Optimization Model By Fuzzy Environment

E., M. Afwat A.; Salama, A. A.M.

doi:10.21608/icmep.2008.29890

Optimization Model By Fuzzy Environment

Document Type : Original Article

Authors

10.21608/icmep.2008.29890

Abstract

Abstract
A well known linear programming model and its equivalent model are introduced as a
handling type of Fuzzy optimal problem. Linear programming (LP) with Crisp objective
function and crisp constraints is modified and presented to be Fuzzy linear programming
(FLP) with Fuzzy objective function and Fuzzy constraints (Zimmermann 1983, Wemers
1984).
For each value ri of the objective function r = cTx, ro < ri < r1, the membership r C
~μ
of the
constraints obtained by the min-max method and the membership r G
~μ
of the objective
function are to be found. The Fuzzy set { ri, r G
~μ
. r C
~μ
} implies the optimal value ri which
satisfies the equality approach r G
~μ
= r C
~μ
, or the product approach : i
max
{ r G
~μ
. r C
~μ
}.

Keywords