In this paper we prove that, under suitable conditions, Atanassov’s Ka operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from Ka operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation fun...

Several authors have introduced global aggregation operators as families of aggregation operators {Tn}n, being each one of these Tn the n-ary operator in charge of aggregation, if and only if the number of items being actually aggregated is n. But according to this general definition, it is clear that operators within the same family may be not related at all. In this paper we shall point out t...

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study ...

Aggregation operators (AOs) have been studied by many scholars. As many AOs are proposed, there is still lacking approach to classify the categories of AO, and to select the appropriate AO within the AO candidates. In this research, each AO can be regarded as a cognitive style or individual difference. A Cognitive Style and Aggregation Operator (CSAO) model is proposed to analyze the mapping re...

We develop a new decision-making model using the Dempster-Shafer (D-S) belief structure when available information is uncertain and can be assessed with interval numbers. We use a wide range of aggregation operators involving interval numbers such as the uncertain weighted average (UWA), the uncertain ordered weighted average (UOWA), the uncertain generalized weighted average (UGWA) and the unc...

The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based on t-conorm...

Fuzzy ontologies extend classical ontologies to allow the representation of imprecise and vague knowledge. Although a relatively important amount of work has been carried out in the field during the last years and they have been successfully used in several applications, several notions from fuzzy logic have not been considered yet in fuzzy ontologies. Among them are aggregation operators, math...

We propose a generalization of the notion of the absorbent element of aggregation operators. Our construction involves tuples of values that are absorbent, that is, that decide the result of aggregation. We analyze some basic properties of this generalization and determine the absorbent tuples of some popular classes of aggregation operators.

In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed.

Double aggregation operators are introduced and several basic properties are studied, as neutral and annihilator elements, idempotency, etc., which are illustrated by some examples. The classes of additive and comonotone additive double aggregation operators are characterized.