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On the reduction of a random basis

Ali Akhavi, Jean-François Marckert, Alain Rouault (2009)

ESAIM: Probability and Statistics

For p ≤ n, let b1(n),...,bp(n) be independent random vectors in ℝ n with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If b ^ 1 ( n ) , ... , b ^ p ( n ) is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...

Relative co-annihilators in lattice equality algebras

Sogol Niazian, Mona Aaly Kologani, Rajab Ali Borzooei (2024)

Mathematica Bohemica

We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among ∨ -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra 𝔼 and 𝔽 a filter of 𝔼 , we define the set of all 𝔽 -involutive filters of 𝔼 and show that by defining some operations on it, it makes a BL-algebra.

Rotations of λ -lattices

Jiří Karásek (1996)

Mathematica Bohemica

In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called l -lattices introduced in [3] by V. Snasel.

The embedding of the formal concept analysis into the L-Fuzzy concept theory.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1998)

Mathware and Soft Computing

In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal...

The study of the L-fuzzy concept lattice.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1994)

Mathware and Soft Computing

The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive method to...

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