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.