The present paper introduces aggregative spaces and their category AGS, and then establishes a dual adjunction between AGS and the category Agop of aggregation operators on bounded partially ordered sets. Spatial aggregation operators and sober aggregative spaces, enabling us to restrict the dual adjunction between AGS and Agop to a dual equivalence between the full subcategory of Agop consisti...

Our paper deals with constructions of upper and lower general aggregation operators, which are based in their definitions on a fuzzy equivalence relation. We study some properties of these aggregation operators which are important in the context of aggregation of fuzzy sets. In particular we consider different types of monotonicity and show that obtained results allow us to describe approximate...

Techniques of information aggregation are mainly being used in decision making or when a system needs a comprehensive representation of its application domain. Recently, aggregation operators have been also applied for defuzzification where the defuzzified value is calculated as an aggregation of all possible solutions according to their attached possibility. In this paper we propose and analyz...

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...