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The Effects of Fuzzy Weight Matrices on the Results of Least Squares Adjustments

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Geodetic Theory Today

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 114))

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Abstract

In practice stochastical models or their representation in form of weight matrices for least squares adjustments are formulated empirically and so they are fuzzy. Uncertain or “fuzzy” weight matrices are considered here not in the statistical context of the fuzzy-function introduced by Zadeh (1965); in contrast, the effects of fuzzy weight matrices on the results of an adjustment are regarded with respect to fixed intervals of uncertainty. Some previous approaches will be discussed. They lead to a simultaneous treatment of all interesting weight matrices by means of interval mathematics. Numerical examples will conclude the considerations.

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References

  • Ackermann F. (1963): Ein Beispiel zur Vernachlässigung von Korrelationen bei der Ausgleichung von bedingten Beobachtungen. ZfV, 5, 196–204.

    Google Scholar 

  • Alefeld G. und J. Herzberger (1983): Introduction to Interval Computations. New York, Academic Press.

    Google Scholar 

  • Gotthardt E. (1962): Die Auswirkung unrichtiger Annahmen über Gewichte und Korrelationen auf die Genauigkeit von Ausgleichungen. ZfV, 2, 65–68.

    Google Scholar 

  • Hahn M. und J. van Mierlo (1987): Die Abhängigkeit der Ausgleichungsergebnisse von der Genauigkeitsänderung einer Beobachtung. ZfV, 3, 105–115.

    Google Scholar 

  • Klatte R., Kulisch U., Neaga M., Ratz, D. und Ch. Ullrich (1991): PASCAL-XSC. Springer, Berlin Heidelberg New York.

    Book  Google Scholar 

  • Krarupt. (1972): On the Geometry of Adjustment. ZfV, 10, 440–445.

    Google Scholar 

  • Kulisch U. und W.L. Miranker (1981): Computer Arithmetic in Theory and Practice. Academic Press, New York.

    Google Scholar 

  • Kutterer H. (1994): Intervallmathematische Behandlung endlicher Unscharfen linearer Ausgleichungsmodelle. DGK C, 423, Munich. ( In print )

    Google Scholar 

  • Linkwitz K. (1960): Über den Einfluß verschiedener Gewichtsannahmen auf das Ausgleichungsergebnis bei bedingten Beobachtungen. Part I: ZfV, 6, 179–186, Part II: ZfV, 7, 239–245, Part III: ZfV, 9, 344–354

    Google Scholar 

  • Moore R.E. (1966): Interval Analysis. Prentice Hall, Englewood Cliffs, N.J..

    Google Scholar 

  • Moore R.E. (1979): Methods and Applications of Interval Analysis. SIAM, Philadelphia.

    Book  Google Scholar 

  • Neumaier A. (1990): Interval methods for systems of equations. University Press, Cambridge.

    Google Scholar 

  • Wolf H. (1961): Der Einfluß von Gewichts-Änderungen auf die Ausgleichungsergebnisse. ZfV, 10, 361–362.

    Google Scholar 

  • Zadeh L.A. (1965): Fuzzy Sets. Information & Control, 8, 338–353.

    Article  Google Scholar 

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© 1995 Springer-Verlag Berlin Heidelberg

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Kutterer, H. (1995). The Effects of Fuzzy Weight Matrices on the Results of Least Squares Adjustments. In: Sansò, F. (eds) Geodetic Theory Today. International Association of Geodesy Symposia, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79824-5_31

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  • DOI: https://doi.org/10.1007/978-3-642-79824-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59421-5

  • Online ISBN: 978-3-642-79824-5

  • eBook Packages: Springer Book Archive

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