Fuzzy zeroes and indistinguishability of real numbers

  • Bernard De Baets
  • Milan Mareš
  • Radko Mesiar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1226)


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.


T-equivalence fuzzy number fuzzy zero generator T-idempotent shape t-norm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Bernard De Baets
    • 1
    • 4
  • Milan Mareš
    • 2
  • Radko Mesiar
    • 3
  1. 1.Department of Applied Mathematics and Computer ScienceUniversity of GentGentBelgium
  2. 2.Academy of Sciences of the Czech RepublicÚTIAPraha 8Czech Republic
  3. 3.Department of MathematicsSlovak Technical UniversityBratislavaSlovakia
  4. 4.Fund for Scientific Research - FlandersBelgium

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