Abstract
We state the fundamental problem of measurement— comparison of quantities determined with accuracy up to an interval. We construct a mathematical theory of comparison for such quantities; for this theory we introduce interval relations similar to numerical relations, and we study their properties. Our results make it possible to solve measurement and control problems in interval form.
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References
G. Alefeld and W. Hertsberg, Introduction to Interval Computations [Russian translation], Mir, Moscow (1987).
Yu. I. Shokin, Interval Analysis [in Russian], Nauka, Novosibirsk (1981).
S. A. Kalmykov, Yu. I. Shokin, and Z. Kh. Yuldashev, Methods of Interval Analysis [in Russian], Nauka, Novosibirsk (1986).
V. I. Levin, Structurally Logical Methods for Complex Systems with Computers [in Russian], Nauka, Moscow (1987).
V. I. Levin, Abstracts of the Twelfth All-Union Symposium on Logical Control Using Computers [in Russian], Moscow (1989), p. 20.
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Translated from Izmeritel'naya Tekhnika, No. 5, pp. 3–8, May, 1998.
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Levin, V.I. Mathematical theory of interval comparison and its application to measurement problems. Meas Tech 41, 399–406 (1998). https://doi.org/10.1007/BF02506611
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DOI: https://doi.org/10.1007/BF02506611