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.
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Michel Grabisch. Aggregation on bipolar scales. Harrie C. M. de Swart, Ewa Orlowska, Gunther Schmidt, Marc Roubens. Theory and Applications of Relational Structures as Knowledge Instruments II, Springer, pp.355-371, 2006, Lecture Notes in Computer Science. ⟨halshs-00187155⟩

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