Pythagorean fuzzy sets in UP-algebras and approximations

Akarachai Satirad; Ronnason Chinram; Aiyared Iampan; Akarachai Satirad; Ronnason Chinram; Aiyared Iampan

doi:10.3934/math.2021354

AIMS Mathematics

2021, Volume 6, Issue 6: 6002-6032. doi: 10.3934/math.2021354

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Research article

Pythagorean fuzzy sets in UP-algebras and approximations

1.
Department of Mathematics, School of Science, University of Phayao, Mae Ka, Phayao 56000, Thailand
2.
Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand

Received: 20 November 2020 Accepted: 25 March 2021 Published: 31 March 2021
MSC : 03E72, 03G25, 08A72

The aim of this paper is to apply the concept of Pythagorean fuzzy sets to UP-algebras, and then we introduce five types of Pythagorean fuzzy sets in UP-algebras. In addition, we will also discuss the relationship between some assertions of Pythagorean fuzzy sets and Pythagorean fuzzy UP-subalgebras (resp., Pythagorean fuzzy near UP-filters, Pythagorean fuzzy UP-filters, Pythagorean fuzzy UP-ideals, Pythagorean fuzzy strong UP-ideals) in UP-algebras and study upper and lower approximations of Pythagorean fuzzy sets.
Citation: Akarachai Satirad, Ronnason Chinram, Aiyared Iampan. Pythagorean fuzzy sets in UP-algebras and approximations[J]. AIMS Mathematics, 2021, 6(6): 6002-6032. doi: 10.3934/math.2021354

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Abstract

The aim of this paper is to apply the concept of Pythagorean fuzzy sets to UP-algebras, and then we introduce five types of Pythagorean fuzzy sets in UP-algebras. In addition, we will also discuss the relationship between some assertions of Pythagorean fuzzy sets and Pythagorean fuzzy UP-subalgebras (resp., Pythagorean fuzzy near UP-filters, Pythagorean fuzzy UP-filters, Pythagorean fuzzy UP-ideals, Pythagorean fuzzy strong UP-ideals) in UP-algebras and study upper and lower approximations of Pythagorean fuzzy sets.

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