A new equivalence relation to classify the fuzzy subgroups of finite groups

Marius Tărnăuceanu

A new equivalence relation to classify the fuzzy subgroups of finite groups

Group Theory 2016-04-19 v1

Authors: Marius Tărnăuceanu

Abstract

In this paper a new equivalence relation $\approx$ to classify the fuzzy subgroups of finite groups is introduced and studied. This generalizes the equivalence relation $\sim$ defined on the lattice of fuzzy subgroups of a finite group that has been used in our previous papers (see e.g. \cite{16,24}). Explicit formulas for the number of distinct fuzzy subgroups with respect to $\approx$ are obtained in some particular cases.

Keywords

fuzzy subgroups finite groups equivalence relation classification lattice explicit formulas

Cite

@article{arxiv.1506.08300,
  title  = {A new equivalence relation to classify the fuzzy subgroups of finite groups},
  author = {Marius Tărnăuceanu},
  journal= {arXiv preprint arXiv:1506.08300},
  year   = {2016}
}

Comments

accepted for publication in Fuzzy Sets and Systems

A new equivalence relation to classify the fuzzy subgroups of finite groups

Abstract

Keywords

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