Abstract
Probability measures are well-defined ones that satisfy additivity. However, it is slightly tight because of its condition of additivity. Fuzzy measures that do not satisfy additivity have been proposed as the substitute measures. The only belief function involves a density function among them. In this paper, we propose two density functions by extending values of probability functions to interval values, which do not satisfy additivity. According to the definition of interval probability functions, lower and upper probabilities are defined, respectively. A combination rule and a conditional probability can be defined well. The properties of the proposed measure are clarified.
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© 2001 Springer-Verlag Berlin Heidelberg
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Tanaka, H., Sugihara, K., Maeda, Y. (2001). Non-additive Measures by Interval Probability Functions. In: Terano, T., Ohsawa, Y., Nishida, T., Namatame, A., Tsumoto, S., Washio, T. (eds) New Frontiers in Artificial Intelligence. JSAI 2001. Lecture Notes in Computer Science(), vol 2253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45548-5_39
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DOI: https://doi.org/10.1007/3-540-45548-5_39
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