In this paper, we apply fuzzy set theory to a single-manufacturer singleretailer supply chain, where both players try to determine their optimal pricing and advertising decisions. The interaction between manufacturer and retailer is analyzed by means of a Stackelberg game. Moreover, a vertical cooperative advertising program is considered, which represents a financial agreement where the manufacturer offers to share a certain fraction of his retailer's advertising expenditures. Even though this topic gained substantial interest in recent years' operations research literature and studies reveal that results strongly depend on demand parameters, most analyses are limited to deterministic model formulations. Here, fuzzy set theory has the advantage that it is not only able to incorporate the uncertainty of demand parameters into analysis. Furthermore, it enables us to take into consideration the experience of decision makers, which is often not expressed numerically, but rather in vague linguistic terms.