Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T -transitivity. It will be shown that preservation of T -transitivity is closely relat...

Two different characterizations of self-dual aggregation operators are available in the literature: one based on C(x, y) = x/(x + 1 − y) and one based on the arithmetic mean. In this contribution, we fit the existing approaches into a more general framework and characterize N -invariant aggregation operators, with N an involutive negator. Special attention is drawn to the equivalence classes th...

In this paper the relationship between symmetric minitive, maxitive, and modular aggregation operators is considered. It is shown that the intersection between any two of the three discussed classes is the same. Moreover, the intersection is explicitly characterized. It turns out that the intersection contains families of aggregation operators such as OWMax, OWMin, and many generalizations of t...

Yager et al. first introduce compensatory operators. This paper further introduces a kind of weighted compensatory operators, and a kind of prioritized compensatory operators. The difference between these similar classes of operators are identified. In addition, the paper introduces the concepts of ordered weighted/prioritized compensatory aggregation.

We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented...

This paper presents the fuzzy induced heavy ordered weighted averaging (FIHOWA) operator. It is an aggregation operator that uses the main characteristics of three well known aggregation operators: the heavy OWA, the induced OWA and the fuzzy OWA operator. Therefore, this operator provides a parameterized family of aggregation operators that includes the OWA operator and the total operator as s...

Sliding-window aggregation is a widely-used approach for extracting insights from the most recent portion of a data stream. Most aggregation operations of interest can be cast as binary operators that are associative, but not necessarily commutative nor invertible. However, non-invertible operators are nontrivial to support efficiently. The best existing algorithms for this setting require Oplo...

It is difficult to deal with the traditional weight problems of MCDM ( multiple criteria decision making). However, the previous aggregation operators (include OWA) do not take into account the situational factors when processes the aggregation, i.e. these operators and aggregation situation are independent. In order to solve this problem mentioned above, we propose a new powerful OWA aggregati...

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer relia...

The paper addresses the problem of extending aggregation operators typically defined on [0, 1] to the symmetric interval [−1, 1], where the “0” value plays a particular role (neutral value). We distinguish the cases where aggregation operators are associative or not. In the former case, the “0” value may play the role of neutral or absorbant element, leading to pseudo-addition and pseudo-multip...