Triangular norms on bounded trellises

Article Computer Science, Theory & Methods

On triangular norms representable as ordinal sums based on interior operators on a bounded meet semilattice

Yao Ouyang et al.

Summary: In this paper, we first present construction methods for interior operators on a meet semilattice. Then, under the assumption that the underlying meet semilattices constitute the range of an interior operator, we prove an ordinal sum theorem for countably many triangular norms on bounded meet semilattices, and characterize triangular norms that can be represented as the ordinal sum of countably many triangular norms on given bounded meet semilattices.

FUZZY SETS AND SYSTEMS (2022)

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Article Computer Science, Theory & Methods

Ordinal sums of triangular norms on a bounded lattice

Yao Ouyang et al.

Summary: The ordinal sum construction provides an effective way to generate new triangular norms, but it may not always result in a triangular norm on subintervals of a bounded lattice.

FUZZY SETS AND SYSTEMS (2021)

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Article Mathematics

Some characterizations of pseudo-chains in pseudo-ordered sets

Shashirekha B. Rai et al.

Summary: In this paper, the equivalence between the minimum condition and the descending pseudo-chain condition in pseudo-ordered sets is proved, using a graph-theoretic approach and a counterexample to show the relationship between complete trellises and Fixed Point Property. The concepts of weakly isotone mapping and Strong Fixed Point Property in psosets are introduced, with the result that connected psosets containing nontrivial cycles do not have the Strong Fixed Point Property.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS (2021)

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Article Computer Science, Theory & Methods