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**A theoretical framework for possibilistic independence in a weakly ordered setting.**
*(English)*
Zbl 1084.68126

Summary: The notion of independence is central in many information processing areas, such as multiple criteria decision making, databases, or uncertain reasoning. This is especially true in the later case, where the success of Bayesian networks is basically due to the graphical representation of independence they provide. This paper first studies qualitative independence relations when uncertainty is encoded by a complete pre-order between states of the world. While a lot of work has focused on the formulation of suitable definitions of independence in uncertainty theories our interest in this paper is rather to formulate a general definition of independence based on purely ordinal considerations, and that applies to all weakly ordered settings. The second part of the paper investigates the impact of the embedding of qualitative independence relations into the scale-based possibility theory. The absolute scale used in this setting enforces the commensurateness between local pre-orders (since they share the same scale). This leads to an easy decomposability property of the joint distributions into more elementary relations on the basis of the independence relations. Lastly we provide a comparative study between already known definitions of possibilistic independence and the ones proposed here.

### MSC:

68T30 | Knowledge representation |

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

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\textit{N. Ben Amor} et al., Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10, No. 2, 117--155 (2002; Zbl 1084.68126)

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### References:

[1] | DOI: 10.1016/S0004-3702(97)00042-8 · Zbl 0903.68055 |

[2] | DOI: 10.1016/S0165-0114(97)00160-7 · Zbl 0951.68150 |

[3] | DOI: 10.1016/S0165-0114(97)00161-9 · Zbl 0971.68150 |

[4] | Dubois D., Computers and Artificial Intelligence 5 pp 403– (1986) |

[5] | DOI: 10.1016/0165-0114(95)00243-X · Zbl 0877.90002 |

[6] | DOI: 10.1016/S0377-2217(98)00307-5 · Zbl 0945.90087 |

[7] | DOI: 10.1016/S0377-2217(00)00031-X · Zbl 1068.90617 |

[8] | DOI: 10.1016/0004-3702(91)90101-O · Zbl 0749.03019 |

[9] | Dubois D., Procs. of the Eleventh Conference on Uncertainty pp 149– (1995) |

[10] | Dubois D., Journal of Japan Society for Fuzzy Theory and Systems 10 pp 21– (1998) |

[11] | DOI: 10.1016/S0888-613X(96)00095-3 · Zbl 0939.68115 |

[12] | Friedman N., Procs. of American Association pp 1297– (1996) |

[13] | Halpern J., Journal of Artificial Intelligence Research 7 pp 1– (1997) |

[14] | Hisdal E., Fuzzy Sets and Systems pp 1– (1978) |

[15] | DOI: 10.1016/S0004-3702(97)00038-6 · Zbl 0904.68162 |

[16] | DOI: 10.1007/BF01535841 · Zbl 0857.68096 |

[17] | DOI: 10.1016/0020-0255(75)90017-1 · Zbl 0404.68075 |

[18] | DOI: 10.1016/0165-0114(78)90029-5 · Zbl 0377.04002 |

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