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A fuzzy application of the group \(\mathbb {Z}_n\) to complete hypergroups

  • Irina CristeaEmail author
  • Elhan Hassani Sadrabadi
  • Bijan Davvaz
Methodologies and Application
  • 30 Downloads

Abstract

The purpose of this paper is the study of intuitionistic fuzzy subhypergroups of some special finite complete hypergroups. More exactly, in this paper we determine all m-tuples, characterizing the considered complete hypergroups, such that the grade intuitionistic fuzzy set \((\overline{\mu },\overline{\lambda })\) is an intuitionistic fuzzy subhypergroup of such hypergroups. Here, we deal with complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo \(p^2\) or modulo pq, with p and q distinct odd primes. This article is a continuation of a previous work, concerning the complete hypergroups obtained from groups isomorphic with the additive groups of integers modulo p or modulo 2p, with p a prime number. It represents the starting point, the mathematical base, for writing a general algorithm for characterizing all complete hypergroups obtained from a group G and having the grade intuitionistic fuzzy set as an intuitionistic fuzzy subhypergroup.

Keywords

Complete hypergroup Intuitionistic fuzzy set Intuitionistic fuzzy subhypergroup Wieferich prime 

Notes

Acknowledgements

This study was partially funded by the Slovenian Research Agency (research core funding No. P1 - 0285).

Compliance with ethical standards

Conflict of Interest

The first author acknowledges the financial support from the Slovenian Research Agency (research core funding No. P1 - 0285). The second and the third author declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Information Technologies and Applied MathematicsUniversity of Nova GoricaNova GoricaSlovenia
  2. 2.Department of MathematicsYazd UniversityYazdIran

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