Construction methods for implications on bounded lattices (original) (raw)
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New structures for uninorms on bounded lattices1
Journal of Intelligent and Fuzzy Systems, 2023
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are sufficient and necessary for the uninorms. Second, we show that the additional constraints on t-norms (t-conorms) and t-subnorms (t-subconorms) of some uninorms are exactly sufficient and necessary. At last, we give new constructions of uninorms on arbitrary bounded lattices by interation based on t-conorms and t-conorms.
M.: Reconciliation of approaches to the construction of canonical extensions of bounded lattices
2014
ABSTRACT. 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 representation and to the concept lattice of a specific context, and how to translate our construction to the original construction of Gehrke and Harding (2001). In addition, we identify the completely join- and completely meet-irreducible elements of the complete lattice of maximal partial maps. c©2014
Topology and its Applications, 2000
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Complemented tolerances on lattices
Časopis pro pěstování matematiky, 1984
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz Časopis pro pěstování matematiky, roč. 109 (1984), Praha
Some nonstandard methods applied to distributive lattices
Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1990
In memory of Abraham Robinson, on the occasion of his 70th birthday Distributive lattices are locally finite algebras, i.e. their finitely generated sublattices are finite. The general theory of finite distributive lattices is remarkably transparent, due to one or both of the following principles: (i) Any filter (or ideal) is principal. (ii) The lattice is join-generated by its join-irreducible elements, namely by those elements z for which x v y = z implies x = z or y = z .
Generalized continuous and hypercontinuous lattices
Rocky Mountain Journal of Mathematics, 1981
A class of complete lattices which have recently received a considerable deal of attention is the class of continuous lattices introduced by D. Scott [13] (see also ). One of the interesting features of this class of lattices is the fact that these lattices admit a unique compact Hausdorff topology for which the meet operation is continuous (i.e., they admit the structure of a compact topological semilattice). This topology turns out to be an "intrinsic" topology, i.e., one that can be defined directly from the lattice structure. We refer to this topology as the CL-topology.