“…Osman et al [43] extended the fuzzy approach of Abo-Sinna [15] for solving non-linear bi-level and tri-level multi-objective decision making under fuzziness. Their method based on the concept that the lower level decision maker maximizes membership goals taking a goal or preference of the ULDM into consideration.…”
“…Osman et al [43] extended the fuzzy approach of Abo-Sinna [15] for solving non-linear bi-level and tri-level multi-objective decision making under fuzziness. Their method based on the concept that the lower level decision maker maximizes membership goals taking a goal or preference of the ULDM into consideration.…”
“…Lai [1] at first proposed a new solution concept based on tolerance membership functions as well as multiple objective optimizations to develop an effective fuzzy approach for solving MLPP. Shih et al [2] extended Lai's concept and proposed a supervised search procedure by employing non-compensatory max-min aggregation operator for solving MLPP.…”
In this paper a Large-Scale three level fractional problem is considered with random rough coefficient in objective function, in order to solve this problem, The intervals technique used to convert rough nature in objective into equivalent crisp , Then Tailor Series transformation is used to convert the Large-Scale three level fractional to an equivalent three level linear programming problem , then a Traditional Method used to constructed solution of the three-level programming problem, then we will use Decomposition Technique to solve Large-ScaleProblem. Finally an auxiliary problem is discussed as well as an example is presented.
“…Abo-Sinha [23] discussed multi-objective optimization for solving non-linear multi-objective bi-level programming problems in fuzzy environment. Osman et al [24] extended fuzzy approaches [23] for solving non-linear bi-level and tri-level multi-objective decision making under fuzziness. Baky [25] studied FGP algorithm for solving decentralized bi-level multi-objective programming problems.…”
This paper deals with fuzzy goal programming approach to solve fuzzy linear bilevel integer programming problems with fuzzy probabilistic constraints following Pareto distribution and Frechet distribution. In the proposed approach a new chance constrained programming methodology is developed from the view point of managing those probabilistic constraints in a hybrid fuzzy environment. A method of defuzzification of fuzzy numbers using α−cut has been adopted to reduce the problem into a linear bilevel integer programming problem. The individual optimal value of the objective of each DM is found in isolation to construct the fuzzy membership goals. Finally, fuzzy goal programming approach is used to achieve maximum degree of each of the membership goals by minimizing under deviational variables in the decision making environment. To demonstrate the efficiency of the proposed approach, a numerical example is provided.
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