Abstract
We investigate how and when a t-norm on a bounded meet semilattice can be represented by a t-norm on some sub-semilattice and a collection of interior operators. We present such a representation using a novel notion of consistent triplet consisting of a t-norm, a commutative semigroup of interior operators, and a meet semilattice of symmetric lower sets. Furthermore, we study a related problem of extension of a t-norm from a sub-semilattice to the whole semilattice given a consistent triplet. This gives us a new construction method for t-norms on bounded semilattices that covers several known methods. Our results are illustrated by several examples.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
