Selection of appropriate bonds between [formula omitted]-fuzzy formal contexts for recommendation tasks

Abstract

The bond between L-fuzzy formal contexts can be defined as a (Galois) connection between L-fuzzy concept lattices of L-fuzzy formal contexts. The selection of appropriate bond from the set of all bonds between L-fuzzy formal contexts is an important challenge to apply it in recommendation tasks. We propose the general method for the selection of bonds regarding external information given by L-fuzzy relation. The alternative versions of direct products of L-fuzzy formal contexts are formulated and explored since we demonstrate that the extent of direct product is a bond between input L-fuzzy formal contexts. We present examples of the benevolent and rigorous recommendations in several application domains including the real dataset about music genres. Finally, the connections with factorization of L-fuzzy formal contexts and Sugeno integral are thoroughly studied in our paper.