Formal Ordinal Sums of Triangular Norms on Modular Lattices
Year: 2026
Type: article
Abstract: The formal ordinal sums of t-norms on the bounded lattice is defined by Saminger, but the formal ordinal sum need not be a t-norm. Hence, she provides a necessary and sufficient condition such that the formal ordinal sum is a t-norm indeed. In this paper, we first give several conditions that are equivalent to Saminger’s condition. Secondly, we prove that there is a largest sublattice containing all the pairwise non-overlapped subintervals such that the formal ordinal sum is a t-norm on this sublattice when the bounded lattice is modular.
Source: Mathematics
DOI: 10.3390/math14061084
Author: Yang Luo
Institution: Chengdu Technological University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7140073391