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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. |

### Keywords:

fuzzy sets; aggregation of scores; self-identity; commutativity; noncommutative aggregation operators
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\textit{R. R. Yager} and \textit{A. Rybalov}, Fuzzy Sets Syst. 85, No. 1, 72--82 (1997; Zbl 0903.04005)

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### References:

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