TITLE:
A New Approach for Solving Fuzzy Linear Multi-Criterion Problems: An Approach Based on Minimization of the Errors Functions
AUTHORS:
Joél Lema Makubikua, Amani Wema, Yves Tinda Mangongo, Joseph-Désiré Kyemba Bukweli, Justin Dupar Busili Kampempe
KEYWORDS:
Deviation Variable, Compromise Solution, Membership Function, Error Function, Decision-Making Function
JOURNAL NAME:
American Journal of Operations Research,
Vol.13 No.1,
January
20,
2023
ABSTRACT: The main purpose of this paper is to build a new approach for solving a
fuzzy linear multi-criterion problem by defining a function called “error
function”. For this end, the concept of level set is used to construct
the error function. In addition, we introduce the concept of deviation variable
in the definition of the error function. The algorithm of the new approach is
summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing
a specific level . second, we solve separately each uni-criteria problem and we compute the error
function for each criteria. Finally, we minimize the sum of error functions in
order to obtain the desired compromise solution. A numerical example is done
for a comparative study with some existing approaches to show the effectiveness
of the new approach.