Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial functions, that is, functions built only on projections and minimum and maximum operations

Ts-Tribes andTs-Measures

AbstractWe show that any fundamental triangular norm-basedTs-tribe T,s∈(0,∞), is a weakly generated tribe. Consequently, T is aT-tribe for any measurable t-normTif and only if it is aTs-tribe for somes∈(0,∞). Further we prove that eachTs-measurem,s∈(0,∞], defined on aTs-tribe T, is a generated measure; i.e., the irreducible part in the Butnariu–Klement decomposition ofTs-measures is always trivial

On the direct product of uninorms on bounded lattices

summary:In this paper, we study on the direct product of uninorms on bounded lattices. Also, we define an order induced by uninorms which are a direct product of two uninorms on bounded lattices and properties of introduced order are deeply investigated. Moreover, we obtain some results concerning orders induced by uninorms acting on the unit interval $[0,1]$