Simplex Method for Fuzzy Variable Linear Programming Problems

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.





References:
[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] J.C. Bezdek, "Fuzzy models - What are they, and Why?", IEEE
Transactions on Fuzzy Systems 1 (1993) 1--9.
[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] P. Vasant, R. Nagarajan, and S. Yaacab, ÔÇÿÔÇÿDecision making in industrial
production planning using fuzzy linear programming", IMA, Journal of
Management Mathematics 15 (2004) 53--65.
[10] H. J. Zimmermann, "Fuzzy programming and linear programming with
several objective functions", Fuzzy Sets and Systems 1 (1978) 45--55.