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Noncommutative self-identity aggregation. (English) Zbl 0903.04005

Summary: We introduce a number of properties associated with the aggregation of scores. Notable among these is the property of self-identity. The property of commutativity is discussed and a number of situations in which this is an inappropriate condition to assume are presented. Motivated by these examples, we consider a linear class of noncommutative aggregation operators. We show how the requirement of self-identity imposes a useful restriction on the weights associated with this aggregation. A number of special families of this class are investigated.

MSC:

03E72 Theory of fuzzy sets, etc.
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