New construction approaches of uninorms on bounded lattices

Alternative approaches to obtain t-norms and t-conorms on bounded lattices

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

Reconciliation of Approaches to the Construction of Canonical Extensions of Bounded Lattices

We provide new insights into the relationship between different constructions of the canonical extension of a bounded lattice. This follows on from the recent construction of the canonical extension using Ploščica’s maximal partial maps into the two-element set by Craig, Haviar and Priestley (2012). We show how this complete lattice of maps is isomorphic to the stable sets of Urquhart’s represe...

On Equations in Bounded Lattices

The following properties of Boolean equations are well known: every system of equations is equivalent to a single equation of the form f(x1, . . . , xn) = 1, the consistency condition for such an equation, the method of successive elimination of variables, and the formula for the general (reproductive) solution using a particular solution. These features are shared by Post equations and by equa...

Construction of new extremal unimodular lattices

A New Edge Detector Based on Uninorms

A new fuzzy edge detector based on uninorms is proposed and deeply studied. The behaviour of different classes of uninorms is discussed. The obtained results suggest that the best uninorm in order to improve the edge detection process is the uninorm Umin, with underlying Lukasiewicz operators. This algorithm gets statistically substantial better results than the others obtained by well known ed...