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Assist. Mahmoud Atya Mahmoud Ibrahim Khatab :: Publications:

Lattice-based Sum Construction of Nullnorms on Bounded Lattices
Authors: M. Khattab; M. El-Zekey
Year: 2018
Keywords: Lattice-based sum; Bounded lattice; Nullnorm; Idempotent nullnorm; T-norm; T-conorm.
Journal: Circulation In Computer Science
Volume: 3
Issue: 4
Pages: 1-9
Publisher: CSL Press, NY, USA
Local/International: International
Paper Link:
Full paper Mahmoud Atya Mahmoud Ibrahim Khatab_ccs-2018-252-84.pdf
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Nullnorms on bounded lattices are generalizations of t-norms and t-conorms with a zero element laying anywhere in the underlying lattices. In this paper, new methods for constructing nullnorms on bounded lattices are proposed. The proposed construction methods are based on the lattice-based sum of lattices that has been recently introduced by El-Zekey et al. (see [9]), for building new (bounded) lattices from fixed ones indexed by a (finite) lattice-ordered index set. Subsequently, the new construction methods are applied for building several new families of nullnorms on bounded lattices. As a by-product, lattice-based sum constructions of t-norms and t-conorms on bounded lattices have been obtained. Furthermore, new idempotent nullnorms on bounded lattices have been also obtained.

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