Abstract
Dempster Shafer theory of evidence (DS theory) and possibility theory are two main formalisms in modelling and reasoning with uncertain information. These two theories are inter-related as already observed and discussed in many papers (e.g. [DP82, DP88b]). One aspect that is common to the two theories is how to quantitatively measure the degree of conflict (or inconsistency) between pieces of uncertain information. In DS theory, traditionally this is judged by the combined mass value assigned to the emptyset. Recently, two new approaches to measuring the conflict among belief functions are proposed in [JGB01, Liu06]. The former provides a distance-based method to quantify how close a pair of beliefs is while the latter deploys a pair of values to reveal the degree of conflict of two belief functions. On the other hand, in possibility theory, this is done through measuring the degree of inconsistency of merged information. However, this measure is not sufficient when pairs of uncertain information have the same degree of inconsistency. At present, there are no other alternatives that can further differentiate them, except an initiative based on coherence-intervals ([HL05a, HL05b]). In this paper, we investigate how the two new approaches developed in DS theory can be used to measure the conflict among possibilistic uncertain information. We also examine how the reliability of a source can be assessed in order to weaken a source when a conflict arises.
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References
Benferhat, S., Dubois, D., Prade, H.: From semantic to syntactic approach to information combination in possibilistic logic. In: Bouchon-Meunier, B. (ed.) Aggregation and Fusion of Imperfect Information, pp. 141–151. Physica Verlag, Heidelberg (1997)
Benferhat, S., Kaci, S.: Logical representation and fusion of prioritized information based on guaranteed possibility measures: Application to the distance-based merging of classical bases. Artificial Intelligence 148, 291–333 (2001)
Dubois, D., Prade, H.: On several representations of an uncertain body of evidence. In: Gupta, Sanchez (eds.) Fuzzy Information and Decision Processes, pp. 167–181. North-Holland Publishing Company, Amsterdam (1982)
Dubois, D., Prade, H.: The principle of minimum specificity as a basis for evidential reasoning. In: Bouchon, Yager (eds.) Uncertainty in Knowledge-Based Systems, pp. 75–84. Springer, Heidelberg (1987)
Dubois, D., Prade, H.: Possibility theory: An approach to the computerized processing of uncertainty. Plenum Press, New York (1988)
Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4, 244–264 (1988)
Dubois, D., Prade, H.: Possibility theory and data fusion in poorly informed environments. Control Engineering Practice 2(5), 811–823 (1994)
Dubois, D., Prade, H. (eds.): Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 3. Kluwer, Dordrecht (1998)
Dubois, D., Prade, H.: Possibility theory: Qualitative and quantitative aspects. In: Gabbay, Smets (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer Academic Publisher, Dordrecht (1998)
Dubois, D., Prade, H.: Possibility theory in information fusion. In: Riccia, Lenz, Kruse (eds.) Data Fusion and Perception. CISM Courses and Lectures, vol. 431, pp. 53–76. Springer, Heidelberg (2001)
Dubois, D., Nguyen, H., Prade, H.: Possibility theory, probability and fuzzy sets, Misunderstandings, bridges and gaps. In: Dubois, Prade (eds.) Fundamentals of Fussy Sets. The Handbooks of Fuzzy Sets Series, Ch. 7, pp. 343–438
Hunter, A., Liu, W.: Assessing the quality of merged information in possibilistic logic. In: Godo, L. (ed.) ECSQARU 2005. LNCS, vol. 3571, pp. 415–426. Springer, Heidelberg (2005)
Hunter, A., Liu, W.: A context-dependent algorithm for merging uncertain information in possibility theory (submitted, 2005)
Hunter, A., Liu, W.: Fusion rules for merging uncertain information. Information Fusion Journal 7(1), 97–134 (2006)
Jousselme, A.L., Grenier, D., Bosse, E.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)
Liu, W.: Analyzing the degree of conflict among belief functions. Artificial Intelligence (in press, 2006)
Sandri, S., Dubois, D., Kalfsbeek, H.: Elicitation, assessment and polling of expert judgements using possibility theory. IEEE Transactions on Fuzzy Systems 3, 313–335 (1995)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Smets, P., Kennes, K.: The transferable belief model. Artificial Intelligence 66(2), 191–234 (1994)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. International Journal of Approximate Reasoning 38, 133–147 (2004)
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Liu, W. (2006). Measuring Conflict Between Possibilistic Uncertain Information Through Belief Function Theory. In: Lang, J., Lin, F., Wang, J. (eds) Knowledge Science, Engineering and Management. KSEM 2006. Lecture Notes in Computer Science(), vol 4092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11811220_23
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DOI: https://doi.org/10.1007/11811220_23
Publisher Name: Springer, Berlin, Heidelberg
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