Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems

Baky, Ibrahim A.

doi:10.1016/j.fss.2009.02.022

Cited by 104 publications

(69 citation statements)

References 17 publications

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“…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. Arora and Gupta [26] presented interactive FGP approach for linear BLPP with the characteristics of dynamic programming.…”

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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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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“…For example, Toksar [13] proposed a Taylor series approach to solve multi-objective linear fractional programming. Ibrahim [10] proposed fuzzy goal programming approach to solve decentralized bilevel multi-objective programming problems. Lai and Hwang [21] used the fuzzy ranking function to solve FMOLP problem with triangular fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Stratified simplex method for solving fuzzy multi-objective linear programming problem

Liu

Shi

2015

IFS

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Abstract. This paper is to deal with a kind of fuzzy multi-objective linear programming (FMOLP) problem with symmetric trapezoidal fuzzy numbers. Several methods has been proposed in order to obtain fuzzy efficient solution to FMOLP problem. In this paper, we change FMOLP problem into the complete stratified fuzzy linear programming problem, then use the stratified simplex method to obtain the fuzzy optimal solution directly without converting them to crisp linear programming problem. We then prove that this fuzzy optimal solution is the fuzzy efficient solution of the original FMOLP problem. A numerical example is given to illustrate the proposed method.

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“…Fuzzy programming approach to multi-level programming problems was studied by Sinha [11]. The Baky investigated the problem of Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems [12]. In this paper, membership functions, which are associated with each objectives of each levels of FLFBL-MOP.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy linear fractional bi-level multi-objective programming problems

Safaei¹,

Saraj²

2012

International Journal of Applied Mathematical Research

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The Kuhn-Tuker condition has become nowadays an important tool in the hands of investigation for checking the optimality in optimization literature. In the present paper with use of a Taylor series and KuhnTucker conditions approach, we solve a fuzzy linear fractional bilevel multi-objective programming (FLFBL-MOP) problem. The Taylor series is an expansion of a series that represents a function. In the proposed approach, membership functions associated with each level(s) of the objective(s) of FLFBL-MOP problems are transformed and unified by using a Taylor series approach. By using the Kuhn-Tucker conditions, the problem is reduced to a single objective and finally, numerical example is given to illustrates the efficiency and superiority of the proposed approach.

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Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems

Cited by 104 publications

References 17 publications

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

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

Stratified simplex method for solving fuzzy multi-objective linear programming problem

Fuzzy linear fractional bi-level multi-objective programming problems

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