Fuzzy Goal Programming Approach for Tri-Level Nonlinear Programming
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Date
2014-12
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Addis Ababa University
Abstract
Multi-level programming problem (MLPP) is an optimization problem which
has other optimization problems in its constraint set and has a decision maker
for each objective function controlling part of the variables. In this thesis
we try to investigate some special multilevel programming problem which
is a tri-level programming with the quadratic fractional objective functions
and polyhedral constraints. Fuzzy goal programming approach is one of the
methods used for solving multilevel programming problems through fuzzy
goal programming (FGP) model formulation, corresponding objectives of
equivalent multi-level programming problem are transformed into fuzzy goals
(membership functions) by means of assigning an aspiration level to each of
them and suitable membership function is de_ned for each objectives. Then
achievement of the highest membership value of each of the fuzzy goals is formulated
by minimizing the sum of negative deviational variables. However,
due to the conicting nature of each DM's objective function and hierarchical
nature of the problem, solving the formulated problem for one level may not
produce a satisfactory solution for the system. So this nature of the problem
can be controlled by de_ning a new membership function of _rst level decision
maker (FLDM) and second level decision maker (SLDM) based on the
solution we obtained in the _rst formulation. Therefore, after some iterations
FLDM and SLDM arrive at a satisfactory level and this intern produce
a satisfactory solution for the system.
Keywords: Tri-level programming, Quadratic fractional programming, Fuzzy
goal programming, membership functions, deviational variables
Description
Keywords
Tri-Level Programming, Quadratic Fractional Programming, Fuzzy Goal Programming, Membership Functions, Deviational Variables