Aggregation on Bipolar Scales | Zendy

Michel Grabisch | Zendy

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Aggregation on Bipolar Scales

Author(s) -

Michel Grabisch

Publication year - 2006

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-69223-1

DOI - 10.1007/11964810_17

Subject(s) - interpolation (computer graphics) , mathematics , ternary operation , value (mathematics) , associative property , interval (graph theory) , class (philosophy) , pure mathematics , multiplication (music) , discrete mathematics , combinatorics , computer science , statistics , artificial intelligence , motion (physics) , programming language

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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