Abstract

\textit{N. D. Yen} and \textit{T. D. Phuong} [in: Vector variational inequalities and vector equilibria. Mathematical theories. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 38, 479–489 (2000; Zbl 0995.90088)] have shown that the efficient solution set of a linear fractional vector optimization problem can be regarded as the image of the solution map of a specific parametric monotone affine variational inequality. This paper establishes some facts about the domain, the image and the continuity of this solution map (called the basic multifunction), provided that the linear fractional vector optimization problem under consideration satisfies an additional assumption. The results can lead to some upper estimates for the number of components in the solution sets of linear fractional vector optimization problems.