An approach for solving a fuzzy multiobjective programming problem

• We present an approach for solving a fuzzy multiobjective program.
• It is based on the Nearest Interval Approximation (NIA) Operator.
• K.K.T like conditions of efficiency have been obtained for the resulting program.
• To solve our problem, we first replace fuzzy values by their NIA counterparts.
• After this, we make use of obtained efficiency conditions to generate the solution.

In this paper we present a new approach, based on the Nearest Interval Approximation Operator, for dealing with a multiobjective programming problem with fuzzy-valued objective functions.By the way we have established a Karush–Kuhn–Tucker (K.K.T) kind of Pareto optimality conditions, for the resulting interval multiobjective program. To this end, we made use of gH-differentiability of involved interval-valued functions.Two algorithms play a pivotal role in the proposed method. The first one returns a nearest interval approximation to a given fuzzy number. The other one makes use of K.K.T conditions to deliver a Pareto optimal solution of the above mentioned resulting interval program.