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Journal of Advances in Applied Mathematics
JAAM > Volume 6, Number 1, January 2021

Some Approaches for Fuzzy Multiobjective Programming Problems

Download PDF  (205.7 KB)PP. 15-26,  Pub. Date:February 7, 2021
DOI: 10.22606/jaam.2021.61002

Author(s)
Yves Mangongo Tinda, Justin Dupar Kampempe Busili
Affiliation(s)
Department of Mathematics and Computer Science, University of Kinshasa, Kinshasa, D.R.Congo
Department of Mathematics and Computer Science, University of Kinshasa, Kinshasa, D.R.Congo
Abstract
In this paper we discuss two approaches to bring a balance between effectiveness and efficiency while solving a multiobjective programming problem with fuzzy objective functions. To convert the original fuzzy optimization problem into deterministic terms, the first approach makes use of the Nearest Interval Approximation Operator (Approximation approach) for fuzzy numbers and the second one takes advantage of an Embedding Theorem for fuzzy numbers (Equivalence approach). The resulting optimization problem related to the first approach is handled via Karush- Kuhn-Tucker like conditions for Pareto Optimality obtained for the resulting interval optimization problem. A Galerkin like scheme is used to tackle the deterministic counterpart associated to the second approach. Our approaches enable both faithful representation of reality and computational tractability. They are thus in sharp contrast with many existing methods that are either effective or efficient but not both. Numerical examples are also supplemented for the sake of illustration.
Keywords
multiobjective programming, fuzzy numbers, nearest interval approximation, embedding theorem.
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