A Bi-Level Non-Linear Multi-Objective Decision Making under Fuzziness

Abo-Sinna, Mahmoud A.

doi:10.1007/bf03398652

Cited by 38 publications

(33 citation statements)

References 16 publications

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“…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.…”

Section: Related Workmentioning

confidence: 99%

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Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Pramanik¹,

Dey²,

Ghosh³

et al. 2011

IJSEA

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Section: Related Workmentioning

confidence: 99%

“…Edmund and Bard [13] discussed nonlinear bilevel mathematical problems in 1991. In contrast to BLPPs, nonlinear BLPPs [14,15] have not been discussed extensively. Malhotra and Arora [16] developed an algorithm for solving linear fractional bi-level programming problem (LFBLPP) based on preemptive goal programming.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Pramanik¹,

Dey²,

Ghosh³

et al. 2011

IJSEA

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show abstract

“…Moitra and Pal [22] adopted fuzzy goal programming (FGP) approach for solving linear BLPP. 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.…”

Section: Introductionmentioning

confidence: 99%

A new methodological development for solving linear bilevel integer programming problems in hybrid fuzzy environment

Biswas¹,

Kumar²

2016

ntmsci

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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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“…AboSinna [1] and Osman et al [18] presented some approaches via fuzzy set theory for solving bilevel and multiple level multiobjective problem, and Teng et al [21], Deb and Sinha [5,6] proposed some evolutionary algorithms for some bilevel multiobjective programming problems. Besides, Bonnel and Morgan [3], Zheng and Wan [25] considered a so-called semivectorial bilevel optimization problem and proposed solution methods based on penalty approach.…”

Section: Introductionmentioning

confidence: 99%

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

Wan

2014

J. Oper. Res. Soc. China

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In this paper, a bilevel multiobjective programming problem, where the lower level is a convex parameter multiobjective program, is concerned. Using the KKT optimality conditions of the lower level problem, this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem. Then, a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced. It is shown that the Pareto optimal solutions (stationary points) of the approximate problems converge to a Pareto optimal solution (stationary point) of the original bilevel multiobjective programming problem. Numerical results showing the viability of the smoothing approach are reported.

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A Bi-Level Non-Linear Multi-Objective Decision Making under Fuzziness

Cited by 38 publications

References 16 publications

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

A new methodological development for solving linear bilevel integer programming problems in hybrid fuzzy environment

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

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