We present a general formula for the intent–extent mappings of a Galois lattice generated by individual descriptions which lie in any arbitrary lattice. The formulation is unique if a natural maximality condition is required. This formulation yields, as particular cases, formal concept binary Galois lattices of Wille, those de0ned by Brito or Blyth–Janowitz, as well as fuzzy or stochastic Galoi...

We present a duality theorem for bounded lattices that improves and strengthens Urquhart's topological representation for lattices. Rather than using maximal, disjoint lter-ideal pairs, as Urquhart does, we use all disjoint lter-ideal pairs. This allows not only for establishing a bijective correspondance between lattices and a certain kind of doubly ordered Stone Spaces (Urquhart), but for a f...

2014 We formulate a conjecture concerning the critical frontiers of q-state Potts ferromagnets on d-dimensional lattices (d > 1) which generalize a recent one stated for planar lattices. The present conjecture is verified within satisfactory accuracy (exactly in some cases) for all the lattices or arrays whose critical points are known. Its use leads to the prediction of : a) a considerabl...

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

Micciancio defined a generalization of cyclic lattices, called ideal lattices. These lattices can be used in cryptosystems to decrease the number of parameters necessary to describe a lattice by a square root, making them more efficient. He proves that the computational intractability of classic lattice problems for these lattices gives rise to provably secure one-way and collision-resistant ha...

In this talk we will present and analyze the efficiency of various algorithms in lattice theory. For finite lattices this will include recognition of various properties such as subdirect irreducibility, semidistributivity, and boundedness (in the sense of McKenzie) as well as efficient algorithms for computing the congruence lattice. For free and finitely presented lattices we will discuss algo...

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plücker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Moutard transformation, it is constructed the discrete analog of the W–congruences...