Block relations in formal fuzzy concept analysis

• We generalize known results on the correspondence of block relations and complete tolerances.
• We provide an illustrative example of using block relations to reduce the size of a concept lattice.
• We consider both, the antitone and the isotone case.

One of the main problems in formal concept analysis (especially in fuzzy setting) is to reduce a concept lattice of a formal context to appropriate size to make it graspable and understandable. A natural way to do it is to substitute the formal context by its block relation which is equivalent to factorization of the concept lattice by a complete tolerance. We generalize known results on the correspondence of block relations of formal contexts and complete tolerances on concept lattices to fuzzy setting and we provide an illustrative example of using block relations to reduce the size of a concept lattice.