Relaxations of associativity and preassociativity for variadic functions

Miguel Couceiro (1) , Jean-Luc Marichal (2) , Bruno Teheux (2)

1 ORPAILLEUR - Knowledge representation, reasonning
2 FSTC

In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research.

Mots clés: Preassociativity; Variadic function; Associativity; String function; Functional equation; Axiomatization

Domaines: Anneaux et algèbres [math.RA]

Miguel Couceiro, Jean-Luc Marichal, Bruno Teheux. Relaxations of associativity and preassociativity for variadic functions. Fuzzy Sets and Systems, 2016, 229, pp.89-97. ⟨10.1016/j.fss.2015.11.003⟩. ⟨hal-01184334⟩