\((\inf, \sup)\)-Hesitant Fuzzy Subalgebras of BCK/BCI-Algebras

Volume 29, Issue 2, pp 142--155 http://dx.doi.org/10.22436/jmcs.029.02.04

Publication Date: August 24, 2022 Submission Date: May 27, 2022 Revision Date: June 14, 2022 Accteptance Date: July 07, 2022

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Authors

N. Chunsee - Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit 53000, Thailand. R. Prasertpong - Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand. P. Khamrot - Department of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna of Phitsanulok, Phitsanulok 65000, Thailand. T. Gaketem - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, Mae Ka, University of Phayao, Phayao 56000, Thailand. A. Iampan - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, Mae Ka, University of Phayao, , Phayao 56000, Thailand. P. Julatha - Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.

Abstract

In this paper, we introduce the concept of \((\inf, \sup)\)-hesitant fuzzy subalgebras, which is a general concept of interval-valued fuzzy subalgebras, in BCK/BCI-algebras and investigate its properties. We characterize \((\inf, \sup)\)-hesitant fuzzy subalgebras in terms of sets, fuzzy sets, hesitant fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, negative fuzzy sets and bipolar fuzzy sets. Furthermore, characterizations of subalgebras, fuzzy subalgebras, anti-fuzzy subalgebras, negative fuzzy subalgebras, Pythagorean fuzzy subalgebras and bipolar fuzzy subalgebras of BCK/BCI-algebras are given in terms of \((\inf, \sup)\)-hesitant fuzzy subalgebras and interval-valued fuzzy subalgebras.

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Keywords

• BCK/BCI-algebra
• hesitant fuzzy subalgebra
• \((\inf, \sup)\)-hesitant fuzzy subalgebra
• interval-valued fuzzy subalgebra
• Pythagorean fuzzy subalgebra
• bipolar fuzzy subalgebra

MSC

•  03B52
•  03G25
•  06F35
•  08A72

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