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**Fair division under interval uncertainty.**
*(English)*
Zbl 1113.68542

Summary: It is often necessary to divide a certain amount of money between \(n\) participants, i.e., to assign, to each participant, a certain portion \(w_{i}\geq 0\) of the whole sum (so that \(w_{1}+ \dots + w_{n}=1)\). In some situations, from the fairness requirements, we can uniquely determine these “weights” \(w_{i}\). However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the intervals \([w_i^-,w_i^+]\) of possible fair weights. We show that natural fairness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncertainty.

### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |

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\textit{R. R. Yager} and \textit{V. Kreinovich}, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 8, No. 5, 611--618 (2000; Zbl 1113.68542)

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### References:

[1] | DOI: 10.1007/978-1-4613-3440-8_11 |

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