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**Totally coherent set-valued probability assessments.**
*(English)*
Zbl 1274.68525

Summary: We introduce the concept of total coherence of a set-valued probability assessment on a family of conditional events. In particular we give sufficient and necessary conditions of total coherence in the case of interval-valued probability assessments. Some relevant cases in which the set-valued probability assessment is represented by the unitary hypercube are also considered.

### MSC:

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

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\textit{A. Gilio} and \textit{S. Ingrassia}, Kybernetika 34, No. 1, 3--15 (1998; Zbl 1274.68525)

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### References:

[1] | Adams E. W.: The Logic of Conditionals. D. Reidel, Dordrecht 1975 · Zbl 0324.02002 |

[2] | Capotorti A., Vantaggi B.: The consistency problem in belief and probability assessments. Proceedings of the Sixth International Conference on “Information Processing and Management of Uncertainty in Knowledge-Based Systems” (IPMU ’96), Granada 1996, pp. 55-59 |

[3] | Coletti G.: Numerical and qualitative judgements in probabilistic expert systems. Proceedings of the International Workshop on “Probabilistic Methods in Expert Systems” (R. Scozzafava, SIS, Roma 1993, pp. 37-55 |

[4] | Coletti G.: Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Systems Man Cybernet. 24 (1994), 12, 1747-1754 · Zbl 1371.68265 |

[5] | Coletti G., Gilio A., Scozzafava R.: Conditional events with vague information in expert systems. Uncertainty in Knowledge Bases (Lecture Notes in Computer Science 521; B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh, Springer-Verlag, Berlin - Heidelberg 1991, pp. 106-114 · Zbl 0800.68922 |

[6] | Coletti G., Gilio A., Scozzafava R.: Comparative probability for conditional events: a new look through coherence. Theory and Decision 35 (1993), 237-258 · Zbl 0785.90006 |

[7] | Coletti G., Scozzafava R.: Learning from data by coherent probabilistic reasoning. Proceedings of ISUMA-NAFIPS ’95, College Park 1995, pp. 535-540 |

[8] | Coletti G., Scozzafava R.: Characterization of coherent conditional probabilities as a tool for their assessment and extension. J. Uncertainty, Fuzziness and Knowledge-Based Systems 4 (1996), 2, 103-127 · Zbl 1232.03010 |

[9] | Biase G. Di, Maturo A.: Checking the coherence of conditional probabilities in expert systems: remarks and algorithms. Mathematical Models for Handling Partial Knowledge in Artificial Intelligence (G. Coletti, D. Dubois and R. Scozzafava, Plenum Press, New York 1995, pp. 191-200 · Zbl 0859.68108 |

[10] | Doria S., Maturo A.: A hyperstructure of conditional events for Artificial Intelligence. Mathematical Models for Handling Partial Knowledge in Artificial Intelligence (G. Coletti, D. Dubois and R. Scozzafava, Plenum Press, New York 1995, pp. 201-208 · Zbl 0859.68098 |

[11] | Dubois D., Prade H.: Probability in automated reasoning: from numerical to symbolic approaches. Probabilistic Methods in Expert Systems, Proc. of the International Workshop (R. Scozzafava, SIS, Roma 1993, pp. 79-104 |

[12] | Holzer S.: On coherence and conditional prevision. Boll. Un. Mat. Ital. 4 (1985), 4-B, 441-460 · Zbl 0584.60001 |

[13] | Gilio A.: Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilità. Boll. Un. Mat. Ital. 7 (1990), 4-B, 645-660 |

[14] | Gilio A.: Conditional events and subjective probability in management of uncertainty. Uncertainty in Intelligent Systems (B. Bouchon-Meunier, L. Valverde and R. R. Yager, Elsevier Science Publishing B. V., North-Holland, 1993, pp. 109-120 |

[15] | Gilio A.: Probabilistic consistency of conditional probability bounds. Advances in Intelligent Computing - IPMU’94 (Lecture Notes in Computer Science 945; B. Bouchon-Meunier, R. R. Yager and L. A. Zadeh, Springer-Verlag, Berlin - Heidelberg 1995, pp. 200-209 |

[16] | Gilio A.: Algorithms for precise and imprecise conditional probability assessments. Mathematical Models for Handling Partial Knowledge in Artificial Intelligence (G. Coletti, D. Dubois and R. Scozzafava, Plenum Press, New York 1995, pp. 231-254 · Zbl 0859.68042 |

[17] | Gilio A.: Algorithms for conditional probability assessments. Bayesian Analysis in Statistics and Econometrics (D. A. Berry, K. M. Chaloner and J. K. Geweke, J. Wiley, New York 1996, pp. 29-39 |

[18] | Gilio A., Ingrassia S.: Geometrical aspects in checking coherence of probability assessments. Proceedings of the Sixth International Conference on “Information Processing and Management of Uncertainty in Knowledge-Based Systems” (IPMU’96), Granada, 1996, pp. 55-59 |

[19] | Gilio A., Scozzafava R.: Le probabilità condizionate coerenti nei sistemi esperti In: Ricerca Operativa e Intelligenza Artificiale, Atti Giornate di Lavoro A. I.R.O., IBM, Pisa 1988, pp. 317-330 |

[20] | Goodman I. R., Nguyen H. T.: Conditional objects and the modeling of uncertainties. Fuzzy Computing Thoery, Hardware and Applications (M. M. Gupta and T. Yamakawa, North-Holland, New York 1988, pp. 119-138 |

[21] | Lad F.: Coherent prevision as a linear functional without an underlying measure space: the purely arithmetic structure of logical relations among conditional quantities. Mathematical Models for Handling Partial Knowledge in Artificial Intelligence (G. Coletti, D. Dubois and R. Scozzafava, Plenum Press, New York 1995, pp. 101-111 · Zbl 0859.68104 |

[22] | Regoli G.: Comparative probability assessments and stochastic independence. Proceedings of the Sixth International Conference on “Information Processing and Management of Uncertainty in Knowledge-Based Systems” (IPMU’96), Granada 1996, pp. 49-53 |

[23] | Scozzafava R.: How to solve some critical examples by a proper use of coherent probability. Uncertainty in Intelligent Systems (B. Bouchon-Meunier, L. Valverde and R. R. Yager, Elsevier Science Publishing B.V., North-Holland, Amsterdam 1993, pp. 121-132 |

[24] | Scozzafava R.: Subjective probability versus belief functions in artificial intelligence. Internat. J. Gen. Systems 22 (1994), 197-206 · Zbl 0795.60002 |

[25] | Vicig P.: An algorithm for imprecise conditional probability assessments in expert systems. Proceedings of the Sixth International Conference on “Information Processing and Management of Uncertainty in Knowledge-Based Systems” (IPMU’96), Granada 1996, pp. 61-66 |

[26] | Walley P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London 1991 · Zbl 0732.62004 |

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