On Parametric Multi-level Multi-objective Fractional Programming Problems with Fuzziness in the Constraints

Osman, M. S.; Emam, O. E.; Sayed, Mohamed A. El

doi:10.9734/bjmcs/2016/28531

Cited by 15 publications

(13 citation statements)

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“…Sakawa [15] introduced interactive fuzzy programming for two level linear fractional programming problems. Parametric multi-level multi-objective fractional programming problem solution is given by Osman et al [9]. Pramanik and Roy [14] uses fuzzy goals for solving MLPP.…”

Section: Ml-mofqfommentioning

confidence: 99%

FGP in Multi-objective Non-Linear Fractional Optimization Model including Triangular Fuzzy Numbers

Gupta¹,

Kumar²,

Rani³

2019

IJITEE

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The motivation behind this paper is to propose method to obtain compromized solution of Non-Linear fractional Optimization Model. In this paper, Multi-level multi-objective fully quadratic fractional optimization model (ML-MOFQFOM) is studied in which various objective functions are involved, generally have conflicting nature. FGP approach is being used to solve ML-MOFQFOM involving triangular fuzzy numbers. This paper deals with the ML-MOFQFOM in which fuzzy model converted into deterministic form through the help of  -cuts where  is the combined choice of all objective functions. An algorithm and examples are also presented to validate the proposed method.

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Section: Ml-mofqfommentioning

confidence: 99%

FGP in Multi-objective Non-Linear Fractional Optimization Model including Triangular Fuzzy Numbers

Gupta¹,

Kumar²,

Rani³

2019

IJITEE

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“…Definition 5: If , is a feasible solution of the BL-MODM problem; no other feasible solution ̅ , ̅ ∈ exist, such that % " ̅ , ̅ ≤ % " , ; at least one / / = 1,2, … , ! is strict inequality, then , is the noninferior solution of the BL-MODM problem [2,22,40].…”

Section: Bi-level Multi-objective Programmingmentioning

confidence: 99%

“…Often these groups are arranged within a hierarchical administrative structure, each with independent and perhaps conflicting objectives. Multi-level decision making has always been regarded as an important aspect of the planning process [1][2][3][4][5]. Frequently, the impacts of directives from supervisors and reactions from subordinates have been viewed as externalities, beyond the control of planner.…”

Section: Introductionmentioning

confidence: 99%

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On Various Approaches for Bi-level Optimization Problems

Sayed¹,

Farahat²

2019

IJMFS

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In this paper we review some different basic approaches for solving bi-level optimization problems (BLOP).Firstly, the formulation and some basic concepts of such BLOP are presented. Secondly, some conventional approaches for solving the BLOP such as; vertex enumeration method, branch and bound algorithm, Karush Kuhn-Tucker (KKT) transformation are exhibited. The vertex enumeration based approaches which use the important characteristic that at least one global optimal solution is attained at an extreme point of the constraints set. The KKT approaches in which a BLOP is transformed into a single level problem that solves the upper level decision maker (ULDM) problem while including the lower level decision maker (LLDM) optimality conditions as extra constraints. Fuzzy programming approach mainly based on the fuzzy set theory. Finally, formulation of the bi-level multi-objective decision making (BL-MODM) problem and recently developed approaches, such as; fuzzy goal programming (FGP) and technique for order preference by similarity to ideal solution (TOPSIS) approach, for solving such problem are presented. Numerical illustrations are presented for each technique to ensure the applicability and efficiency.

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“…FGP approach to solve stochastic fuzzy multi-level multi-objective fractional programming problem was extended in [4]. Parametric multi-level multi-objective fractional programming problems with fuzziness in the constraints has been presented in [21].…”

Section: Introductionmentioning

confidence: 99%

Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

Osman

Emam

Sayed

2017

ARJOM

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The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the-cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in each level are transformed into non-linear objective functions based on a proposed transformation. Secondly, in the proposed model, separate non-linear membership functions for each objective function of the ML-MOQFP problem are defined. Then, the fuzzy goal programming (FGP) approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.

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On Parametric Multi-level Multi-objective Fractional Programming Problems with Fuzziness in the Constraints

Cited by 15 publications

References 0 publications

FGP in Multi-objective Non-Linear Fractional Optimization Model including Triangular Fuzzy Numbers

FGP in Multi-objective Non-Linear Fractional Optimization Model including Triangular Fuzzy Numbers

On Various Approaches for Bi-level Optimization Problems

Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

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