QA268 : Necessary and sufficient conditions for efficiency in fuzzy multiobjective optimization problems
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2015
Authors:
Fateme Soleimani [Author], Mehrdad Ghaznavi[Supervisor], Maryam Ghorani[Advisor]
Abstarct: In real conditions some situations may happen that single objective mathematical models can not express the demands of decision maker, and it reduces the effectiveness and desirability of the models results. Also in real conditions, various parameters and factors are uncertain which cause great complexity in decision maxing. So, for solving these probable problems, fuzzy multiobjective optimization problems have been proposed. This thesis investigates some methods for solving fuzzy multiobjective optimization problems. One of the most widely used methods of solving these problems, is scalsrization. At first, an scalarization method baxsed on the consepts of convex cone and embedding function has been proposed. Then, the weighted sum method which is one of the most important scalarization techniques has been studied. Also, another method baxsed on the distance minimization of the functions and ideal points has been considered. In this method the importance of functions has been considered for decision makers. Next, another method has been expressed baxsed on Karush-Kahn-Tucker optimization conditions for solving fuzzy multiobjective problems. In this method, using the interval valued multiobjective optimization a fuzzy multiobjective optimization problem has been approximated and then by applying two algorithms an efficient solution for interval valued multiobjective optimization problem and a satisficing solution for the fuzzy multiobjective optimization problem are obtained.
Keywords:
#Fuzzy multiobjective optimization #Fuzzy numbers #Pareto optimal solution #Partial ordering #Convex cone Link
Keeping place: Central Library of Shahrood University
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