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Solving Fully Rough Interval Multi-level Multi-objective linear Fractional Programming Problems via FGP |
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PP: 115-126 |
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doi:10.18576/jsap/070111
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Author(s) |
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Mohamed S. Osman,
Osama. E. Emam,
Kamal. R. Raslan,
Farahat. A. Farahat,
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Abstract |
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| This paper introduces an algorithm for solving fully rough intervalmulti-level multi-objective linear fractional programming problems where all of its coefficients in objective functionsand in constraints are rough intervals. At the first phases of the solution approach and to avoid the complexity of the problem, the shifting method proposed by Osman and El-sherbiny [20] will be used to split the rough problem into four crisp problems which will be solved simultaneously. At the second phase, for each problem, a membership function was constructed to develop a fuzzy goal programming model for obtaining the satisfactory solution of the multilevel multi-objective fractional programming problem. The linearization process introduced by Pal et. al [1] will be applied to linearize the membership functions. Finally, an illustrative numerical example is given to demonstrate the algorithm. |
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