### Abstract

In this paper, the two-level linear programming problem with at least two leaders and one follower is considered. To find a satisfactory solution for the problem, an interactive fuzzy programming approach is introduced. The method is aimed so that all the decision makers at the upper level achieve their minimum satisfaction levels together with the suitable satisfaction balance between the decision maker at the lower level and each decision maker at the upper level. So as to exemplify the method, a numerical example is given. Additionally, it is shown that a k-level programming problem can also be changed into a two-level programming problem with k-1 decision makers at the upper level.

Original language | English |
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Pages (from-to) | 3585-3600 |

Number of pages | 16 |

Journal | Global Journal of Pure and Applied Mathematics |

Volume | 12 |

Issue number | 4 |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

- Interactive fuzzy programming
- Membership function
- Multi-level programming
- Optimization
- Satisfactory solution

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**An interactive fuzzy programming approach for the two-level linear programming problem with many leaders.** / Borza, M.; Rambely, Azmin Sham.

Research output: Contribution to journal › Article

*Global Journal of Pure and Applied Mathematics*, vol. 12, no. 4, pp. 3585-3600.

}

TY - JOUR

T1 - An interactive fuzzy programming approach for the two-level linear programming problem with many leaders

AU - Borza, M.

AU - Rambely, Azmin Sham

PY - 2016

Y1 - 2016

N2 - In this paper, the two-level linear programming problem with at least two leaders and one follower is considered. To find a satisfactory solution for the problem, an interactive fuzzy programming approach is introduced. The method is aimed so that all the decision makers at the upper level achieve their minimum satisfaction levels together with the suitable satisfaction balance between the decision maker at the lower level and each decision maker at the upper level. So as to exemplify the method, a numerical example is given. Additionally, it is shown that a k-level programming problem can also be changed into a two-level programming problem with k-1 decision makers at the upper level.

AB - In this paper, the two-level linear programming problem with at least two leaders and one follower is considered. To find a satisfactory solution for the problem, an interactive fuzzy programming approach is introduced. The method is aimed so that all the decision makers at the upper level achieve their minimum satisfaction levels together with the suitable satisfaction balance between the decision maker at the lower level and each decision maker at the upper level. So as to exemplify the method, a numerical example is given. Additionally, it is shown that a k-level programming problem can also be changed into a two-level programming problem with k-1 decision makers at the upper level.

KW - Interactive fuzzy programming

KW - Membership function

KW - Multi-level programming

KW - Optimization

KW - Satisfactory solution

UR - http://www.scopus.com/inward/record.url?scp=84988667223&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988667223&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 3585

EP - 3600

JO - Global Journal of Pure and Applied Mathematics

JF - Global Journal of Pure and Applied Mathematics

SN - 0973-1768

IS - 4

ER -