On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

0457466 - ÚI 2016 RIV CH eng M - Monography Chapter
Vetterlein, T. - Petrík, Milan
The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids.
On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Cham: Springer, 2016 - (Saminger-Platz, S.; Mesiar, R.), s. 83-108. Studies in Fuzziness and Soft Computing, 336. ISBN 978-3-319-28807-9
R&D Projects: GA ČR GJ15-07724Y
Keywords : triangular norm * direction cone * monomial pre-order * finite totally ordered monoids * Rees coextension of totally ordered monoids * tomonoid partition
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Fuzzy logic generalises classical logic; in addition to the latter’s truth values "false" and "true", the former allows also intermediary truth degrees. The conjunction is, accordingly, interpreted by an operation acting on a chain, making the set of truth degrees into a totally ordered monoid. We present in this chapter two different ways of investigating this type of algebras. We restrict to the finite case.
Permanent Link: http://hdl.handle.net/11104/0257863