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Reseach Article

Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach

by Surapati Pramanik, Partha Pratim Dey
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 25 - Number 11
Year of Publication: 2011
Authors: Surapati Pramanik, Partha Pratim Dey
10.5120/3155-4360

Surapati Pramanik, Partha Pratim Dey . Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach. International Journal of Computer Applications. 25, 11 ( July 2011), 34-40. DOI=10.5120/3155-4360

@article{ 10.5120/3155-4360,
author = { Surapati Pramanik, Partha Pratim Dey },
title = { Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach },
journal = { International Journal of Computer Applications },
issue_date = { July 2011 },
volume = { 25 },
number = { 11 },
month = { July },
year = { 2011 },
issn = { 0975-8887 },
pages = { 34-40 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume25/number11/3155-4360/ },
doi = { 10.5120/3155-4360 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:11:33.631856+05:30
%A Surapati Pramanik
%A Partha Pratim Dey
%T Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach
%J International Journal of Computer Applications
%@ 0975-8887
%V 25
%N 11
%P 34-40
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper presents fuzzy goal programming approach for bi-level linear fractional programming problem with a single decision maker at the upper level and a single decision maker at the lower level. Here, each level has single objective function, which are fractional in nature and the system constraints are linear functions. In the proposed approach, we first construct fractional membership functions by determining individual best solution of the objective functions subject to the system constraints. The fractional membership functions are then transformed into equivalent linear membership functions by first order Taylor polynomial series. Since the objectives of both level decision makers are potentially conflicting in nature, a possible relaxation of both level decisions is considered for avoiding decision deadlock. Then, the fuzzy goal programming approach is used for achieving highest degree of each of the membership goals to the maximum possible by minimizing the negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is solved and Euclidean distance function is used to obtain compromise optimal solution.

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Index Terms

Computer Science
Information Sciences

Keywords

Bi-level programming Bi-level linear fractional programming Fuzzy programming Fuzzy goal programming