In the previous work we accomplished the problem of defining fuzzy dependency as well as projection and join operators which allow us to decompose a database in such a way that this process is fuzzy loss less. The definition of rules-based fuzzy dependency did not satisfy the transitivity axiom, which is crucial to obtaining the completeness of the counterpart of Armstrong axioms for fuzzy depe...

5 Goguen’s category of V-sets whose objects are functions with values in a pre-ordered set and morphisms are suitable maps is shown to be a topological construct if and only if the pre-ordered set is a complete lattice; in particular the category Set(L) of L-sets, 7 also considered by Goguen, is topological over Set. The special case when the considered pre-ordered set is L with the “mapping to...

A new notion of SP-compactness is introduced in L-topological spaces by means of semi-preopen L-sets and their inequality, where L is a complete De Morgan algebra. This new notion does not depend on the structure of basis lattice L and L does not require any distributivity. This new notion implies semicompactness, hence it also implies compactness. This new notion is a good extension and it has...

This paper presents four new recursive constructions for large sets of v − 1 STS(v). These facilitate the production of several new infinite families of such large sets. In particular, we obtain for each n ≥ 2 a large set of 3 − 1 STS(3) whose systems intersect in 0 or 3 blocks.

Antibodies readily neutralize acute, epidemic viruses, but are less effective against more indolent pathogens such as herpesviruses. Murid herpesvirus 4 (MuHV-4) provides an accessible model for tracking the fate of antibody-exposed gammaherpesvirus virions. Glycoprotein L (gL) plays a central role in MuHV-4 entry: it allows gH to bind heparan sulfate and regulates fusion-associated conformatio...

The condition of t-resilience stipulates that an n-process program is only obliged to make progress when at least n− t processes are correct. Put another way, the live sets, the collection of process sets such that progress is required if all the processes in one of these sets are correct, are all sets with at least n− t processes. We show that the ability of arbitrary collection of live sets L...

Intuitionistic fuzzy sets in the sense of Atanassov and interval-valued fuzzy sets can be seen as L-fuzzy sets w.r.t. a special lattice L . Deschrijver [2] introduced additive and multiplicative generators on L based on a special kind of addition introduced in [3]. Actually, many other additions can be introduced. In this paper we investigate additive generators on L as far as possible independ...

In a previous work we have introduced the (P,Q)-superlattice, a hyperstructure of the form (L, P ∨, Q ∧). Here (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined by a P ∨b . = a∨b∨P , a Q ∧b . = a∧b∧Q; when the sets P,Q ⊆ L satisfy appropriate conditions (L, P ∨, Q ∧) is a superlattice. In this work we continue the investigation of (P,Q)superlattice and consider the structure of ...

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

The (P,Q)-superlattice is a hyperstructure of the form (L, P ∨, Q ∧), where (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined as follows: a P ∨ b . = a ∨ b ∨ P , a Q ∧ b . = a ∧ b ∧ Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. We examine the properties of the sets a P ∨ b and a Q ∧ b in connection to the properties of P,Q. Especial...