Reducts of fuzzy contexts: Formal concept analysis vs. rough set theory

We postulate the intuitive idea of reducts of fuzzy contexts based on formal concept analysis and rough set theory. For a complete residuated lattice $L$, it is shown that reducts of $L$-contexts in formal concept analysis are interdefinable with reducts of $L$-contexts in rough set theory via negation if, and only if, $L$ satisfies the law of double negation.