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The Cancellation Law for Addition of Fuzzy Intervals

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Computational Intelligence, Theory and Applications

Part of the book series: Advances in Soft Computing ((AINSC,volume 33))

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Abstract

The cancellativity A ⊕T B = A ⊕T C ⇒ B = C means that the equation A ⊕T X = D has unique solution. The cancellation law for sum of fuzzy quantities based on the strongest t-norm T M holds for arbitrary fuzzy interval A, see e.g. [2], [7], [8]. For the weakest t-norm T D the cancellation law holds only for very special fuzzy intervals. Based on our results from [1] and Zagrodny’s results [10] we will present conditions for validity of the cancellation law for addition based on a continuous Archimedean t-norm.

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References

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Slovak University of Technology, Radlinského 11, Sk-813 68, Bratislava, Slovakia

    Andrea Stupňanová

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  1. Andrea Stupňanová
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Editor information

Editors and Affiliations

  1. Department of Computer Science 1, University of Dortmund, FB 8 Ektrotechnik FB Informatik LS Informatik I, Postfach 50 05 00, 44221, Dortmund, Germany

    Bernd Reusch

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© 2005 Springer-Verlag Berlin Heidelberg

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Stupňanová, A. (2005). The Cancellation Law for Addition of Fuzzy Intervals. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_34

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  • DOI: https://doi.org/10.1007/3-540-31182-3_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22807-3

  • Online ISBN: 978-3-540-31182-9

  • eBook Packages: EngineeringEngineering (R0)

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