Relating Kleene algebras with pseudo uninorms

This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect is potentially useful as a source of formalism to capture and model programs acting with fuzzy behaviours and domains.publishe

Primeness in Quantales

In this paper we propose a new concept of primeness in quantales. It is proved that this concept coincide with classical definition in commutative quantales, but no longer valid in the noncommutative setting. Also, the notions of strong and uniform strong primeness are investigated

Extension of Quasi-Overlap and Quasi-Grouping Functions Defined on Bounded Lattices Via Retractions

In this paper, we propose a method of extending quasi-overlap and grouping functions defined on a sublattice $M$ of a bounded lattice $L$ to this lattice considering a more general version of sublattice definition, introduced by Palmeira and Bedregral

On Monotonicities of Interval Valued Functions

In this paper, we develop the notions of weak/directional monotonicity (developed by Sesma-Sara et al. in terms of the \emph{Kulisch-Miranker order}) and the notion of $G$-monotonicity (introduced by Santiago et al. for $[0,\!1]$) for intervals endowed with admissible orders.Comment: 3 page