Abstract
Importance measures are a well-known concept developed in reliability theory. Here, we apply this concept to assumption-based reasoning, a field which in fact is quite close to reliability theory. Based on quasi-supporting and supporting arguments, we develop two concepts of importance measures and show how they are related to the ones from reliability theory.
Research supported by grant No. 2000-061454.00 of the Swiss National Foundation for Research.
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Anrig, B. 2000. Probabilistic Model-Based Diagnostics. Ph.D. thesis, University of Fribourg, Institute of Informatics.
Anrig, B. 2001. Importance Measures for Probabilistic A s sumption-Based Reasoning. Tech. rept. 01-02. University of Fribourg, Department of Informatics.
Barlow, R.E., & Proschan, R. 1975. Statistical Theory of Reliability and Life Testing. New York.
Beichelt, F. 1993. Zuverlässigkeits-und Instandhaltungstheorie. Teubner, Stuttgart.
Bertschy, R., & Monney, P.A. 1996. A Generalization of the Algorithm of Heidtmann to Non-Monotone Formulas. J. of Computational and Applied Mathematics, 76, 55–76.
Birnbaum, Z.W. 1969. On the Importance of Different Components in a Multicomponent System. In: Multivariate Analysis II. Academic Press.
Darwiche, A. 2001. Decomposable Negation Normal Form. To appear in J. of ACM.
Fussel, B.J. 1973. How to Hand-Calculate System Reliability Characteristics. IEEE Trans. on Reliability, 24.
Haenni, R. 2001. Cost-bounded Argumentation. International Journal of Approximate Reasoning, 26(2), 101–127.
Haenni, R., & Lehmann, N. 2001. Approximation Based on Incomplete Belief Functions. Internal Paper, University of Fribourg, Department of Informatics.
Haenni, R., Anrig, B., Bissig, R., & Lehmann, N. 2000. ABEL homepage. http://www-iiuf.unifr.ch/tcs/abel.
Kohlas, J. 1987. Zuverlässigkeit und Verfügbarkeit. Teubner.
Kohlas, J., & Monney, P.A. 1995. A Mathematical Theory of Hints. An Approach to the Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems, vol. 425. Springer.
Kohlas, J., Anrig, B., Haenni, R., & Monney, P.A. 1998. Model-Based Diagnostics and Probabilistic Assumption-Based Reasoning. Artif. Intell., 104, 71–106.
Kohlas, J., Haenni, R., & Lehmann, N. 2000. Probabilistic Argumentation Systems. In: Kohlas, J., & Moral, S. (eds), Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5: Algorithms for Uncertainty and Defeasible Reasoning. Kluwer, Dordrecht.
Kohlas, J., Anrig, B., & Bissig, R. 2001. Reliability and Diagnostic of Modular Systems. South African J. on Operations Research ORiON.
Lauritzen, S.L., & Shenoy, P.P. 1995. Computing Marginals Using Local Computation. Working Paper 267. School of Business, University of Kansas.
Lauritzen, S.L., & Spiegelhalter, D.J. 1988. Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems. J. of Royal Stat. Soc., 50(2), 157–224.
Lehmann, N. 2001. Probabilistic Approaches to A s sumption-Based Reasoning. Ph.D. thesis, University of Fribourg, Department of Informatics.
Reiter, R. 1987. A Theory of Diagnosis From First Principles. Artif. Intell., 32, 57–95.
Shenoy, P.P., & Shafer, G. 1990. Axioms for Probability and Belief Functions Propagation. In: Shachter, R.D., Levitt, T.S., Kanal, L.N., & Lemmer, J.F. (eds), Uncertainty in Artif. Intell. 4. North Holland.
Vesley, W. 1970. A Time-Dependent Methodology for Fault Tree Evaluation. Nuclear Engineering and Design, 13, 339–360.
Viswanadham, N., Sarma, V.V.S., & Singh, M.G. 1987. Reliability of Computer and Control Systems. North Holland.
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Anrig, B. (2001). Importance Measures from Reliability Theory for Probabilistic Assumption-Based Reasoning. In: Benferhat, S., Besnard, P. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Lecture Notes in Computer Science(), vol 2143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44652-4_61
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DOI: https://doi.org/10.1007/3-540-44652-4_61
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