Issue:Natural requirements for natural roundings lead to a hardware-independent characterization of standard rounding procedures

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Title of paper: Natural requirements for natural roundings lead to a hardware-independent characterization of standard rounding procedures Author(s): T. E. Kaminsky Department of Informatics and Computer Science, Vologda State Pedagogic Institute, Orlova ul., 6, Vologda 160000, Russia Vladik Kreinovich Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA vladik@cs.utep.edu Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 4 (1998) Number 3, pages 57—64 Download:  PDF (5144  Kb, File info) Abstract: Roundings are usually described in an ad hoc manner, by simply describing the way rounding off is done in the actual computer. It is desirable to have a more abstract, hardware-independent description of possible roundings. In this paper, we propose an axiomatic description of rounding procedures. It turns out that reasonable axioms uniquely determine the roundings that are actually used in the existing computers. References: K. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy sets and Systems, Vol. 20 (1986), No. 87-96. Kaminskaja, E. L. and Kaminsky, T. E. On the theory of roundings. In: “Numerical Mathematics and Programming”, Moscow State Pedagogic Institute, 1983, pp. 89-97 (in Russian). Kaminsky, T. E. Interval roundings of lattice. In: “Intern. Congr. on Computer Systems and Applied Mathematics, Abstracts”, St.Petersburg, 1993, pp. 90-91. Kaminsky, T. E. On semigroup of interval roundings. In: “Intern. Conference on Interval and Computer-Algebraic Methods in Science and Engineering, Abstracts”, St.Petersburg, 1994, pp. 29-130. Kulisch, U. An axiomatic approach to rounded computation. Numer. Math. 18 (1971), pp. 1-17. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.