### Abstract

The literature involving fuzzy Arrow results uses the same independence of irrelevant alternatives condition. We introduce three other types of independence of irrelevant alternative conditions and show that they can be profitably used in the examination of Arrow's theorem. We also generalize some known nondictatorship results. One known fuzzy aggregation rule that is nondictatorial is the average of the individual preferences. We show that a weighted average is also nondictatorial. Moreover, it is not an automorphic image of the ordinary average, which demonstrates that we have proposed a framework unique from the present known results.

Original language | English |
---|---|

Pages (from-to) | 219-237 |

Number of pages | 19 |

Journal | New Mathematics and Natural Computation |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jul 2012 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Computational Mathematics
- Computer Science Applications
- Computational Theory and Mathematics
- Human-Computer Interaction

### Cite this

*New Mathematics and Natural Computation*,

*8*(2), 219-237. https://doi.org/10.1142/S1793005712400121

**Independence of irrelevant alternatives and fuzzy Arrow's theorem.** / Mordeson, John N.; Gibilisco, Michael B.; Clark, Terry D.

Research output: Contribution to journal › Article

*New Mathematics and Natural Computation*, vol. 8, no. 2, pp. 219-237. https://doi.org/10.1142/S1793005712400121

}

TY - JOUR

T1 - Independence of irrelevant alternatives and fuzzy Arrow's theorem

AU - Mordeson, John N.

AU - Gibilisco, Michael B.

AU - Clark, Terry D.

PY - 2012/7

Y1 - 2012/7

N2 - The literature involving fuzzy Arrow results uses the same independence of irrelevant alternatives condition. We introduce three other types of independence of irrelevant alternative conditions and show that they can be profitably used in the examination of Arrow's theorem. We also generalize some known nondictatorship results. One known fuzzy aggregation rule that is nondictatorial is the average of the individual preferences. We show that a weighted average is also nondictatorial. Moreover, it is not an automorphic image of the ordinary average, which demonstrates that we have proposed a framework unique from the present known results.

AB - The literature involving fuzzy Arrow results uses the same independence of irrelevant alternatives condition. We introduce three other types of independence of irrelevant alternative conditions and show that they can be profitably used in the examination of Arrow's theorem. We also generalize some known nondictatorship results. One known fuzzy aggregation rule that is nondictatorial is the average of the individual preferences. We show that a weighted average is also nondictatorial. Moreover, it is not an automorphic image of the ordinary average, which demonstrates that we have proposed a framework unique from the present known results.

UR - http://www.scopus.com/inward/record.url?scp=84864225887&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864225887&partnerID=8YFLogxK

U2 - 10.1142/S1793005712400121

DO - 10.1142/S1793005712400121

M3 - Article

AN - SCOPUS:84864225887

VL - 8

SP - 219

EP - 237

JO - New Mathematics and Natural Computation

JF - New Mathematics and Natural Computation

SN - 1793-0057

IS - 2

ER -