Rees Coextensions of Finite, Negative Tomonoids

0448464 - ÚI 2017 RIV GB eng J - Článek v odborném periodiku
Petrík, Milan - Vetterlein, T.
Rees Coextensions of Finite, Negative Tomonoids.
Journal of Logic and Computation. Roč. 27, č. 1 (2017), s. 337-356. ISSN 0955-792X. E-ISSN 1465-363X
Grant CEP: GA ČR GPP201/12/P055
Grant ostatní: GA MŠk(CZ) EE2.3.20.0051
Institucionální podpora: RVO:67985807
Klíčová slova: totally ordered monoids * tomonoid partition * Rees coextension
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impakt faktor: 0.740, rok: 2017

A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We deal in this article with tomonoids that are finite and negative, where negativity means that the monoidal identity is the top element. Examples can be found, for instance, in the context of finite-valued fuzzy logic. By a Rees coextension of a negative tomonoid S, we mean a negative tomonoid T such that a Rees quotient of T is isomorphic to S. We characterize the set of all those Rees coextensions of a finite, negative tomonoid that are by one element larger. We thereby define a method of generating all such tomonoids in a stepwise fashion. Our description relies on the level-set representation of tomonoids, which allows us to identify the structures in question with partitions of a certain type.
Trvalý link: http://hdl.handle.net/11104/0250158