Geodesic
Penalty Method for Fuzzy Linear Programming With Trapezoidal Numbers
Yugoslav journal of operations research, Tome 19 (2009) no. 1, p. 149 .

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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.
Classification : 90C70 90C08
Keywords: Linear programming, trapezoidal fuzzy number, penalty method. 
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     author = {Bogdana Stanojevi\'c and Milan Stanojevi\'c},
     title = {Penalty {Method} for {Fuzzy} {Linear} {Programming} {With} {Trapezoidal} {Numbers}},
     journal = {Yugoslav journal of operations research},
     pages = {149 },
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2009},
     zbl = {1274.90526},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2009_19_1_a10/}
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Bogdana Stanojević; Milan Stanojević. Penalty Method for Fuzzy Linear Programming With Trapezoidal Numbers. Yugoslav journal of operations research, Tome 19 (2009) no. 1, p. 149 . http://geodesic.mathdoc.fr/item/YJOR_2009_19_1_a10/