Abstract
The clarification of the concepts of independence, marginalization, and combination of modularized information is one of the major topics concerning the efficient treatment of imperfect data in complex domains of knowledge. Confining to the uncertainty calculus of possibility theory, we consider a syntactic (based on a set of axioms) as well as a semantic approach (in a random set framework) to appropriate definitions of possibilistic independence. It turns out that well-known, but also new proposals for the concept of possibilistic independence can be justified.
This work has been supported by the European Economic Community under Project ESPRIT III BRA 6156 (DRUMS II), and by the DGICYT under Project PB92-0939
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Benferhat, S., Dubois, D., and Prade, H.: Expressing independence in a possibilistic framework and its application to default reasoning, in: Proceedings of the Eleventh ECAI Conference, 150–154 (1994).
Campos, L.M. de: Independence relationships in possibility theory and their application to learning belief networks, to appear in Proceedings of the ISSEK Workshop ‘Mathematical and Statistical Methods in Artificial Intelligence’ at Udine, Italy (1995).
Campos, L.M. de and Huete, J.F.: Independence concepts in upper and lower probabilities, in: Uncertainty in Intelligent Systems (Eds. B. Bouchon-Meunier, L. Valverde, R.R. Yager), North-Holland, 49–59 (1993).
Campos, L.M. de and Huete, J.F.: Learning non probabilistic belief networks, in: Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Computer Science 747 (Eds. M. Clarke, R. Kruse, S. Moral), Springer Verlag, 57–64 (1993).
Cooman, G. de and Kerre, E.E.: A new approach to possibilistic independence, in: Proceedings of the Third IEEE International Conference on Fuzzy Systems, 1446–1451 (1994).
Dawid, A.P.: Conditional independence in statistical theory, J.R. Statist. Soc. Ser. B 41, 1–31 (1979).
Dubois, D., Farinas del Cerro, L., Herzig, A. and Prade, H.: An ordinal view of independence with applications to plausible reasoning, in: Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference (Eds. R. López de Mántaras, D. Poole), Morgan Kaufmann, 195–203 (1994).
Dubois, D. and Prade, H.: Possibility Theory: An approach to computerized processing of uncertainty, Plenum Press (1988).
Dubois, D. and Prade, H.: Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems 40, 143–202 (1991).
Dubois, D. and Prade, H.: Belief revision and updates in numerical formalisms — An overview, with new results for the possibilistic framework, in: Proceedings of the 13th IJCAI Conference, Morgan and Kaufmann, 620–625 (1993).
Farinas del Cerro, L. and Herzig, A.: Possibility theory and independence, in: Proceedings of the Fifth IPMU Conference, 820–825 (1994).
Fonck, P.: Conditional independence in possibility theory, in: Uncertainty in Artificial Intelligence, Proceedings of the Tenth Conference (Eds. R. López de Mántaras, D. Poole) Morgan and Kaufmann, 221–226 (1994).
Gebhardt, J. and Kruse, R.: A new approach to semantic aspects of possibilistic reasoning, in: Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Computer Science 747 (Eds. M. Clarke, R. Kruse, S. Moral), Springer Verlag, 151–160 (1993).
Gebhardt, J. and Kruse, R.: On an information compression view of possibility theory, in; Proc. of the Third IEEE Int. Conf. on Fuzzy Systems, Orlando, 1285–1288 (1994).
Gebhardt, J. and Kruse, R.: Learning possibilistic networks from data, in: Proc. of the Fifth Int. Workshop on Artificial Intelligence and Statistics, Fort Lauderdale, Florida, 233–244 (1995).
Hestir, K., Nguyen, H.T., and Rogers, G.S.: A random set formalism for evidential reasoning, in: Conditional Logic in Expert Systems, (Eds. I.R. Goodman, M.M. Gupta, H.T. Nguyen, and G.S. Rogers), North Holland, New York, 209–344 (1991).
Hisdal, E.: Conditional possibilities, independence and noninteraction, Fuzzy Sets and Systems 1, 283–297 (1978).
Kruse, R., Gebhardt, J., and Klawonn, F.: Foundations of Fuzzy Systems, Wiley, Chichester (1994).
Lauritzen, S.L., Dawid, A.P., Larsen, B.N., and Leimer, H.G.: Independence properties of directed Markov fields, Networks 20, 491–505 (1990).
Pearl, J.: Probabilistic reasoning in intelligent systems: Networks of plausible inference, Morgan and Kaufmann (1988).
Shafer, G.: Mathematical theory of evidence, Princeton University Press, Princeton (1976).
Shenoy, P.P.: Conditional independence in uncertainty theories, in: Uncertainty in Artificial Intelligence, Proceedings of the Eighth Conference (Eds. D. Dubois, M.P. Wellman, B. D'Ambrosio, P. Smets), Morgan and Kaufmann, 284–291 (1992).
Smets, P. and Kennes, R.: The transferable belief model, Artificial Intelligence 66, 191–234 (1994).
Spirtes, P., Glymour, C., and Scheines, R.: Causation, Prediction and Search, Lecture Notes in Statistics 81, Springer-Verlag (1993).
Studený, M.: Formal properties of conditional independence in different calculi of AI, in: Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Computer Science 747, (Eds. M. Clarke, R. Kruse, S. Moral Springer Verlag, 341–348 (1993).
Ullman, J.D.: Principles of Database and Knowledge-Base Systems, Vol. 1, Computer Science Press Inc., Rockville, Maryland (1988).
Wang, P.Z.: From the fuzzy statistics to the falling random subsets, in: Advances in Fuzzy Sets, Possibility and Applications, (Eds. P.P. Wang), Plenum Press, New York, 81–96 (1983).
Wilson, N.: Generating graphoids from generalized conditional probability, in: Uncertainty in Artificial Intelligence, Proceedings of the Tenth Conference, (Eds. R. López de Mántaras, D. Poole) Morgan and Kaufmann, 221–226 (1994).
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci. 8, 199–249, 301–37, Inform. Sci. 9, 43–80 (1975)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3–28 (1978).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Campos, L.M., Gebhardt, J., Kruse, R. (1995). Axiomatic treatment of possibilistic independence. In: Froidevaux, C., Kohlas, J. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1995. Lecture Notes in Computer Science, vol 946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60112-0_10
Download citation
DOI: https://doi.org/10.1007/3-540-60112-0_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60112-8
Online ISBN: 978-3-540-49438-6
eBook Packages: Springer Book Archive