Similarity relations in fuzzy attribute-oriented concept lattices

The study of concept lattices and oriented concept lattices with fuzzy attributes provides complementary conceptual structures, which can be used to search, analyze and extract information from large datasets. In this paper, we put forward new types of similarity relations between objects or attributes in fuzzy attribute-oriented concept lattices. We analyze how these similarities are related using the definitions and considering the reducibility between antitone and isotone fuzzy concept lattices as well. A comparison is made between two relations which measure the similarity of fuzzy oriented concepts. These relations are employed in factorizing the fuzzy attribute-oriented concept lattice, in order to reduce its complexity.