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**General framework for multidimensional models.**
*(English)*
Zbl 1029.68131

Summary: This article is an attempt to build a unifying theoretical framework in which both probabilistic and possibilistic multidimensional models can be described. This novel approach is applied to presenting models based on iterative application of operators of composition, which were introduced in previous articles separately for probabilistic and possibilistic distributions. It appears that, although not all of the proofs are elegant, the apparatus is quite efficient, and enables the authors to deduce all the necessary properties in a uniform way. Because the described models are, in the probabilistic setting, fully equivalent to Bayesian networks, our main result describes how to compute marginal distributions of both Bayesian networks and possibilistic belief networks (when represented in the form of generating sequences).

### MSC:

68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |

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\textit{R. Jiroušek} and \textit{J. Vejnarová}, Int. J. Intell. Syst. 18, No. 1, 107--127 (2003; Zbl 1029.68131)

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### References:

[1] | Jiroušek, Proc 13th Conf on Uncertainty in Artificial Intelligence (UAI’97) pp 274– (1997) |

[2] | Jiroušek, Proc 16th Conf on Uncertainty in Artificial Intelligence (UAI’00) pp 301– (2000) |

[3] | Jiroušek, Belief functions in business decision pp 252– (2002) · doi:10.1007/978-3-7908-1798-0_9 |

[4] | Vejnarová, Prague Stochastics’98 pp 575– (1998) |

[5] | Dubois, Possibility theory (1988) · doi:10.1007/978-1-4684-5287-7 |

[6] | Jiroušek, Decomposition of multidimensional distributions represented by perfect sequences, Ann Math Artif Intell 35 pp 215– (2002) · Zbl 1004.60010 · doi:10.1023/A:1014591402750 |

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