Abstract
This paper addresses the issue of measuring similarity between pieces of uncertain information in the framework of possibility theory. In a first part, natural properties of such functions are proposed and a survey of the few existing measures is presented. Then, a new measure so-called Information Affinity is proposed to overcome the limits of the existing ones. The proposed function is based on two measures, namely, a classical informative distance, e.g. Manhattan distance which evaluates the difference, degree by degree, between two normalized possibility distributions and the well known inconsistency measure which assesses the conflict between the two possibility distributions. Some potential applications of the proposed measure are also mentioned in this paper.
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References
Abellan, J., Gomez, M.: Measures of divergence on credal sets. Fuzzy Sets and Systems 157, 1514–1531 (2006)
Ben Amor, N., Benferhat, S., Elouedi, Z.: Qualitative classification and evaluation in possibilistic decision trees. In: FUZZ-IEEE 2004 (2004)
Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy sets and systems 84(2), 143–153 (1996)
Chan, H., Darwiche, A.: A distance measure for bounding probabilistic belief change. International Journal of Approximate Reasoning 38, 149–174 (2005)
Choquet, G.: Theory of capacities. Annales de L’Institut Fourier 54, 131–295 (1953)
De Baets, B., De Meyer, H.: Transitivity-preserving fuzzification schemes for cardinality-based similarity measures. EJOR 160(1), 726–740 (2005)
Dubois, D., Prade, H.: Possibility theory: An approach to computerized processing of uncertainty. Plenum Press, New York (1988)
Fixsen, D., Mahler, R.P.S.: The modified Dempster-Shafer approach to classification. IEEE Trans. Syst. Man and Cybern. 27, 96–104 (1997)
Fono, L.A., Gwet, H., Bouchon-Meunier, B.: Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison. EJOR 183, 314–326 (2007)
Higashi, M., Klir, G.J.: Measures of uncertainty and information based on possibility distributions. Int. J. General Systems 9(1), 43–58 (1983)
Higashi, M., Klir, G.J.: On the notion of distance representing information closeness: Possibility and probability distributions. IJGS 9, 103–115 (1983)
Hüllermeier, E.: Possibilistic instance-based learning. AI 148(1-2), 335–383 (2003)
Jenhani, I., Ben Amor, N., Elouedi, Z., Mellouli, K.: Decision Trees as Possibilistic Classifiers (paper submitted)
Jousselme, A.L., Grenier, D., Bossé, E.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)
Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems 1(2), 98–110 (1993)
Kroupa, T.: Measure of divergence of possibility measures. In: Proceedings of the 6th Workshop on Uncertainty Processing, Prague, pp. 173–181 (2003)
Kullback, S., Leibler, R.A.: On information and sufficiency. Annals of Mathematical Statistics 22, 79–86 (1951)
Sanguesa, R., Cabos, J., Cortes, U.: Possibilistic conditional independence: a similarity based measure and its application to causal network learning. IJAR (1997)
Sanguesa, R., Cortes, U.: Prior knowledge for learning networks in non-probabilistic settings. IJAR 24, 103–120 (2000)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Tessem, B.: Approximations for efficient computation in the theory of evidence. Artificial Intelligence 61, 315–329 (1993)
Tversky, A.: Features of similarity. Psychological Review 84, 327–352 (1977)
Wang, X., De Baets, B., Kerre, E.: A comparative study of similarity measures. Fuzzy Sets and Systems 73(2), 259–268 (1995)
Williams, M.-A.: An Operational Measure of Similarity for Belief Revision Systems (1997)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets ans Systems 1, 3–28 (1978)
Zouhal, L.M., Denoeux, T.: An evidence-theoric k-NN rule with paprameter optimization. IEEE Trans. Syst. Man Cybern. C 28(2), 263–271 (1998)
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Jenhani, I., Ben Amor, N., Elouedi, Z., Benferhat, S., Mellouli, K. (2007). Information Affinity: A New Similarity Measure for Possibilistic Uncertain Information. In: Mellouli, K. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2007. Lecture Notes in Computer Science(), vol 4724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75256-1_73
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DOI: https://doi.org/10.1007/978-3-540-75256-1_73
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