An Interactive Model for Fully Fuzzy Multi-level Linear Programming Problem based on Multi-objective Linear Programming Technique

O. E. Emam

Department of Information Systems, Faculty of Computer Science and Information, Helwan University, Egypt.

E. Fathy

Department of Mathematics, Faculty of Science, Helwan University, Egypt.

M. A. Helmy *

Department of Basic Science, Elgazeera High Institute for Engineering and Technology, Egypt.

*Author to whom correspondence should be addressed.


Abstract

An interactive approach is proposed to find the optimal fuzzy solution of fully fuzzy multi-level linear programming (FFMLLP) problem. Firstly, convert the problem under consideration into non-fuzzy multi-level multi-objective linear programming (MLMOLP) problem by using the bound and decomposition method. Secondly, simplify the MLMOLP problem by transforming it into separate multi-objective decision-making problems with hierarchical structure, and solving it by using ε-constraint method. The main results obtained in this paper will be explained by an illustrative numerical example. Finally, compare the proposed approach for solving FFMLLP with The result found in O. Emam et al. [21] to show its effectiveness.

Keywords: Multi-level programming, multi-objective programming, interactive approach, bound and decomposition method, fuzzy linear programming.


How to Cite

Emam, O. E., E. Fathy, and M. A. Helmy. 2017. “An Interactive Model for Fully Fuzzy Multi-Level Linear Programming Problem Based on Multi-Objective Linear Programming Technique”. Journal of Advances in Mathematics and Computer Science 23 (4):1-19. https://doi.org/10.9734/JAMCS/2017/34811.

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