Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Counting fuzzy subgroups in particular cases of semi-dihedral group

Document Type : Original Article

Author
‎Faculty of Engineering, ‎Ardakan University. ‎P.O‎. ‎Box 184‎, ‎Ardakan‎, ‎Iran
10.22034/jfsa.2024.430619.1192
Abstract
One of the significant aspects of fuzzy group theory is the classification of the fuzzy subgroups of finite groups. The main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of the semi-dihedral group of order 8n in particular cases n=p^m and n=pq; by using the natural equivalence relation. The corresponding equivalence classes of fuzzy subgroups of the semi-dihedral group are closely connected to the chains of subgroups of the semi-dihedral group. ‎In this regard‎; Inclusion-Exclusion principle and structure of the maximal subgroups play an‎ ‎essential role and in some situations give relations which lead to explicit formulas. Finally; by the obtained results; we determine the fuzzy subgroups of all semi-dihedral groups of order less than 100.
Keywords
Subjects

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Volume 6, Issue 2 - Serial Number 13
Open Access Statement
December 2024
Pages 215-235

  • Receive Date 14 December 2023
  • Revise Date 09 May 2024
  • Accept Date 19 June 2024