzzy set theory has been applied in many fields,
such as operations research, control theory, and management
sciences, etc. In particular, an application of this theory in decision
making problems is linear programming problems with fuzzy
numbers. In this study, we present a new method for solving fuzzy
number linear programming problems, by use of linear ranking
function. In fact, our method is similar to simplex method that was
used for solving linear programming problems in crisp environment
before.", keywords = "Fuzzy number linear programming, rankingfunction, simplex method.", volume = "1", number = "10", pages = "468-5", }