Narrow Results

This paper deals with the problem of establishing a new class of aggregation operators, which are close to the averaging, without being necessarily idempotent. An axiomatic approach is followed through the definition of crucial properties which characterize these aggregators, the mathematical consequences are illustrated and many examples that extend some important classical averaging operators are shown.

This paper deals with aggregation operators. A new form of idempotency, called asymptotic idempotency, is introduced. A critical discussion of the basic notion of aggregation operator, strictly connected with asymptotic idempotency, is provided. Some general construction methods of symmetric, asymptotically idempotent aggregation operators admitting a neutral element are illustrated.

An exhaustive study of uninorm operators is established. These operators are generalizations of t-norms and t-conorms allowing the neutral element lying anywhere in the unit interval. It is shown that uninorms can be built up from t-norms and t-conorms by a construction similar to ordinal sums. De Morgan classes of uninorms are also described. Representability of uninorms is characterized and a general representation theorem is proved. Finally, pseudo-continuous uninorms are defined and completely classified.

In this paper, some results about interval uninorms with the additional property of monotonicity inclusion are introduced; e.g construction of interval uninorms from usual uninorms and constructions of interval t-norms and t-conorms from interval uninorms. It is also shown that the neutral element of this type of interval uninorm must be a degenerate interval.