Fuzzy Normed Spaces and Fuzzy Metric Spaces

  • Yeol Je Cho
  • Themistocles M. Rassias
  • Reza Saadati


In this chapter, we define fuzzy normed spaces and show that every fuzzy normed space induces a fuzzy metric space. Then we consider the topology induced by fuzzy normed (metric) spaces and show some important topological properties of them. Next, we study fuzzy inner product spaces and some properties of these spaces.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yeol Je Cho
    • 1
    • 2
  • Themistocles M. Rassias
    • 3
  • Reza Saadati
    • 4
  1. 1.Department of Mathematical EducationGyeongsang National UniversityJinjuKorea (Republic of)
  2. 2.School of Mathematical ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece
  4. 4.Department of MathematicsIran University of Science and TechnologyTehranIran

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