Stability in Multiobjective Possibilistic Linear Programming

Abstract

We consider certain multiobjective possibilistic linear programming problems (MPLP) introduced by Buckley in [1]:

$$ \max \quad Z = \left( {{{\tilde c}_1}x, \ldots ,{{\tilde c}_k}x} \right) $$

$$ subject\;to\quad {\tilde a_i}x\; * \;{\tilde b_i},\;\;i = 1, \ldots m,\;\;x \geqslant 0 $$

where ã_i=(ã_i1,...,ã_in), c̃_k=(c̃_k1,...,c̃_kn) are vectors of fuzzy numbers, b̃_i is a fuzzy number, x=(x₁,..., x_n) is a vector of (non-fuzzy) decision variables, and * denotes <, ≤, =, ≥ or > for each i.