Abstract
In this paper, the well-known indistinguishability problem of real numbers is addressed. It is explained that T-equivalences form a suitable mathematical model for dealing with this problem. Firstly, it is shown that, for a continuous Archimedean t-norm T with additive generator f, from any pseudometric a T-equivalence can be constructed, by applying the pseudo-inverse of f. Secondly, a particular pseudo-metric d g on ℝ is constructed from a scale or generator g. It is investigated how this pseudo-metric can be transformed into a T-equivalence on ℝ. The answer lies in the study of the T-idempotents of the T-addition of fuzzy numbers. It is explained that by suitably modelling ‘fuzzy zero’, the pseudo-metric d g allows to propagate this ‘indistinguishability from O’ across the real line, thus obtaining a description of indistinguishability of real numbers in general.
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© 1997 Springer-Verlag Berlin Heidelberg
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De Baets, B., Mareš, M., Mesiar, R. (1997). Fuzzy zeroes and indistinguishability of real numbers. In: Reusch, B. (eds) Computational Intelligence Theory and Applications. Fuzzy Days 1997. Lecture Notes in Computer Science, vol 1226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62868-1_122
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DOI: https://doi.org/10.1007/3-540-62868-1_122
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