### 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 (US) |
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Pages (from-to) | 219-237 |

Number of pages | 19 |

Journal | New Mathematics and Natural Computation |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1 2012 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Mordeson, J. N., Gibilisco, M. B., & Clark, T. D. (2012). Independence of irrelevant alternatives and fuzzy Arrow's theorem.

*New Mathematics and Natural Computation*,*8*(2), 219-237. https://doi.org/10.1142/S1793005712400121