General types of \(\sup\)-hesitant fuzzy ideals of ternary semigroups

Volume 33, Issue 1, pp 108--123 http://dx.doi.org/10.22436/jmcs.033.01.08

Publication Date: December 05, 2023 Submission Date: April 16, 2023 Revision Date: June 10, 2023 Accteptance Date: August 25, 2023

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Authors

A. Iampan - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand. N. Lekkoksung - Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand. S. Lekkoksung - Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand. P. Julatha - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.

Abstract

General types of the paper [P. Julatha, A. Iampan, Int. J. Fuzzy Log. Intell. Syst., \({\bf 21}\) (2021), 169--175] are discussed. The concepts of \(\sup^{+}_{\gamma}\)-hesitant and \(\sup^{-}_{\delta}\)-hesitant fuzzy (resp., left, right, lateral) ideals of ternary semigroups are introduced, and their properties are investigated. Characterizations of the concepts are given in terms of fuzzy sets, Lukasiewicz (anti-) fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, and interval-valued fuzzy sets. Moreover, we show relationships among interval-valued, hesitant, \(\sup\)-hesitant, \(\sup^{+}_{\gamma}\)-hesitant and \(\sup^{-}_{\delta}\)-hesitant fuzzy ideals.

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Keywords

• General type of \(\sup\)-hesitant fuzzy ideal
• \(\sup\)-hesitant fuzzy ideal
• hesitant fuzzy ideal
• interval-valued fuzzy ideal
• Pythagorean fuzzy ideal
• Lukasiewicz (anti-) fuzzy set

MSC

•  03E72
•  08A72
•  20M10

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