A Mathematical Theory of Fuzzy Numbers

Granular Computing Approach
  • Tsau Young Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8170)


The essence of granular computing (GrC) is to replace the concept of points in classical mathematics by that of granules. Usual fuzzy number systems are obtained by using type I fuzzy sets as granules. These fuzzy number systems have a common weakness - lack of existence theorem. Let R be the real number system, the trapezoidal membership functions at r ∈ R is a base of fuzzified topological neighborhood system FNS(r). By taking FNS(r) as the granule, a new (but not type I) fuzzy number system \(\mathcal{F}\) is formed. Surprisingly, we have found that such a new \(\mathcal{F}\) is abstractly isomorphic to the classical real number system.


Fuzzy numbers Fuzzified topological neighborhood systems Granular computing Qualitative fuzzy set Topology 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tsau Young Lin
    • 1
    • 2
  1. 1.Department of Computer ScienceSan Jose State UniversitySan JoseUSA
  2. 2.GrC SocietyUSA

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