A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s image 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 image 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 functions – the generalized Atanassov operators – that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.