Rough Set Model and Approximations in Fuzzy Formal Contexts

Given a set of objects G with a set of attributes M and a binary relation I, a formal context (G, M, I) corresponds to a Boolean-valued information table in rough set theory, and the kernel relation of the function from G to M which maps each object of G to its afterset. This coincides with the indiscernibility relation of the Boolean-valued information table. Rough set model and Variable-Precision model (VP-model) under a formal context can be formulated based on the associated kernel relation on the objects set. $\alpha$-fuzzified rough set model and VP-model under a fuzzy formal context are formulated analogously. We present an example to demonstrate the proposed $\alpha$-fuzzified rough set model and VP-model under a fuzzy formal context.