the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

We consider the problems of straightening polygonal trees and convexifying polygons by continuous motions such that rigid edges can rotate around vertex joints and no edge crossings are allowed. A tree can be straightened if all its edges can be aligned along a common straight line such that each edge points “away” from a designated leaf node. A polygon can be convexified if it can be reconfigu...

Ward and Dilworth 1 introduced the concept of residuated lattices as generalization of ideal lattices of rings. The residuated lattice plays the role of semantics for a multiple-valued logic called residuated logic. Residuated logic is a generalization of intuitionistic logic. Therefore it is weaker than classical logic. Important examples of residuated lattices related to logic are Boolean alg...

In this paper, we present a novel algorithm for dithering of gray-scale images. Our algorithm is based on the lattice Boltzmann method, a well-established and powerful concept known from computational physics. We describe the method and show the consistency of the new scheme to a partial differential equation. In contrast to widelyused error diffusion methods our lattice Boltzmann model is rota...

In this paper we study particular classes of pseudo-BCK algebras, bounded or not bounded, as pseudo-BCK(pP) algebras, pseudo-BCK(pP) lattices, pseudo-Hájek(pP) algebras and pseudo-Wajsberg algebras. We introduce new classes of pseudo-BCK(pP) lattices, we establish hierarchies and we give some examples. We work with left-defined algebras and we work with → and ; as primitive operations, not with...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...