Lattice-based sums

Authors:
Moataz El-Zekey;JesúS Medina;Radko Mesiar
Affiliations:
Department of Basic Sciences, Faculty of Engineering, Benha University, Egypt;Department of Mathematics, University of Cádiz, Spain;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia and Institute for Research and Applications of Fuzzy Modelli ...
Venue:
Information Sciences: an International Journal
Year:
2013

Citing 7
Cited 0

The equational theory of pomsets

Theoretical Computer Science
Structure of uninorms

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
A note on the ordinal sum theorem and its consequence for the construction of triangular norms

Fuzzy Sets and Systems
Ordinal sums of aggregation operators

Technologies for constructing intelligent systems
On ordinal sums of triangular norms on bounded lattices

Fuzzy Sets and Systems
Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes

Information Sciences: an International Journal
An Introduction to Copulas

An Introduction to Copulas

Quantified Score

Hi-index	0.07

Visualization

Abstract

In this contribution, the well-known ordinal sum technique of posets is generalized by allowing for a lattice ordered index set instead of a linearly ordered index set, and we argue for the merits of this generalization. We will call such a proposed sum-type construction a lattice-based sum. Our new approach of lattice-based sum extends also the horizontal sum. We show that the lattice-based sum of posets is again a poset. Subsequently, we apply the results for constructing new lattices by investigating lattice-based sums when the summand posets are lattices. We show that under certain assumptions, the lattice-based sum of lattices will be a lattice.