Irreducible elements in multi-adjoint concept lattices

Jesus Medina-Moreno, Maria Eugenia Cornejo, Eloisa Ramirez
2013 Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology  
One of the most important elements in a lattice are the irreducible elements. For example, when the lattice is finite, which is usual in the computational case, it forms a base from which the complete lattice is obtained. These elements are also important in Formal Concept Analysis, since they are the basic information of a relational system. In the general fuzzy framework of multi-adjoint concept lattices, this paper presents a characterization of the irreducible elements and so, a mechanism
more » ... detect the base information given in a general relational system. This result is applied to reduce the size of the concept lattices without losing and modifying important information. In order to make this paper as self-contained as possible, first of all, we recall the well-known definition of irreducible elements of a lattice. (L, ), such that ∧, ∨ are the meet and the join operators, and an element x ∈ L verifying 1. If L has a top element , then x = . Definition 1 Given a lattice 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013)
doi:10.2991/eusflat.2013.18 dblp:conf/eusflat/Medina-MorenoCR13 fatcat:ur5yq2fb55hhxf74mb2zqalzca