Unifying fuzzy concept lattice construction methods

Formal Concept Analysis (FCA) and its fuzzy extension have been widely used to arrange data into a lattice that is an effective data structure useful to address several aims, such as: data mining, ontology learning and merging, and so on. In literature it is possible to distinguish two main approaches to address fuzzy FCA implementation: The one-sided threshold and the fuzzy closure one. This work focuses on a specific definition of one-sided threshold algorithm and fuzzy closure one. Specifically, it shows that these methods can be unified, since the onesided threshold approach can be seen as a specialization of the fuzzy closure. The lattice generated using onesided fuzzy threshold approach is a substructure of the lattice generated using the fuzzy closure approach. In addition, an experimentation has been performed on both implementations of the fuzzy FCA, one-sided threshold and fuzzy closure. In particular, the results are compared in terms of running time and number of extracted fuzzy concepts by varying the t-norm function Łukasiewicz, Gödel, and Product.