On characterization of fuzzy vectors and its applications to fuzzy mathematical programming problems

In this paper, we consider fuzzy mathematical programming problems which involve fuzzy vectors only in the objective function. First, we define fuzzy vectors on n-dimensional Euclidean space Rn and investigate their properties. Especially, we extend the concepts of the fuzzy max order and the possibility and the necessity measures given in fuzzy number to those of fuzzy vectors. Next, based on the results, we consider fuzzy mathematical programming problems, including fuzzy multicriteria optimization problems, which involve fuzzy vectors only in the objective function and we give the concepts of optimal solutions and characterize their properties.