| Title:
|
Totally coherent set-valued probability assessments (English) |
| Author:
|
Gilio, Angelo |
| Author:
|
Ingrassia, Salvatore |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
[3]-15 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
uncertainty |
| Keyword:
|
total coherence |
| Keyword:
|
set-valued probability |
| MSC:
|
03B48 |
| MSC:
|
60A05 |
| MSC:
|
68T30 |
| MSC:
|
68T35 |
| MSC:
|
68T37 |
| idZBL:
|
Zbl 1274.68525 |
| idMR:
|
MR1619051 |
| . |
| Date available:
|
2009-09-24T19:13:11Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135181 |
| . |
| Reference:
|
[1] Adams E. W.: The Logic of Conditionals.D. Reidel, Dordrecht 1975 Zbl 0324.02002, MR 0485189 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[4] Coletti G.: Coherent numerical and ordinal probabilistic assessments.IEEE Trans. Systems Man Cybernet. 24 (1994), 12, 1747–1754 MR 1302033, 10.1109/21.328932 |
| Reference:
|
[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 0800.68922 |
| Reference:
|
[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, MR 1259282, 10.1007/BF01075200 |
| Reference:
|
[7] Coletti G., Scozzafava R.: Learning from data by coherent probabilistic reasoning.In: Proceedings of ISUMA-NAFIPS ’95, College Park 1995, pp. 535–540 |
| Reference:
|
[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, MR 1390898, 10.1142/S021848859600007X |
| Reference:
|
[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 Zbl 0859.68108, MR 1408211 |
| Reference:
|
[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 Zbl 0859.68098, MR 1408212 |
| Reference:
|
[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 |
| Reference:
|
[12] Holzer S.: On coherence and conditional prevision.Boll. Un. Mat. Ital. 4 (1985), 4–B, 441–460 Zbl 0584.60001, MR 0805231 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 Zbl 0859.68042, MR 1408214 |
| Reference:
|
[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 1367309 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 1018860 |
| Reference:
|
[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 Zbl 0859.68104, MR 1408206 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[24] Scozzafava R.: Subjective probability versus belief functions in artificial intelligence.Internat. J. Gen. Systems 22 (1994), 197–206 Zbl 0795.60002, 10.1080/03081079308935206 |
| Reference:
|
[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 |
| Reference:
|
[26] Walley P.: Statistical Reasoning with Imprecise Probabilities.Chapman and Hall, London 1991 Zbl 0732.62004, MR 1145491 |
| . |
