Abstract
We study interval-valued fuzzy sets as a model for the imprecise knowledge of the membership function of a fuzzy set. We compare three models for the probabilistic information about this membership function: the set of distributions of the measurable selections, the upper and lower probabilities of the associated random interval, and its p-box. We give sufficient conditions for the equality between these sets, and establish a connection with the notion of probability induced by an intuitionistic fuzzy set. An alternative approach to the problem by means of sets of finitely additive distributions is also considered.
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Montes, I., Miranda, E., Montes, S. (2015). Connecting Interval-Valued Fuzzy Sets with Imprecise Probabilities. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_6
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DOI: https://doi.org/10.1007/978-3-319-10765-3_6
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