4 research outputs found
Characterizations of quasitrivial symmetric nondecreasing associative operations
We provide a description of the class of n-ary operations on an arbitrary
chain that are quasitrivial, symmetric, nondecreasing, and associative. We also
prove that associativity can be replaced with bisymmetry in the definition of
this class. Finally we investigate the special situation where the chain is
finite
Characterization of quasi-arithmetic means without regularity condition
In this paper we show that bisymmetry, which is an algebraic property, has a
regularity improving feature. More precisely, we prove that every bisymmetric,
partially strictly monotonic, reflexive and symmetric function is
continuous. As a consequence, we obtain a finer characterization of
quasi-arithmetic means than the classical results of Acz\'el, Kolmogoroff,
Nagumo and de Finetti.Comment: 12 page
Characterizations of idempotent discrete uninorms
In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an alternative characterization involving the bisymmetry property. Finally, we provide a graphical characterization of these operations in terms of their contour plots, and we mention a few open questions for further research