Simplex Method for Fuzzy Variable Linear Programming Problems

Authors: S.H. Nasseri, E. Ardil

Abstract:

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.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332118

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.