Fuzzy Operator Theory in Mathematical Analysis pp 1-9 | Cite as

Preliminaries

• Authors
• Authors and affiliations

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

Chapter

First Online: 13 August 2018

• 83 Downloads

Abstract

In this chapter, we recall some definitions and results as triangular norms (co-norm), fuzzy sets, and lattices which will be used later on in this book.

This is a preview of subscription content, log in to check access.

References

1. 16.
   K.T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)MathSciNetCrossRefGoogle Scholar
2. 39.
   G. Deschrijver, E.E. Kerre, On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 23, 227–235 (2003)MathSciNetCrossRefGoogle Scholar
3. 54.
   J. Goguen, \(\mathcal {L}\)-fuzzy sets. J. Math. Anal. Appl. 18, 145–174 (1967)Google Scholar
4. 66.
   O. Hadžić, E. Pap, Fixed Point Theory in PM-Spaces (Kluwer Academic Publishers, Dordrecht, 2001)CrossRefGoogle Scholar
5. 68.
   O. Hadžić, E. Pap, M. Budincević, Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces. Kybernetica 38, 363–381 (2002)MathSciNetzbMATHGoogle Scholar
6. 71.
   P. Hajek, Metamathematics of Fuzzy Logic (Kluwer Academic Publishers, Dordrecht, 1998)CrossRefGoogle Scholar
7. 93.
   E.P. Klement, R. Mesiar, E. Pap, Triangular Norms (Kluwer Academic Publishers, Dordrecht, 2000)CrossRefGoogle Scholar
8. 96.
   E.P. Klement, R. Mesiar, E. Pap, Triangular norms, Position paper III: continuous t-norms. Fuzzy Sets Syst. 145, 439–454 (2004)MathSciNetCrossRefGoogle Scholar
9. 105.
   K. Menger, Statistical metrics. Proc. Natl. Acad. Sci. USA 28, 535–537 (1942)MathSciNetCrossRefGoogle Scholar
10. 135.
    B. Schweizer, A. Sklar, Probabilistic Metric Spaces (Elsevier, North Holand, 1983)zbMATHGoogle Scholar
11. 148.
    J.Z. Xiao, X.H. Zhu, X.Y. Liu, An alternative characterization of probabilistic Menger spaces with H-type triangular norms. Fuzzy Sets Syst. 227, 107–114 (2013)MathSciNetCrossRefGoogle Scholar
12. 149.
    L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar
13. 153.
    H.J. Zimmermann, Fuzzy Set Theory and Its Application (Kluwer, Dordrecht, 1985)CrossRefGoogle Scholar

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