Bipolar Fuzzy Sets Are Intuitionistic Fuzzy Sets

Authors

  • Krassimir T. Atanassov Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
  • Janusz Kacprzyk Systems Research Institute, Polish Academy of Sciences and Warsaw School of Information Technology, Poland

DOI:

https://doi.org/10.7546/CRABS.2024.12.02

Keywords:

bipolar fuzzy set, fuzzy set, intuitionistic fuzzy set

Abstract

In 1983 the Intuitionistic Fuzzy Sets (IFSs) were introduced as an extension of Zadeh's fuzzy sets. Fifteen years later the Bipolar Fuzzy Sets (BFSs) were introduced as a new extension of fuzzy sets. In the article it is proved that each BFS can be transformed injectively or bijectively to an IFS.

Author Biographies

Krassimir T. Atanassov, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

Mailing Address:
Department of Bioinformatics and Mathematical Modelling,
Institute of Biophysics and Biomedical Engineering,
Bulgarian Academy of Sciences,
Akad. G. Bonchev St, Bl. 105, 1113 Sofia, Bulgaria

E-mails: krat@bas.bg,
k.t.atanassov@gmail.com

Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences and Warsaw School of Information Technology, Poland

Mailing Addresses:
Systems Research Institute,
Polish Academy of Sciences,
6 Newelska St,
01-447 Warsaw, Poland

and

Warsaw School of Information Technology,
6 Newelska St,
01-447 Warsaw, Poland

E-mail: kacprzyk@ibspan.waw.pl

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Published

25-12-2024

How to Cite

[1]
K. Atanassov and J. Kacprzyk, “Bipolar Fuzzy Sets Are Intuitionistic Fuzzy Sets”, C. R. Acad. Bulg. Sci., vol. 77, no. 12, pp. 1752–1756, Dec. 2024.

Issue

Vol. 77 No. 12 (2024)

Section

Mathematics

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