Aggregation on bipolar scales

Michel Grabisch

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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.

Keywords: bipolar scale; bi-capacity; aggregation (search for similar items in EconPapers)
Date: 2006
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00187155
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Citations: View citations in EconPapers (9)

Published in 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

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Working Paper: Aggregation on bipolar scales (2006)
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