Geodesic
Totally coherent set-valued probability assessments
Kybernetika, Tome 34 (1998) no. 1, pp. 3-15 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 03B48, 60A05, 68T30, 68T35, 68T37
Keywords: uncertainty; total coherence; set-valued probability 
@article{KYB_1998_34_1_a1,
     author = {Gilio, Angelo and Ingrassia, Salvatore},
     title = {Totally coherent set-valued probability assessments},
     journal = {Kybernetika},
     pages = {3--15},
     year = {1998},
     volume = {34},
     number = {1},
     mrnumber = {1619051},
     zbl = {1274.68525},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a1/}
}
TY  - JOUR
AU  - Gilio, Angelo
AU  - Ingrassia, Salvatore
TI  - Totally coherent set-valued probability assessments
JO  - Kybernetika
PY  - 1998
SP  - 3
EP  - 15
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a1/
LA  - en
ID  - KYB_1998_34_1_a1
ER  - 
%0 Journal Article
%A Gilio, Angelo
%A Ingrassia, Salvatore
%T Totally coherent set-valued probability assessments
%J Kybernetika
%D 1998
%P 3-15
%V 34
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a1/
%G en
%F KYB_1998_34_1_a1
Gilio, Angelo; Ingrassia, Salvatore. Totally coherent set-valued probability assessments. Kybernetika, Tome 34 (1998) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a1/

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

[2] Capotorti A., Vantaggi B.: The consistency problem in belief and probability assessments. In: 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. In: Proceedings of the International Workshop on “Probabilistic Methods in Expert Systems” (R. Scozzafava, ed.), 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 | DOI | MR

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

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

[7] Coletti G., Scozzafava R.: Learning from data by coherent probabilistic reasoning. In: 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 | DOI | MR | Zbl

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

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

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

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

[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. In: Uncertainty in Intelligent Systems (B. Bouchon–Meunier, L. Valverde and R. R. Yager, eds.), Elsevier Science Publishing B. V., North–Holland, 1993, pp. 109–120

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

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

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

[18] Gilio A., Ingrassia S.: Geometrical aspects in checking coherence of probability assessments. In: 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. In: Fuzzy Computing Thoery, Hardware and Applications (M. M. Gupta and T. Yamakawa, eds.), North–Holland, New York 1988, pp. 119–138 | MR

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

[22] Regoli G.: Comparative probability assessments and stochastic independence. In: 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. In: Uncertainty in Intelligent Systems (B. Bouchon–Meunier, L. Valverde and R. R. Yager, eds.), 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 | DOI | Zbl

[25] Vicig P.: An algorithm for imprecise conditional probability assessments in expert systems. In: 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 | MR | Zbl