Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Graph Associated to a Fuzzy Hypergroupoid

Document Type : Original Article

Authors
Reza Ameri 1
Zahra Nazem Ashura 2
1 Department of Mathematics, , School of Mathematics,, Statistics and Computer Science, College of Sciences, University of Tehran,, Tehran,, Iran
2 Department of Mathematics, Faculty of Science, University of Tehran, Tehran, Iran
10.22034/jfsa.2022.316186.1107
Abstract
In this paper, our aim is to study the graph associated to a fuzzy hypergroupoids(hypergroup). For a (S, ∘) is a fuzzy hypergroup, we associate a graph Γ_S to S, such that its vertices are the elements of S and two distinct vertices x and y are adjacent if xαy , where α is a relation on S, with transitive closure α*, is the smallest equivalence relation on S, such that the quotient space(S/ α *, ⊗) is a groupoid (group). We will proceed to study the relationship between algebraic properties of (S, ∘) and graph theoretic properties of graph Γ_S. Finally, we apply the graph Γ_S are advanced in COVID-19 context to modeling this phenomenon.


Keywords
Hypergroup
Graph associated
Fundamental relation
Connected graph
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Fuzzy Systems and its Applications
Volume 5, Issue 1 - Serial Number 10
Open Access Statement
June 2022
Pages 55-81

  • Receive Date 15 December 2021
  • Revise Date 18 March 2022
  • Accept Date 15 June 2022