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For p ≤ n, let b1(n),...,bp(n) be independent random vectors in 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 is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends
upon the sequence of ratios...
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 and a filter of , we define the set of all -involutive filters of and show that by defining some operations on it, it makes a BL-algebra.
In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called -lattices introduced in [3] by V. Snasel.
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 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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