On Relations between Some Types of (α,β)-Intuitionistic Fuzzy Ideals of Ternary Semigroups

Authors

  • Damarian Prawira Hutama Department of Mathematics, Brawijaya University
  • Noor Hidayat Department of Mathematics, Brawijaya University
  • Abdul Rouf Al-ghofari Department of Mathematics, Brawijaya University

DOI:

https://doi.org/10.31764/jtam.v5i2.5171

Keywords:

Ternary Semigroup, Fuzzy Set, Intuitionistic Fuzzy Set, (α, β)-IF Ideal.

Abstract

In this article, the notion of (α,β)-intuitionistic fuzzy ideals (briefly, (α,β)-IF ideals) of ternary semigroups is described using â€belong to†relation (ϵ) and “quasi-coincidence with†relation (q) connecting two objects, i.e., an intuitionistic fuzzy point (IFP, for short) and an intuitionistic fuzzy set (briefly, IFS). Throughout this paper, α∈{ϵ,q,ϵ∨q} and β∈{ϵ,q,ϵ∨q,ϵ∧q}.  The main purposes of this research are to construct the definition of (α,β)-intuitionistic fuzzy ideals of ternary semigroups and to investigate the relations between some types of these ideals. To achieve these goals, we use literature review method to study previous researches regarding (α,β)-fuzzy ideals of ternary semigroups and (α,β)-IF ideals of semigroups. As a result, we find the conditions for an IFS and an ideal of a ternary semigroup to be classified as an (α,ϵ∨q)-IF ideal of ternary semigroup. Relations between some types of (α,β)-IF ideals of a ternary semigroup are also discussed here.

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Published

2021-10-26

Issue

Vol. 5 No. 2 (2021): October

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