’FLIP’: An Interactive Method for Multiobjective Linear Programming with Fuzzy Coefficients

FLIP is an interactive method for solving multiobjective linear programming problems with fuzzy coefficients in the objective functions and on the both sides of the constraints. Taking into account that fuzzy aspiration levels are defined on all the objectives, the key question is how to compare left- and right-hand-sides in objectives and constraints which are fuzzy numbers for given x. Assuming an L-R representation of fuzzy numbers, a comparison principle has been proposed enabling transformation of the fuzzy MOLP problem into a multiobjective linear fractional program. It is then solved with an interactive method using a linear programming procedure as the only optimiser. In FLIP, interaction with the user takes place at two levels: first, when safety parameters have to be defined in the transformation phase, and second, when the associate deterministic problem is solved. At the latter level, the user is assisted by a graphical display of solutions.

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