Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach

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

doi:10.1007/s12597-017-0307-8

Cited by 18 publications

(14 citation statements)

References 32 publications

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“…3 ., , 4 0, . ∈ 6 7 (2) such that & P N 3 & P NS , " 1,2, … , R = 1 . Then solving the ULDM problem is equivalent to finding the index O * B" ∈ 01, … , R7C P N ∈ G D yielding the global optimal solution P T * .…”

Section: Vertex Enumeration Approach: Kth Best Algorithmmentioning

confidence: 99%

“…However, there have been attempts to model the ability of one planner to indirectly influence the decisions of others to his benefits. The BLOP, which we are interested in our work, are merely a special case of the multi-level decision making problems [6][7][8][9][10]. An important feature of hierarchy structures is that a planner at one level of the hierarchy may have his objective function and decision space determined, in a part, by the other level.…”

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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Section: Vertex Enumeration Approach: Kth Best Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Various Approaches for Bi-level Optimization Problems

Sayed¹,

Farahat²

2019

IJMFS

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“…These solutions are modified by the FLDM in line with the organizational objectives. This process proceeds to a satisfactory solution [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…Sakawa et al [5] proposed interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. FGP algorithm for solving a decentralized bi-level multi-objective programming problem was developed in [4]. Arora and Gupta [1] presented interactive FGP approach for linear bi-level programming problem with the characteristics of dynamic programming.…”

Section: Introductionmentioning

confidence: 99%

“…Multilevel decision-making problems were recently studied in [3]. Pramanik and Roy [4] adopted fuzzy goals to specify the decision variables of higher level DMs and proposed weighted/ unweighted FGP models for solving MLMP to obtain a satisfactory solution. Also, FGP approach was extended for solving bi-level multi-objective programming problems with fuzzy demands [10].…”

Section: Introductionmentioning

confidence: 99%

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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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Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem

2019

Self Cite

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Fully fuzzy quadratic programming became emerge naturally in numerous realworld applications. Therefore, an effective model based on the bound and decomposition method and the separable programming method is proposed in this paper for solving Fully Fuzzy Multi-Level Quadratically Constrained Quadratic Programming (FFMLQCQP) problem, where the objective function and the constraints are quadratic, also all the coefficients and variables of both objective functions and constraints are described fuzzily as fuzzy numbers. The bound and decomposition method is recommended to decompose the given (FFMLQCQP) problem into series of crisp Quadratically Constrained Quadratic Programming (QCQP) problems with bounded variable constraints for each level. Each (QCQP) problem is then solved independently by utilizing the separable programming method, which replaces the quadratic separable functions with linear functions. At last, the fuzzy optimal solution to the given (FFMLQCQP) problem is obtained. The effectiveness of the proposed model is illustrated through an illustrative numerical example.

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Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach

Cited by 18 publications

References 32 publications

On Various Approaches for Bi-level Optimization Problems

On Various Approaches for Bi-level Optimization Problems

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

Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem

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