Aggregation on bipolar scales

Abstract

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-multiplication. We address also in this category the special case of minimum and maximum defined on some finite ordinal scale. In the latter case, we find that a general class of extended operators can be defined using an interpolation approach, supposing the value of the aggregation to be known for ternary vectors. © Springer-Verlag Berlin Heidelberg 2006.