On triangular norms representable as ordinal sums based on interior operators on a bounded meet semilattice. (English) Zbl 1522.03275
Summary: First, we present construction methods for interior operators on a meet semilattice. Second, under the assumption that the underlying meet semilattices constitute the range of an interior operator, we prove an ordinal sum theorem for countably many (finite or countably infinite) triangular norms on bounded meet semilattices, which unifies and generalizes two recent results: one by A. Dvořák and M. Holčapek [Inf. Sci. 515, 116–131 (2020; Zbl 1457.03052)] and the other by some of the present authors [the first author et al., Fuzzy Sets Syst. 408, 1–12 (2021; Zbl 1464.03064)]. We also characterize triangular norms that are representable as the ordinal sum of countably many triangular norms on given bounded meet semilattices.
MSC:
| 03E72 | Theory of fuzzy sets, etc. |
| 03G10 | Logical aspects of lattices and related structures |
| 06A12 | Semilattices |
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