On reflexive closed set lattices

Zhongqiang Yang; Dong Sheng Zhao

Displaying similar documents to “On reflexive closed set lattices”

Reflexivity of bilattices

Kamila Kliś-Garlicka (2013)

Czechoslovak Mathematical Journal

Similarity:

We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice $ℒ$ we may associate a bilattice $Σ_{ℒ}$ . Similarly, having a bilattice $Σ$ we may construct a subspace lattice $ℒ_{Σ}$ . Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.

Join-closed and meet-closed subsets in complete lattices

František Machala, Vladimír Slezák (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

To every subset $A$ of a complete lattice $L$ we assign subsets $J (A)$ , $M (A)$ and define join-closed and meet-closed sets in $L$ . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure $J_{L}^{p}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure $J_{L}^{p}$ .

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

Similarity:

In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the $F$ -partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.