Concavity of the Vector-Valued Functions Occurring in Fuzzy Multiobjective Decision-Making

摘要: Werners’ approach to fuzzy multiobjective decision-making Leads a crisp substitute problem which is of lexicographically extended max-min optimization. Nikodem has shown that real-valued function on convex subset R n concave (convex) if and only it midpoint (midpoint convex) quasiconcave (quasiconvex). This paper investigates the question how much Nikodem’s theorem can be transferred vector-valued functions, such as arise in model, where concavity or generalized taken with respect increasing rearrangement ordering. Some intermediate results are derived well.