Note on representing attribute reduction and concepts in concept lattice using graphs

Abstract

Mao H. (2017, Representing attribute reduction and concepts in concept lattice using graphs. Soft Computing 21(24):7293-7311) claims to make contributions to the study of reduction of attributes in concept lattices by using graph theory. We show that her results are either trivial or already well-known and all three algorithms proposed in the paper are incorrect.We use the same notions and the same notations as Mao (2017); however we need to also recall a few notions from (Ganter and Wille, 1999) to explain our case. Thus, for the reader's convenience, we provide full preliminaries.An input to FCA is a triplet (O, P, I), called a formal context, where O, P are finite non-empty sets of objects and attributes, respectively, and I is a binary relation between O and P ; (o, a) ∈ I means that the object o has the attribute a. Finite formal contexts are usually depicted as tables, in which rows represent objects, columns represent attributes, and each entry contains a cross if the corresponding object has the corresponding attribute, and is otherwise left blank (see top parts of Figures 3-5 for examples).The formal context induces the following operators: