Preassociative aggregation functions

We investigate the associativity property for varying-arity aggregation functions and introduce the more general property of preassociativity, a natural extension of associativity. We discuss this new property and describe certain classes of preassociative functions.

[1]  J. Aczél,et al.  Sur les opérations définies pour nombres réels , 1948 .

[2]  P. Mostert,et al.  On the Structure of Semigroups on a Compact Manifold With Boundary , 1957 .

[3]  E. Czogala,et al.  Associative monotonic operations in fuzzy set theory , 1984 .

[4]  Barbara Baccheli.  Representation of continuous associative functions. , 1986 .

[5]  R. Yager.  Quasi-associative operations in the combination of evidence , 1987 .

[6]  Zsolt Páles,et al.  The associativity equation revisited , 1989 .

[7]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[8]  Jean-Luc Marichal,et al.  Aggregation operators for multicriteria decision aid , 1998 .

[9]  Jean-Luc Marichal,et al.  On the associativity functional equation , 2000, Fuzzy Sets Syst..

[10]  Radko Mesiar,et al.  Triangular Norms , 2000, Trends in Logic.

[11]  W. Sander,et al.  Associative aggregation operators , 2002 .

[12]  R. Mesiar,et al.  Aggregation operators: properties, classes and construction methods , 2002 .

[13]  János Aczél,et al.  The Associativity Equation Re‐Revisited , 2004 .

[14]  R. Mesiar,et al.  Logical, algebraic, analytic, and probabilistic aspects of triangular norms , 2005 .

[15]  W. Sander.  Some aspects of functional equations , 2005 .

[16]  M. J. Frank,et al.  Associative Functions: Triangular Norms And Copulas , 2006 .

[17]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[18]  R. Mesiar,et al.  Aggregation Functions (Encyclopedia of Mathematics and its Applications) , 2009 .

[19]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[20]  Jean-Luc Marichal,et al.  A description of n-ary semigroups polynomial-derived from integral domains , 2011 .

[21]  Miguel Couceiro,et al.  Associative Polynomial Functions over Bounded Distributive Lattices , 2009, Order.

[22]  K. Domańska.  An analytic description of the class of rational associative functions , 2012 .

[23]  Miguel Couceiro,et al.  Aczélian n-ary semigroups , 2012 .

[24]  JEAN-LUC MARICHAL,et al.  ASSOCIATIVE AND PREASSOCIATIVE FUNCTIONS (IMPROVED VERSION)∗ , 2014 .

[25]  Jean-Luc Marichal,et al.  Associative string functions , 2014, ArXiv.

[26]  Jean-Luc Marichal,et al.  Associative and preassociative functions , 2014 .