  We define decision-making functions which arise from studying the
multidimensional generalization of the weighted Bajraktarevi\'c means. It
allows a nonlinear approach to optimization problems.
  These functions admit several interesting (from the point of view of
decision-making) properties, for example, delegativity (which states that each
subgroup of decision-makers can aggregate their decisions and efforts),
casuativity (each decision affects the final outcome except two trivial cases)
and convexity-type properties.
  Beyond establishing the most important properties of such means, we solve
their equality problem, we introduce a notion of synergy and characterize the
null-synergy decision-making functions of this type.
