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On Some Stability Notations for Fuzzy Three-level Fractional Programming Problem |
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PP: 23-34 |
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doi:10.18576/msl/100104
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Author(s) |
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Omar M. Saad,
Mervat M. Elshafei,
Marwa M. Sleem,
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Abstract |
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| In this paper, suggested a solution algorithm to a fuzzy three-level fractional programming problem (F-TLFP). This problem involving fuzzy parameters on the right side of the constraints. First, a non-fuzzy problem (α-TLFP) with a crisp set of constraints is established depending on the concept of the α-level set of fuzzy numbers. Second, problem (α-TLFP) could be converted into a real-valued three-level fractional programming problem (RV-TLFP) which could be transformed into a real-valued bi-level fractional programming problem (RV-BLFP) by the duality theorem of linear fractional programming. In the same way, the problem (RV-BLFP) is transformed into a real-valued single-level fractional programming problem (RV-SLFP) again by the duality theorem, which could be solved for obtaining an α-optimal solution of problem (F-TLFP). Also, some stability notions are characterized and defined for the problem of concern by extending the Karush-Kuhn-Tucker optimality conditions equivalent to the problem (RV-SLFP). An algorithm is a presentation of infinite steps to solve and investigate the stability of the solution of the problem (F-TLFP). An illustrative numerical example is provided to demonstrate the proposed solution algorithm.
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