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Research Article Open access CC BY 4.0

A Computational Model for Multi-level Quadratically Constrained Quadratic Optimization under Fully Fuzzy Environment

Hawaf AbdAlhakim, O. E. Emam, A. A. Abd El-Mageed

Journal of Advances in Mathematics and Computer Science · pp. 1–21 · Published 23 Jun 2018

10.9734/JAMCS/2018/42263

Abstract

Fully fuzzy quadratic programming became emerge naturally in numerous real-world 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.

Fully fuzzy programming multi-level programming quadratic programming bound and decomposition method separable programming method.

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A modified fuzzy approach for the fully fuzzy multi-objective and multi-level integer quadratic programming problems based on a decomposition technique

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