Geodesic
Linear Programming Problems With some Multi-Choice Fuzzy Parameters
Yugoslav journal of operations research, Tome 28 (2018) no. 2, p. 249 .

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In this paper, we consider some Multi-choice linear programming (MCLP) problems where the alternative values of the multi-choice parameters are fuzzy numbers. There are some real-life situations where we need to choose a value for a parameter from a set of different choices to optimize our objective, and those values of the parameters can be imprecise or fuzzy. We formulate these situations as a mathematical model by using some fuzzy numbers for the alternatives. A defuzzification method based on in centre point of a triangle has been used to find the defuzzified values of the fuzzy numbers. We determine an equivalent crisp multi-choice linear programming model. To tackle the multi-choice parameters, we use Lagranges interpolating polynomials. Then, we establish a transformed mixed integer nonlinear programming problem. By solving the transformed non-linear programming model, we obtain the optimal solution for the original problem. Finally, two numerical examples are presented to demonstrate the proposed model and methodology.
Classification : 90C05, 90C11, 90C70
Keywords: Linear Programming, Triangular Fuzzy Number, Trapezoidal Fuzzy Number, Multi-choice Programming, Fuzzy Programming 
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     author = {Avik Pradhan and Mahendra Prasad Biswal},
     title = {Linear {Programming} {Problems} {With} some {Multi-Choice} {Fuzzy} {Parameters}},
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Avik Pradhan; Mahendra Prasad Biswal. Linear Programming Problems With some Multi-Choice Fuzzy Parameters. Yugoslav journal of operations research, Tome 28 (2018) no. 2, p. 249 . http://geodesic.mathdoc.fr/item/YJOR_2018_28_2_a6/