International Journal of Intelligent Systems and Applications(IJISA)
ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)
Published By: MECS Press
IJISA Vol.8, No.7, Jul. 2016
Solving a Linear Programming with Fuzzy Constraint and Objective Coefficients
Full Text (PDF, 811KB), PP.65-72
In this paper, we consider a method for solving a linear programming problem with fuzzy objective and coefficient matrix, where the fuzzy numbers are supposed to be triangular. By the proposed method, the Decision Maker will have the flexibility of choosing. The solving method is based on the Pareto algorithm, which converts the problem to a weighted-objective linear programming. For more illustration, after discussing the problem and the algorithm, we present an example, which its solutions are independent from the objective weights.
Cite This Paper
Hamid Reza Erfanian, Mohammad Javad Abdi, Sahar Kahrizi,"Solving a Linear Programming with Fuzzy Constraint and Objective Coefficients", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.7, pp.65-72, 2016. DOI: 10.5815/ijisa.2016.07.07
Bellman, R.E. and Zadeh, L.A., Decision making in fuzzy environment. Management Science. 1970, 17: 141-164.
Dash ,R. B. and Dash, P.D.P., Solving Fuzzy Integer Programming Problem as Multi objective Integer Programming Problem, International Journal of Fuzzy Mathematics and Systems. 2012, 2: 307-314
Delgado M., Verdegay J L., Vila M.A., A general model for fuzzy linear programming. Fuzzy Sets and Systems. 1989, 29: 21-29
Erfanian, H.R., Noori Eskandari, M.H., Vahidian Kamyad A., Solving a Class of Separated Continuous Programming Problems Using Linearization and Discretization, Int. J. Sensing, Computing & Control, 2011, 1: 117-124.
Erfanian, H.R., Noori Eskandari, M.H., Vahidian Kamyad A., A New Approach for the Generalized First Derivative and Extension It to the Generalized Second Derivative of Nonsmooth Functions, I.J. Intelligent Systems and Applications, 2013, 04, 100-107.
Hashem, H.A., Converting Linear Programming Problem with Fuzzy Coefficients into Multi Objective Linear Programming Problem, Australian Journal of Basic and Applied Sciences. 2013, 7(7): 185-189.
Kumar, A., et al. Applied Mathematical Modelling. 2011, 35:817–823
Li G, Guo R. Comments on formulation of fuzzy linear programming problems as four objective constrained optimization problems. Applied Mathematics and Computation. 2007, 186: 941-944
Nasseri, S. H., Behmanesh, E., Linear Programming with Triangular Fuzzy Numbers—A Case Study in a Finance and Credit Institute, Fuzzy Inf. Eng. 2013, 3: 295-315
Negoita, C.V., Fuzziness in management OPSA/TIMS Miami. 1970.
Noori Eskandari, M.H., Erfanian, H.R., Vahidian Kamyad A., Generalized Derivative of Fuzzy Nonsmooth Functions, Journal of Uncertain Systems, 2012, 6 (3):214-222.
Noori Eskandari, M.H., Erfanian, H.R., Vahidian Kamyad A., Farahi,M.H., Solving a Class of Non-Smooth Optimal Control Problems, I.J. Intelligent Systems and Applications, 2013, 07, 16-22.
Pandit, P.k., Portfolio optimization using fuzzy linear programming, AIP Conference Proceedings. 2013, 1557, 206
Ramik J, Rimanek J. Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets and Systems. 1985, 16: 123-138
Takeshi, I., Hiroaki, I. and Teruaki, N., A model of crop planning under uncertainty in Agricultural management, Int. J. of Production Economics. 1991, 1: 159-171.
Tanaka, H., Ichihashi, H. and Asai K., A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control and Cybernetics. 1991, 3(3): 185-194.
Thakre, P.A., Shelar D.S. and Thakre, S.P., Solving fuzzy linear programming problem as multi objective linear programming problem, Proceedings of the World Congress on Engineering WCE, London, U.K. 2009.
Zhang, G., Y.H. Wu, M. Remias and J. Lu. Formulation of fuzzy linear programming problems as four-objective constrained optimization problems, Applied Mathematics and Computation. 2003, 139: 383-399.
Zimmermann, H.J., Description and optimization of fuzzy systems, International Journal of General Systems. 1976, 2(4): 209-215.
Zimmermann, H.J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems. 1978, 1: 45-55.