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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:

[1] | Brown, R. G., Smoothing, (Forecasting and Prediction of Discrete Time Series (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ) · Zbl 0192.25606 |

[2] | Dubois, D.; Prade, H., A review of fuzzy sets aggregation connectives, Inform. Sci., 36, 85-121 (1985) · Zbl 0582.03040 |

[3] | Hart, W. L., Analytic Geometry and Calculus (1957), D.C. Heath: D.C. Heath Boston · Zbl 0077.05701 |

[4] | Yager, R. R., MAM and MOM operators for aggregation, Inform. Sci., 69, 259-273 (1993) · Zbl 0783.04007 |

[5] | Yager, R. R., Aggregation operators and fuzzy systems modeling, Fuzzy Sets and Systems, 67, 129-146 (1994) · Zbl 0845.93047 |

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