Penalty method for fuzzy linear programming with trapezoidal numbers
DOI:
https://doi.org/10.2298/YJOR0901149SKeywords:
Linear programming, trapezoidal fuzzy number, penalty methodAbstract
In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints.References
Buckley, J.J., Feuring, T. (2000) Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming. Fuzzy Sets and Systems, 109(1): 35
Inuiguchi, M., Ramík, J. (2000) Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, 111(1): 3
Jamison, K.D., Lodwick, W.A. (2001) Fuzzy linear programming using a penalty method. Fuzzy Sets and Systems, 119(1): 97
Pop, B., Stancu-Minasian, I.M. (2008) A method of solving fully fuzzified linear fractional programming problems. Journal of Applied Mathematics and Computing, 27(1-2): 227
Rommelfanger, H. (2004) The advantages of fuzzy optimization models in practical use. Fuzzy Optimization and Decision Making, 3(4): 295
Stancu-Minasian, I.M. (1984) Stochastic programming with multiple objective functions. Dordrecht: D. Reidel Publishing Company
Tsoukalas, L.H., Uhrig, R.E. (1998) Fuzzy and neural approaches in engineering. New York, itd: Wiley-Interscience
Zimmermann, H.J. (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, 1, 45-55
Zimmermann, H.J. (1996) Fuzzy set theory and its applications. Dordrecht, itd: Kluwer Academic
Downloads
Published
Issue
Section
License
Copyright (c) YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
