  Motivated by the increasing exposition of decision makers to both statistical
and judgemental based sources of demand information, we develop in this paper a
fuzzy Gaussian Mixture Model (GMM) for the newsvendor permitting to mix
probabilistic inputs with a subjective weight modelled as a fuzzy number. The
developed framework can model for instance situations where sales are impacted
by customers sensitive to online review feedbacks or expert opinions. It can
also model situations where a marketing campaign leads to different stochastic
alternatives for the demand with a fuzzy weight. Thanks to a tractable
mathematical application of the fuzzy machinery on the newsvendor problem, we
derived the optimal ordering strategy taking into account both probabilistic
and fuzzy components of the demand. We show that the fuzzy GMM can be rewritten
as a classical newsvendor problem with an associated density function involving
these stochastic and fuzzy components of the demand. The developed model
enables to relax the single modality of the demand distribution usually used in
the newsvendor literature and to encode the risk attitude of the decision
maker.
