5 research outputs found
Preassociative aggregation functions
The classical property of associativity is very often considered in
aggregation function theory and fuzzy logic. In this paper we provide
axiomatizations of various classes of preassociative functions, where
preassociativity is a generalization of associativity recently introduced by
the authors. These axiomatizations are based on existing characterizations of
some noteworthy classes of associative operations, such as the class of
Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730
Strongly barycentrically associative and preassociative functions
We study the property of strong barycentric associativity, a stronger version
of barycentric associativity for functions with indefinite arities. We
introduce and discuss the more general property of strong barycentric
preassociativity, a generalization of strong barycentric associativity which
does not involve any composition of functions. We also provide a generalization
of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions
to strongly barycentrically preassociative functions.Comment: arXiv admin note: text overlap with arXiv:1406.434
A characterization of barycentrically preassociative functions
We provide a characterization of the variadic functions which are
barycentrically preassociative as compositions of length-preserving associative
string functions with one-to-one unary maps. We also discuss some consequences
of this characterization
Molecular recognition of adenosine derivatives
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 1994.Includes bibliographical references (p. 127-131).by Michael Morgan Conn.Ph.D
Associative and preassociative aggregation functions (invited lecture)
Dans cette présentation, nous étudions la propriété d'associativité pour les fonctions d'agrégation à arités multiples et nous introduisons la propriété plus générale de préassociativité qui n'implique aucune composition de fonctions. Nous étudions cette nouvelle propriété et nous décrivons certaines classes de fonction préassociatives. Nous montrons aussi comment des axiomatisations de plusieurs classes de functions (comme les semi-groupes aczéliens ou les polynômes latticiels associatifs) peuvent être obtenues en affaiblissant l'associativité en la remplaçant par la préassociativité