In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.
For an n-valued Łukasiewicz-Moisil algebra L (or LM n-algebra for short) we denote by F n(L) the lattice of all n-filters of L. The goal of this paper is to study the lattice F n(L) and to give new characterizations for the meet-irreducible and completely meet-irreducible elements on F n(L).
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
In this paper we investigate the relation between the lattice of varieties of pseudo -algebras and the lattice of varieties of lattice ordered groups.
Several open problems posed during FSTA 2006 (Liptovský Ján, Slovakia) are presented. These problems concern the classification of strict triangular norms, Lipschitz t-norms, interval semigroups, copulas, semicopulas and quasi- copulas, fuzzy implications, means, fuzzy relations, MV-algebras and effect algebras.
Closure -algebras are introduced as a commutative generalization of closure -algebras, which were studied as a natural generalization of topological Boolean algebras.
A maximal disjoint subset S of an MV-algebra A is a basis iff {x in A : x ≤ a} is a linearly ordered subset of A for all a in S. Let Spec A be the set of the prime ideals of A with the usual spectral topology. A decomposition Spec A = Ui in I Ti U X is said to be orthogonal iff each Ti is compact open and S = {ai}i in I is a maximal disjoint subset. We prove that this decomposition is unrefinable (i.e. no Ti = Theta ∩ Y with Theta open, Theta ∩ Y = emptyset, int Y = emptyset) iff S is a basis. Many...
The class of overtaker binary relations associated with the order in a lattice is defined and used to generalize the representations of L-fuzzy sets by means of level sets or fuzzy points.