Influence diagrams (IDs) are one of the most commonly used graphical decision models for reasoning under uncertainty. The quantification of IDs which consists in defining conditional probabilities for chance nodes and utility functions for value nodes is not always obvious. In fact, decision makers cannot always provide exact numerical values and in some cases, it is more easier for them to specify qualitative preference orders. This work proposes an adaptation of standard IDs to the qualitative framework based on possibility theory.
[1] A. Akari, microeconomie du consommateur et du producteur,
pages 35:95, 2000.
[2] N. Ben Amor, S.Benferhat and K.Mellouli, Anytime propagation
algorithm for min-based possibilistic graphs, Soft
Computing a fusion of foundations methodologies and
applications, Springer Verlag, Vol 8, pages 150:161, 2001.
[3] N. Ben Amor. Qualitative Possibilistic Graphical Models:
From Independence to Propagation Algorithms. Ph.D.
dissertation, 2002.
[4] G. F. Cooper, A method for using belief networks as
influence diagrams, Fourth workshop on uncertainty in
arti¯cial intelligence, 1988.
[5] D. Dubois and H. Prade, Possibility theory, an approach
to computerized processing of uncertainty, Plenum Press,
New York, NY, 1988.
[6] D. Dubois and .H Prade,Didier Dubois and Henri Prade,
An introductory survey of possibility theory and its recent
developments, 1998.
[7] D. Dubois, H. Prade and P. Smets, New semantics for
quantitative possibility theory, , 2nd International Symposium
on imprecise probabilities and their applications,
Ithaca, new York, 2001.
[8] R.A. Howard and J.E. Matheson, Influence diagrams. In
the principles and applications of decision analysis, Vol II,
R.A Howard and J.E Matheson (eds). Strategic decisions
group, Menlo Park, Calif, 1984.
[9] F.V. Jensen, Introduction to Bayesian networks, UCL
Press, 1996.
[10] F.V. Jensen, Bayesian networks and decision graphs.
Springer, statistics for engineering and information science,
2002.
[11] J. Kim and J. Pearl, Convince, A conversational inference
consolidation engine, IEEE Trains. on Systems, Man and
Cybernetics 17, pages 120:132, 1987.
[12] J.Pearl, Causality Models, Reasoning and Inference, Cambridge
University Press, 2000.
[13] P.P. Shenoy , A comparison of graphical techniques for
decision analysis, European Journal of Operational Research,
Vol 78, pages 1:21, 1994.
[14] P. H. Giang, P.P. Shenoy, Two axiomatic approaches to
decision making using possibility theory, European journal
of operational research, Vol 162 No.2, pages 450:467, 2005.
[15] R. D. Shachter, Evaluating influence diagrams, Operation
Research 34 pages 871:882, 1986.
[16] R. D. Shachter and M. A. Poet, Decision making using
probabilistic inference methods,In Proceedings of 8th
Conference on Uncertainty in Arti¯cial Intelligence, pages
276:283, 1992.
[17] J. Von Neumann and O.Morgenstern, theory of games and
economic behavior, Princeton University Press, 1948.
[18] N. L. Zhang, Probabilistic inference in influence diagrams,
In Proceedings of 14th Conference on Uncertainty in
Artificial Intelligence, pages 514-522, 1998.
[1] A. Akari, microeconomie du consommateur et du producteur,
pages 35:95, 2000.
[2] N. Ben Amor, S.Benferhat and K.Mellouli, Anytime propagation
algorithm for min-based possibilistic graphs, Soft
Computing a fusion of foundations methodologies and
applications, Springer Verlag, Vol 8, pages 150:161, 2001.
[3] N. Ben Amor. Qualitative Possibilistic Graphical Models:
From Independence to Propagation Algorithms. Ph.D.
dissertation, 2002.
[4] G. F. Cooper, A method for using belief networks as
influence diagrams, Fourth workshop on uncertainty in
arti¯cial intelligence, 1988.
[5] D. Dubois and H. Prade, Possibility theory, an approach
to computerized processing of uncertainty, Plenum Press,
New York, NY, 1988.
[6] D. Dubois and .H Prade,Didier Dubois and Henri Prade,
An introductory survey of possibility theory and its recent
developments, 1998.
[7] D. Dubois, H. Prade and P. Smets, New semantics for
quantitative possibility theory, , 2nd International Symposium
on imprecise probabilities and their applications,
Ithaca, new York, 2001.
[8] R.A. Howard and J.E. Matheson, Influence diagrams. In
the principles and applications of decision analysis, Vol II,
R.A Howard and J.E Matheson (eds). Strategic decisions
group, Menlo Park, Calif, 1984.
[9] F.V. Jensen, Introduction to Bayesian networks, UCL
Press, 1996.
[10] F.V. Jensen, Bayesian networks and decision graphs.
Springer, statistics for engineering and information science,
2002.
[11] J. Kim and J. Pearl, Convince, A conversational inference
consolidation engine, IEEE Trains. on Systems, Man and
Cybernetics 17, pages 120:132, 1987.
[12] J.Pearl, Causality Models, Reasoning and Inference, Cambridge
University Press, 2000.
[13] P.P. Shenoy , A comparison of graphical techniques for
decision analysis, European Journal of Operational Research,
Vol 78, pages 1:21, 1994.
[14] P. H. Giang, P.P. Shenoy, Two axiomatic approaches to
decision making using possibility theory, European journal
of operational research, Vol 162 No.2, pages 450:467, 2005.
[15] R. D. Shachter, Evaluating influence diagrams, Operation
Research 34 pages 871:882, 1986.
[16] R. D. Shachter and M. A. Poet, Decision making using
probabilistic inference methods,In Proceedings of 8th
Conference on Uncertainty in Arti¯cial Intelligence, pages
276:283, 1992.
[17] J. Von Neumann and O.Morgenstern, theory of games and
economic behavior, Princeton University Press, 1948.
[18] N. L. Zhang, Probabilistic inference in influence diagrams,
In Proceedings of 14th Conference on Uncertainty in
Artificial Intelligence, pages 514-522, 1998.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50951", author = "Wided GuezGuez and Nahla Ben Amor and Khaled Mellouli", title = "Qualitative Possibilistic Influence Diagrams", abstract = "Influence diagrams (IDs) are one of the most commonly used graphical decision models for reasoning under uncertainty. The quantification of IDs which consists in defining conditional probabilities for chance nodes and utility functions for value nodes is not always obvious. In fact, decision makers cannot always provide exact numerical values and in some cases, it is more easier for them to specify qualitative preference orders. This work proposes an adaptation of standard IDs to the qualitative framework based on possibility theory.
", keywords = "decision making, influence diagrams,
qualitative utility, possibility theory.", volume = "2", number = "9", pages = "633-6", }
