The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids

Authors: T. Vetterlein, Milan Petrík
Publication year: 2016
Publication type: Kapitola v monografii
Periodical: On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory
Projects: Totally ordered monoids
Bibliographic citation: VETTERLEIN, T., PETRÍK, Milan. The Semantics of Fuzzy Logics: Two Approaches to Finite Tomonoids. In: SAMINGER-PLATZ, S., MESIAR, R., eds. On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Cham: Springer, 2016, S. 83-108. Studies in Fuzziness and Soft Computing, 336. ISBN 978-3-319-28807-9
Dostupné z: doi:10.1007/978-3-319-28808-6_6
DOI: 10.1007/978-3-319-28808-6_6
ID: 457466

Abstract

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.