Fully Fuzzy Multi-Level Linear Programming Problem

Emam, O. E.; Fathy, E.; Helmy, M.A.

doi:10.5120/ijca2016912287

IJCA

2016

DOI: 10.5120/ijca2016912287

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Fully Fuzzy Multi-Level Linear Programming Problem

O. E. Emam¹,

E. Fathy²,

M.A. Helmy³

Abstract: This paper focuses on the solution of fully fuzzy multi-level linear programming (FFMLLP) Problem, where all of its decision parameters and variables are fuzzy numbers. An algorithm depending on the fuzzy decision approach and bound and decomposition method will be developed to find a fuzzy optimal solution for the problem under consideration. The main results obtained in this paper will be clarified by an illustrative numerical example. KeywordsMulti-level programming; Fuzzy decision approach; Bound and decom… Show more

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Cited by 2 publications

References 14 publications

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Three different optimization techniques for solving the fully rough interval multi-level linear programming problem

Fathy

Ammar

Helmy³

2023

IFS

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Due to the importance of the multi-level fully rough interval linear programming (MLFRILP) problem to address a wide range of management and optimization challenges in practical applications, such as policymaking, supply chain management, energy management, and so on, few researchers have specifically discussed this point. This paper presents an easy and systematic roadmap of studies of the currently available literature on rough multi-level programming problems and improvements related to group procedures in seven basic categories for future researchers and also introduces the concept of multi-level fully rough interval optimization. We start remodeling the problem into its sixteen crisp linear programming LP problems using the interval method and slice sum method. All crisp LPs can be reduced to four crisp LPs. In addition, three different optimization techniques were used to solve the complex multi-level linear programming issues. A numerical example is also provided to further clarify each strategy. Finally, we have a comparison of the methods used for solving the MLFRILP problem.

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Three different optimization techniques for solving the fully rough interval multi-level linear programming problem

Fathy

Ammar

Helmy³

2023

IFS

View full text Add to dashboard Cite

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On Fuzzy Bi-Level Multi-Objective Large Scale Integer Quadratic Programming Problem

Emam¹,

Fathy²,

Abdullah³

2017

IJCA

Self Cite

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The motivation behind this paper is to focus on the solution of a Bi-Level Multi-Objective Large Scale Integer Quadratic Programming (BLMOLSIQP) problem in which all decision parameters in the objective functions are symmetric trapezoidal fuzzy numbers, and has block angular structure of the constraints. The suggested algorithm based on a linear ranking function, weight method, Taylor's series, decomposition algorithm and branch and bound method is to find a compromised solution for the problem under consideration. In addition, the theoretical results are illustrated with the help of a numerical example.

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Fully Fuzzy Multi-Level Linear Programming Problem

Cited by 2 publications

References 14 publications

Three different optimization techniques for solving the fully rough interval multi-level linear programming problem

Three different optimization techniques for solving the fully rough interval multi-level linear programming problem

On Fuzzy Bi-Level Multi-Objective Large Scale Integer Quadratic Programming Problem

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