<p>The present paper investigates information systems stemming from rough set theory against the backdrop of the Ellsberg Paradox. In the early 1960s, D. Ellsberg introduced and discussed a type of informational uncertainty/ambiguity that could not be adequately modelled by the concept of measurable risk. Twenty years later, Z. Pawlak developed rough set theory—a mathematical framework aimed at modelling and managing different types of informational uncertainty that may be found in data analysis (including various forms of imprecision, vagueness, or indecision). However, as in economics in the 1960s, by uncertainty it has commonly been meant, in default of any other alternative interpretation, a sort of measurable risk. In the present study, we would like to fill this research gap and examine D. Ellsberg’s distinction between measurable risk and unmeasurable ambiguity in the context of various forms of information systems related to rough set theory. It turns out that this distinction brings an interesting reformulation of rough sets and reveals hidden facets of this theory. Specifically, we investigate two versions of ambiguity that can be derived from the Ellsberg paradox and relate them to the row and column oriented representations of information systems.</p>