Attribute implications in L-concept analysis with positive and negative attributes: Validity and properties of models

We further develop our study of the L-fuzzy setting of Formal Concept Analysis with positive and negative attributes (affirmations and denials). While concept lattices in this setting are well described in our previous works, in the present paper we explore the attribute implications; which we call fuzzy containment implications. Among the main results established in the present paper are: results regarding validity of fuzzy containment implications and their models; relationship with previously studied fuzzy attribute implications; definition and properties of semantic entailment. (C) 2020 Elsevier Inc. All rights reserved.